%!PS-Adobe
/wpdict	120 dict def
wpdict	begin
/bdef	{bind def} bind def

/bflg	false def
/Bfont	0 def
/bon	false def

/psz	0 def
/_S	/show load def
/_t	{0 rmoveto} bdef

/_pixelsnap
	{transform .25 sub round .25 add
	 exch .25 sub round .25 add exch itransform
	} bdef
/_pixeldsnap
	{ dtransform round exch round exch idtransform } bdef

/_lt	{_pixelsnap lineto} bdef
/_rlt	{_pixeldsnap rlineto} bdef
/_mt	{_pixelsnap moveto} bdef
/_rmt	{_pixeldsnap rmoveto} bdef

/bshow	{gsave psz 30 div 0 _rmt dup show grestore show} bdef

/DUx	0 def
/DUy	0 def
/hscl	0 def

/M	{_mt
	 2 mul -2 2
	 { -2 roll 0 _rmt _S } for
	} bdef

/makeoutl
	{ dup /OutlineFlag known not
	  { dup dup length 2 add dict begin
	    {1 index /FID ne { def }{ pop pop } ifelse } forall
	    /UniqueID known {/UniqueID UniqueID 10000 add def} if
	    /PaintType PaintType 0 eq { 2 }{ PaintType } ifelse def
	    /StrokeWidth 15 def
	    /OutlineFlag true def
	    /OutlineFont currentdict end definefont
	  } if
	} bdef

/nbuff	50 string def
/orntsv	0 def
/plen	0 def
/pwid	0 def
/picstr	1 string def

/WPencoding StandardEncoding 256 array copy def 0
 [ 127/Aacute/Acircumflex/Adieresis/Agrave/Aring/Atilde/Ccedilla
  /Delta/Eacute/Ecircumflex/Edieresis/Egrave/Eth/Gamma/Iacute
  /Icircumflex/Idieresis/Igrave/Lambda/Ntilde/Oacute
  /Ocircumflex/Odieresis/Ograve/Omega/Otilde/Phi/Pi/Psi
  /Scaron/Sigma/TeXtext32/Theta/Thorn
  209/Uacute/Ucircumflex/Udieresis/Ugrave/Upsilon/Xi/Yacute
  /Ydieresis/Zcaron/aacute/acircumflex/adieresis/agrave
  /aring/atilde/brokenbar
  228/ccedilla/copyright/degree/divide
  236/dotlessj/eacute/ecircumflex/edieresis/egrave
  242/eth/ff/ffi
  246/ffl/iacute
  252/icircumflex/idieresis/igrave/logicalnot
  1/minus/mu/multiply/ntilde/oacute/ocircumflex/odieresis
  /ograve/onehalf/onequarter/onesuperior/otilde/plusminus
  /registered/scaron/thorn/threequarters/threesuperior
  /trademark/twosuperior/uacute/ucircumflex/udieresis
  /ugrave/yacute/ydieresis/zcaron
]
{ dup type /nametype eq
  { WPencoding 2 index 2 index put pop 1 add }
  { exch pop } ifelse
} forall pop

/reencode
{ dup FontDirectory exch known
   { findfont }
   {  dup nbuff cvs dup length 1 sub get 82 eq
   {dup nbuff cvs dup length 1 sub 0 exch getinterval
   findfont begin
   currentdict dup length dict begin
{ 1 index /FID ne {def} {pop pop} ifelse } forall
/FontName exch def

/Encoding WPencoding def
currentdict dup end end
/FontName get exch definefont
     }
     { findfont } ifelse
  } ifelse
} bdef

/WPDLencoding StandardEncoding 256 array copy def 0
[ 127     /SA420000/SD630000/SF010000/SF020000/SF030000
/SF040000/SF050000/SF060000/SF070000/SF080000/SF090000
/SF100000/SF110000/SF140000/SF150000/SF160000/SF190000
/SF200000/SF210000/SF220000/SF230000/SF240000/SF250000/SF260000
/SF270000/SF280000/SF360000/SF370000/SF380000/SF390000/SF400000
/SF410000/SF420000/SF430000
209 /SF440000/SF450000/SF460000/SF470000/SF480000
/SF490000/SF500000/SF510000/SF520000/SF530000/SF540000
/SF570000/SF580000/SF590000/SF600000/SF610000
228 /SM570001/SM590000/SM600000/SM630000
236 /SM680000/SM690000/SM700000/SM750000/SM750002
242 /SM770000/SM790000/SP320000
246 /SS000000/SS010000
252 /SS260000/SS270000/SV040000/apostrophereverse
1/arrowboth/arrowdown/arrowleft/arrowright/arrowup/club
/deutschmark/diamond/diamondopen/exclamdbl/female
/fiveeighths/franc/heart/male/musicalnote/musicalnotedbl
/napostrophe/nsuperior/oneeighths/seveneighths/spade
/threeeights/underscoredbl/SM760000
]
{ dup type /nametype eq
  { WPDLencoding 2 index 2 index put pop 1 add }
  { exch pop } ifelse
} forall pop

/reencodeL
    { dup FontDirectory exch known
      { findfont }
      {  dup nbuff cvs dup length 1 sub get 76 eq
         {    dup nbuff cvs dup length 1 sub 0 exch getinterval
         findfont begin
         currentdict dup length dict begin
         { 1 index /FID ne {def} {pop pop} ifelse } forall
         /FontName exch def
         /Encoding WPDLencoding def
         currentdict dup end end
         /FontName get exch definefont
         }
         { findfont } ifelse
      } ifelse
    } bdef

/ron	false def
/sflg	false def
/slan	0 def
/sp	32 def

/sshow
	{ save exch
	   gsave
	    psz 20 div dup neg _rmt dup show
	   grestore
	   dup
	   save exch
	    Bfont setfont
	    1 setgray show
	   restore
	   currentfont makeoutl setfont show
	   currentpoint 3 -1 roll
	  restore _mt
	} bdef

/Sx	0 def
/Sy	0 def
/Ux	0 def
/Uy	0 def
/W	/widthshow load def

/_B	{/bflg true def
	 sflg not {/_S /bshow load def /bon true def} if
	} bdef
/_b	{/bflg false def
	 bon {/_S /show load def /bon false def} if
	} bdef
/_bd	{save} bdef
/_bp	{save 2 setmiterlimit .06 .06 scale 0 0 _mt} bdef
/_ccprocs
	{/proc2 exch cvlit def
	 /proc1 exch cvlit def
	 /newproc proc1 length proc2 length add
	 array def
	 newproc 0 proc1 putinterval
	 newproc proc1 length proc2 putinterval
	 newproc cvx
	} def
/_clr	{3 {255 div 3 1 roll} repeat
	 ron {6 3 roll pop pop pop} {setrgbcolor} ifelse
	} bdef
/_cp	/closepath load def
/_cw	{stroke initclip _mt 0 2 index
	 _rlt 0 _rlt 0 exch neg
	 _rlt clip newpath
	} bdef
/_d	/setdash load def
/_DU	{currentpoint /DUy exch def /DUx exch def} bdef
/_du	{gsave
	  save
	  8 setlinewidth
      currentpoint -30 add _mt
      DUx DUy -30 add _lt stroke
	  restore
	  8 setlinewidth
	  currentpoint -50 add _mt
	  DUx DUy -50 add _lt stroke
	 grestore
	} bdef
/_ed	{restore} bdef
/_ep	{restore showpage 0 0 _mt} bdef
/_f	/eofill load def
/_ff	{ exch reencode exch
	  3 div dup /psz exch def
	  scalefont dup /Bfont exch def setfont
	} bdef
/_ffs	{ /slan exch 10 div def /hscl exch 1000 div def
	  /psz exch 3 div def
	  [ psz hscl mul 0 slan dup sin exch cos div psz mul psz 0 0 ]
	  exch reencode exch makefont dup /Bfont exch def setfont
	} bdef
/_g	/setgray load def
/_gs	{neg 100 add 100 div setgray} bdef
/_i	{gsave
	  dup /picstr exch 7 add 8 idiv string def
	  3 1 roll translate dup 1 scale
	  dup 1 1 [5 -1 roll 0 0 1 0 0]
	  {currentfile picstr readhexstring pop} image
         grestore
        } bdef
/_is	{save 4 1 roll
	  dup /picstr exch 7 add 8 idiv string def
	  3 1 roll translate dup 1 scale
	  dup 1 1 [5 -1 roll 0 0 1 0 0]
	  {currentfile picstr readhexstring pop} image
	 restore
	} bdef
/_ie	{1 eq { {1 exch sub} currenttransfer _ccprocs settransfer} if
	 /_isx exch def /_isy exch def
	 _isx mul exch _isy mul translate
	 add 2 div /_txc exch def
	 add 2 div /_tyc exch def
	 _txc _isx mul _tyc _isy mul translate
	 360 exch sub rotate
	 1 eq { _isx neg _isy scale }
	 { _isx _isy scale }
	 ifelse _txc neg _tyc neg translate
	} bdef
/_irms	{save
	  12 1 roll
	  1 eq {{1 exch sub} currenttransfer _ccprocs settransfer} if
	  /picstr exch string def translate
	  2 index 6 index sub 2 div 2 index 6 index sub 2 div neg
	  translate
	  5 index 5 index 2 div neg exch 2 div exch
	  2 copy neg exch neg exch 5 2 roll translate
	  360 exch sub rotate
	  3 index 3 index 7 index div exch 8 index div exch scale
	  translate pop pop 2 index 2 index scale
	  3 index 0 eq
	  { [ 3 index 0 0 5 index neg 0 0 ] }
	  { 3 index 1 eq
      { [ 3 index 0 0 5 index 0 7 index ] }
      { 3 index 128 eq
	  { [ 3 index neg 0 0 5 index neg 7 index 0 ] }
	  { [ 3 index neg 0 0 5 index 7 index 7 index ] } ifelse
	    } ifelse
	  } ifelse
          {currentfile picstr readhexstring pop} image
          pop
	 restore
	} bdef

/_l	{_lt} bdef
/_lr	{_rlt} bdef
/_m	{_mt} bdef
/_O	{currentfont makeoutl setfont} bdef
/_o	{Bfont setfont} bdef
/_ornt	{/pwid exch def /plen exch def
	 orntsv 1 eq {0 pwid translate -90 rotate} if
	 orntsv 2 eq {pwid plen translate 180 rotate} if
	 orntsv 3 eq {plen 0 translate 90 rotate} if
	 dup 1 eq {pwid 0 translate 90 rotate} if
	 dup 2 eq {pwid plen translate 180 rotate} if
	 dup 3 eq {0 plen translate -90 rotate} if
	 /orntsv exch def
	} bdef
/_lod1	{currentpoint orntsv plen pwid 6 -1 roll restore save} bdef
/_lod2	{_bp 7 2 roll _ornt _mt} bdef
/_unlod	{currentpoint orntsv plen pwid 7 -2 roll restore restore
	 _bp 6 1 roll _ornt _mt
	} bdef
/_p	{2 copy _mt 1 0 _rlt _mt} bdef
/_pl	{{_lt} repeat} bdef
/_R      { /ron true def /_S /_rshow load def /_t /_red load def} bdef
/_rshow	 { save exch
	   currentpoint
	   /RSy exch def /RSx exch def
	   ron {
		 sflg
		 {	currentpoint
			/Ry exch def /Rx exch def
			dup stringwidth pop Rx Ry psz 4 div add _mt
			Rx psz 15 add setlinewidth .95 setgray 0 setlinecap
			add Ry psz 4 div add _lt stroke Rx Ry _mt 0 0 0 setrgbcolor
			dup show Rx Ry _mt
			sshow
		 }
		 { _redshow
		 }ifelse
	   }
	   {	 sflg {sshow} if
	   }ifelse
	   currentpoint 3 -1 roll
	   restore _mt
	 } bdef
/_red	{ gsave dup
         currentpoint /Ry exch def /Rx exch def
         Rx Ry psz 4 div add _mt
         Rx psz 15 add setlinewidth .95 setgray 0 setlinecap
         add Ry psz 4 div add _lt stroke
         Rx Ry _mt
         grestore
         0 rmoveto
    }bdef
/_redshow {currentpoint
         /Ry exch def /Rx exch def
         dup stringwidth pop Rx Ry psz 4 div add _mt
         Rx psz 15 add setlinewidth .95 setgray 0 setlinecap
         add Ry psz 4 div add _lt stroke Rx Ry _mt 0 0 0 setrgbcolor
         show currentpoint _mt
    }bdef
/_rmxy	{_rmt} bdef
/_s	/stroke load def
/_SH	bon {/bon false def} if
	{/sflg true def /_S /_rshow load def
	} bdef
/_sh	{ ron 	{/sflg false def bflg {_B} if}
		{/_S /show load def /sflg false def bflg {_B} if}ifelse
	}bdef
/_sp	{ gsave stroke grestore } bdef
/_ST     {currentpoint /Sy exch def /Sx exch def} bdef
/_st     {gsave
          currentpoint
          psz 4 div add _mt
          Sx Sy psz 4 div add _lt
          10 setlinewidth
          stroke
          grestore
          } bdef
/_U	{currentpoint /Uy exch def /Ux exch def} bdef
/_u	{gsave
	  currentpoint
	  -30 add _mt
	  Ux Uy -30 add _lt
	  12 setlinewidth
	  stroke
	 grestore
	} bdef
/_w	/setlinewidth load def
end
/#copies 1 def statusdict begin false end /wpdict2 100 dict def
wpdict begin wpdict2 begin

_bd
/_rhs{readhexstring}bdef/_tr{translate}bdef
/_ix{index}bdef/_mx{matrix}bdef
/ife{ifelse}bdef/_x{exch}bdef
/_is{save 4 1 roll
dup/picstr _x 7 add 8 idiv string def
3 1 roll _tr dup 1 scale
dup 1 1[5 -1 roll 0 0 1 0 0]
{currentfile picstr _rhs pop}image restore}bdef
/_epsi{1 eq{{1 _x sub}currenttransfer _ccprocs settransfer}if
/yp _x def/xp _x def/dhgt _x def/dwid _x def
4 copy sub/swid _x def
sub/shgt _x def
add 2 div/icx _x def add 2 div/icy _x def
xp dwid 2 div add icx sub yp dhgt 2 div sub
icy sub _tr icx icy _tr
360 _x sub rotate
dwid swid div/xsc _x def _x
dhgt shgt div/ysc _x def _x
dup 1 eq{xsc neg/xsc _x def pop}
{dup 2 eq{ysc neg /ysc _x def pop}
{3 eq{ysc neg/ysc _x def xsc neg/xsc _x def}
{}ife}ife}ife
xsc ysc scale
100 div _x 100 div _x scale
icx neg icy neg _tr}bdef
/_c{3{255 div 3 1 roll}repeat setrgbcolor}bdef
/eq3{3 copy 2 _ix eq{eq{true}{false}ife}{pop
pop false}ife}bdef
/g{255 div setgray}bdef
/_clr{ron{6 3 roll pop pop pop}{eq3{pop
pop g}{_c}ife}ife}bdef
/_r{/ron false def eq3{1 sub neg g pop
pop}{setrgbcolor}ife}bdef
/_ircms{save 15 1 roll
1 eq{{1 exch sub}currenttransfer _ccprocs settransfer}if
/pstr _x string def _tr
/Cli _x def/USy _x def/USx _x def/Rot _x def/HTd _x def
/WDd _x def/Bdep _x def/HTs _x def/WDs _x def/MIR _x def
USx 100 div USy 100 div scale
WDd WDs sub 2 div HTd HTs sub 2 div neg _tr
WDs HTs 2 div neg _x 2 div _x _tr
Rot 360 _x sub rotate WDd HTd HTs div _x WDs div _x scale
WDs 2 div neg HTs 2 div _tr
WDs HTs scale WDs HTs Bdep MIR 0
eq{[WDs 0 0 HTs neg 0 0]}{MIR 1 eq{[WDs 0 0 HTs 0 HTs]}
{MIR 128 eq{[WDs neg 0 0 HTs neg WDs 0]}
{[WDs neg 0 0 HTs WDs HTs]}ife}ife}ife
{currentfile pstr _rhs pop}Cli
0 eq{image}{false 3 colorimage}ife
restore}bdef
/_bp{save 2 setlinecap 2 setmiterlimit
.06 .06 scale 0 0 moveto}bdef
/tctm _mx def/trot _mx def/tscale _mx def/rmtx _mx def
/fr{72 0 rmtx defaultmatrix dtransform
/yres _x def/xres _x def
xres dup mul yres dup mul add sqrt}bdef
/sus{/spotf _x def/sang _x def/csz _x def
/m tctm currentmatrix def/rm sang trot rotate def
/sm csz dup tscale scale def
sm rm m m concatmatrix m concatmatrix pop
1 0 m dtransform /y1 _x def/x1 _x def
/veclength x1 dup mul y1 dup mul add sqrt def
/frcy fr veclength div def /nsang y1 x1 atan def
frcy nsang/spotf load setscreen}bdef
/bitis{/ybit _x def /xbit _x def
/bval bstring ybit bwidth mul xbit 8 idiv add get def
/mask 1 7 xbit 8 mod sub bitshift def
bval mask and 0 ne}bdef
/bps{/y _x def /x _x def
/xndx x 1 add 2 div bpside mul cvi def
/yndx y 1 add 2 div bpside mul cvi def
xndx yndx bitis
{/onb onb 1 add def 1}{/ofb ofb 1 add def 0}ife}bdef
/stpatt{/csz _x def /angle _x def /bwidth _x def
/bpside _x def /bstring _x def
/onb 0 def /ofb 0 def
csz angle /bps load
sus{}settransfer
ofb ofb onb add div _g}bdef
/_fp{8 1 0 cpi stpatt}bdef
/_pf{gsave eofill grestore}bdef
/_np{newpath}bdef/_lc{setlinecap}bdef
/_sr{/cpi _x def}bdef
/nbuff 50 string def
letter _bp 0 13200 10200 _ornt /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
2674 11255 _m
/Times-BoldR 600 _ff
(VI.)_S 134 _t
(UNDERWATER)_S 67 _t
(VEHICLE)_S 67 _t
(DYNAMICS)_S 67 _t
(MODEL)_S /Times-RomanR 600 _ff
1500 10756 _m
/Times-BoldR 600 _ff
(A.)_S 1980 10756 _m
(INTRODUCTION)_S /Times-RomanR 600 _ff
1980 10407 _m
(Underwater)_S 67 _t
(vehicle)_S 67 _t
(design)_S 67 _t
(and)_S 67 _t
(construction)_S 67 _t
(is)_S 67 _t
(almost)_S 67 _t
(completely)_S 67 _t
(preoccupied)_S 1500 10058 _m
(with)_S 67 _t
(environmental)_S 67 _t
(considerations.)_S 134 _t
(The)_S 67 _t
(ocean)_S 67 _t
(completely)_S 67 _t
(surrounds)_S 67 _t
(the)_S 67 _t
(vehicle,)_S 1500 9709 _m
(affects)_S 67 _t
(the)_S 67 _t
(slightest)_S 67 _t
(nuance)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(and)_S 67 _t
(poses)_S 67 _t
(a)_S 67 _t
(constant)_S 67 _t
(hazard)_S 67 _t
(to)_S 67 _t
(vehicle)_S 1500 9360 _m
(survivability.)_S 134 _t
(Many)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(effects)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(surrounding)_S 67 _t
(environment)_S 67 _t
(on)_S 67 _t
(a)_S 67 _t
(robot)_S 67 _t
(vehicle)_S 1500 9011 _m
(are)_S 67 _t
(unique)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(underwater)_S 67 _t
(domain.)_S 134 _t
(Vehicles)_S 67 _t
(move)_S 67 _t
(through)_S 67 _t
(the)_S 67 _t
(ocean)_S 67 _t
(by)_S 67 _t
(attempting)_S 1500 8662 _m
(to)_S 67 _t
(control)_S 67 _t
(complex)_S 67 _t
(forces)_S 67 _t
(and)_S 67 _t
(reactions)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(predictable)_S 67 _t
(and)_S 67 _t
(reliable)_S 67 _t
(manner.)_S 134 _t
(Thus)_S 1500 8313 _m
(understanding)_S 67 _t
(these)_S 67 _t
(forces)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(key)_S 67 _t
(requirement)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(development)_S 67 _t
(and)_S 67 _t
(control)_S 67 _t
(of)_S 1500 7964 _m
(both)_S 67 _t
(simple)_S 67 _t
(and)_S 67 _t
(sophisticated)_S 67 _t
(vehicle)_S 67 _t
(behaviors.)_S 134 _t
(Unfortunately,)_S 67 _t
(the)_S 67 _t
(underwater)_S 1500 7615 _m
(vehicle)_S 67 _t
(development)_S 67 _t
(community)_S 67 _t
(has)_S 67 _t
(been)_S 67 _t
(hampered)_S 67 _t
(by)_S 67 _t
(a)_S 67 _t
(lack)_S 67 _t
(of)_S 67 _t
(appropriate)_S 1500 7266 _m
(hydrodynamics)_S 67 _t
(models.)_S 134 _t
(Currently)_S 67 _t
(no)_S 67 _t
(single)_S 67 _t
(general)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(is)_S 1500 6917 _m
(available)_S 67 _t
(which)_S 67 _t
(is)_S 67 _t
(computationally)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(predicting)_S 67 _t
(underwater)_S 67 _t
(robot)_S 67 _t
(dynamics)_S 1500 6568 _m
(behavior)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(real-time)_S 67 _t
(virtual)_S 67 _t
(world.)_S 1980 6217 _m
/Times-ItalicR 600 _ff
(The)_S 67 _t
(intended)_S 67 _t
(contributions)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(hydrodynamic)_S 67 _t
(model)_S 67 _t
(in)_S 67 _t
(this)_S 67 _t
(dissertation)_S 67 _t
(are)_S 1500 5868 _m
(clarity,)_S 67 _t
(analytical)_S 67 _t
(correctness,)_S 67 _t
(generality,)_S 67 _t
(nomenclature)_S 67 _t
(standardization)_S 67 _t
(and)_S 67 _t
(suitability)_S 1500 5519 _m
(for)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(virtual)_S 67 _t
(world.)_S /Times-RomanR 600 _ff
134 _t
(Many)_S 67 _t
(interacting)_S 67 _t
(factors)_S 67 _t
(are)_S 67 _t
(involved)_S 67 _t
(in)_S 1500 5169 _m
(underwater)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(behavior.)_S 134 _t
(These)_S 67 _t
(factors)_S 67 _t
(can)_S 67 _t
(result)_S 67 _t
(in)_S 67 _t
(oscillatory)_S 67 _t
(or)_S 1500 4820 _m
(unstable)_S 67 _t
(operation)_S 67 _t
(if)_S 67 _t
(control)_S 67 _t
(algorithms)_S 67 _t
(for)_S 67 _t
(heading,)_S 67 _t
(depth)_S 67 _t
(and)_S 67 _t
(speed)_S 67 _t
(control)_S 67 _t
(do)_S 67 _t
(not)_S 1500 4471 _m
(take)_S 67 _t
(into)_S 67 _t
(account)_S 67 _t
(the)_S 67 _t
(many)_S 67 _t
(complex)_S 67 _t
(possibilities)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(response.)_S 134 _t
(Laboratory)_S 1500 4122 _m
(modeling)_S 67 _t
(of)_S 67 _t
(hydrodynamics)_S 67 _t
(response)_S 67 _t
(to)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(essential)_S 67 _t
(due)_S 67 _t
(to)_S 1500 3773 _m
(the)_S 67 _t
(need)_S 67 _t
(to)_S 67 _t
(avoid)_S 67 _t
(control)_S 67 _t
(law)_S 67 _t
(errors,)_S 67 _t
(sensing)_S 67 _t
(errors,)_S 67 _t
(navigational)_S 67 _t
(errors,)_S 67 _t
(prematurely)_S 1500 3424 _m
(depleted)_S 67 _t
(propulsion)_S 67 _t
(endurance,)_S 67 _t
(loss)_S 67 _t
(of)_S 67 _t
(depth)_S 67 _t
(control,)_S 67 _t
(or)_S 67 _t
(even)_S 67 _t
(catastrophic)_S 67 _t
(failure)_S 67 _t
(due)_S 1500 3075 _m
(to)_S 67 _t
(implosion)_S 67 _t
(at)_S 67 _t
(crush)_S 67 _t
(depth.)_S 134 _t
(An)_S 67 _t
(analytically)_S 67 _t
(valid)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(must)_S 67 _t
(be)_S 1500 2726 _m
(based)_S 67 _t
(on)_S 67 _t
(physical)_S 67 _t
(laws)_S 67 _t
(and)_S 67 _t
(sufficiently)_S 67 _t
(accurate)_S 67 _t
(for)_S 67 _t
(the)_S 67 _t
(study)_S 67 _t
(and)_S 67 _t
(development)_S 67 _t
(of)_S 1500 2377 _m
(robust)_S 67 _t
(control)_S 67 _t
(laws)_S 67 _t
(that)_S 67 _t
(work)_S 67 _t
(under)_S 67 _t
(a)_S 67 _t
(wide)_S 67 _t
(range)_S 67 _t
(of)_S 67 _t
(potential)_S 67 _t
(vehicle)_S 67 _t
(motions.)_S 134 _t
(The)_S 5000 1288 _m
(89)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1500 11855 _m
(real-time)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(is)_S 67 _t
(therefore)_S 67 _t
(an)_S 67 _t
(essential)_S 67 _t
(component)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(robot-centered)_S 1500 11506 _m
(underwater)_S 67 _t
(virtual)_S 67 _t
(world.)_S 1980 11157 _m
(Detailed)_S 67 _t
(analysis)_S 67 _t
(of)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(behavior)_S 67 _t
(is)_S 67 _t
(beyond)_S 67 _t
(the)_S 1500 10808 _m
(current)_S 67 _t
(state)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(art)_S 67 _t
(using)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(techniques.)_S 134 _t
(In)_S 67 _t
(many)_S 67 _t
(cases,)_S 67 _t
(detailed)_S 1500 10459 _m
(data)_S 67 _t
(on)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(response)_S 67 _t
(is)_S 67 _t
(unavailable)_S 67 _t
(even)_S 67 _t
(in)_S 67 _t
(real)_S 67 _t
(world)_S 1500 10110 _m
(test)_S 67 _t
(programs.)_S 134 _t
(Development)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(general)_S 67 _t
(physics-based)_S 67 _t
(real-time)_S 67 _t
(model)_S 67 _t
(fills)_S 67 _t
(a)_S 67 _t
(gap)_S 67 _t
(in)_S 1500 9761 _m
(the)_S 67 _t
(robotics)_S 67 _t
(and)_S 67 _t
(simulation)_S 67 _t
(literature)_S 67 _t
(that)_S 67 _t
(does)_S 67 _t
(not)_S 67 _t
(exist)_S 67 _t
(for)_S 67 _t
(corresponding)_S 67 _t
(robot)_S 1500 9412 _m
(operating)_S 67 _t
(environments)_S 67 _t
(such)_S 67 _t
(as)_S 67 _t
(indoors,)_S 67 _t
(space)_S 67 _t
(or)_S 67 _t
(air.)_S 134 _t
(Inclusion)_S 67 _t
(of)_S 67 _t
(an)_S 67 _t
(analytically)_S 1500 9063 _m
(correct)_S 67 _t
(and)_S 67 _t
(verifiable)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(in)_S 67 _t
(an)_S 67 _t
(underwater)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(will)_S 67 _t
(permit)_S 1500 8714 _m
(meaningful)_S 67 _t
(and)_S 67 _t
(timely)_S 67 _t
(analysis)_S 67 _t
(of)_S 67 _t
(realistic)_S 67 _t
(robot-environment)_S 67 _t
(interactions.)_S 1980 8365 _m
(It)_S 67 _t
(must)_S 67 _t
(be)_S 67 _t
(noted)_S 67 _t
(that)_S 67 _t
("correctness")_S 67 _t
(may)_S 67 _t
(not)_S 67 _t
(be)_S 67 _t
(rigorously)_S 67 _t
(possible)_S 67 _t
(for)_S 67 _t
(any)_S 1500 8016 _m
(hydrodynamics)_S 67 _t
(model.)_S 134 _t
(So)_S 67 _t
(many)_S 67 _t
(interrelated)_S 67 _t
(factors)_S 67 _t
(are)_S 67 _t
(present)_S 67 _t
(that)_S 67 _t
(precise)_S 67 _t
(testing)_S 1500 7667 _m
(and)_S 67 _t
(verification)_S 67 _t
(of)_S 67 _t
(all)_S 67 _t
(parameters)_S 67 _t
(is)_S 67 _t
(unlikely)_S 67 _t
(or)_S 67 _t
(impossible.)_S 134 _t
(While)_S 67 _t
(a)_S 67 _t
(model)_S 67 _t
(of)_S 1500 7318 _m
(hydrodynamics)_S 67 _t
(forces)_S 67 _t
(may)_S 67 _t
(never)_S 67 _t
(be)_S 67 _t
(perfect,)_S 67 _t
(it)_S 67 _t
(can)_S 67 _t
(achieve)_S 67 _t
(sufficiency)_S 67 _t
(in)_S 67 _t
(that)_S 67 _t
(vehicle)_S 1500 6969 _m
(responses)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(predicted)_S 67 _t
(by)_S 67 _t
(physical)_S 67 _t
(laws)_S 67 _t
(at)_S 67 _t
(a)_S 67 _t
(level)_S 67 _t
(of)_S 67 _t
(detail)_S 67 _t
(adequate)_S 67 _t
(to)_S 67 _t
(develop,)_S 1500 6620 _m
(test)_S 67 _t
(and)_S 67 _t
(evaluate)_S 67 _t
(vehicle)_S 67 _t
(performance)_S 67 _t
(under)_S 67 _t
(a)_S 67 _t
(variety)_S 67 _t
(of)_S 67 _t
(control)_S 67 _t
(laws.)_S 134 _t
(The)_S 1500 6271 _m
(quantifiable)_S 67 _t
(goal)_S 67 _t
(for)_S 67 _t
(correctness)_S 67 _t
(in)_S 67 _t
(this)_S 67 _t
(work)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(generalizable)_S 67 _t
(model)_S 67 _t
(that)_S 67 _t
(predicts)_S 1500 5922 _m
(vehicle)_S 67 _t
(physical)_S 67 _t
(response)_S 67 _t
(with)_S 67 _t
(sufficient)_S 67 _t
(rapidity)_S 67 _t
(and)_S 67 _t
(accuracy)_S 67 _t
(to)_S 67 _t
(permit)_S 67 _t
(equivalent)_S 1500 5573 _m
(robot)_S 67 _t
(behavior)_S 67 _t
(whether)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(laboratory)_S 67 _t
(or)_S 67 _t
(underwater.)_S 134 _t
(Such)_S 67 _t
(a)_S 67 _t
(model)_S 67 _t
(will)_S 67 _t
(also)_S 67 _t
(enable)_S 1500 5224 _m
(realistic)_S 67 _t
(and)_S 67 _t
(repeatable)_S 67 _t
(design)_S 67 _t
(and)_S 67 _t
(evaluation)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(control)_S 67 _t
(systems,)_S 67 _t
(again)_S 67 _t
(either)_S 1500 4875 _m
(in)_S 67 _t
(the)_S 67 _t
(laboratory)_S 67 _t
(or)_S 67 _t
(underwater.)_S 1980 4526 _m
(The)_S 67 _t
(model)_S 67 _t
(presented)_S 67 _t
(herein)_S 67 _t
(was)_S 67 _t
(intentionally)_S 67 _t
(developed)_S 67 _t
(with)_S 67 _t
(complete)_S 1500 4177 _m
(independence)_S 67 _t
(from)_S 67 _t
(classified)_S 67 _t
(U.S.)_S 67 _t
(Navy)_S 67 _t
(research)_S 67 _t
(on)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics.)_S 134 _t
(No)_S 1500 3828 _m
(classified)_S 67 _t
(documents)_S 67 _t
(were)_S 67 _t
(consulted)_S 67 _t
(during)_S 67 _t
(the)_S 67 _t
(literature)_S 67 _t
(search)_S 67 _t
(for)_S 67 _t
(this)_S 67 _t
(work.)_S 67 _t
1500 3479 _m
(Research)_S 67 _t
(statements)_S 67 _t
(and)_S 67 _t
(conclusions)_S 67 _t
(are)_S 67 _t
(derived)_S 67 _t
(solely)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(extensive)_S 67 _t
(open)_S 1500 3130 _m
(literature)_S 67 _t
(on)_S 67 _t
(hydrodynamics,)_S 67 _t
(in)_S 67 _t
(no)_S 67 _t
(way)_S 67 _t
(confirming,)_S 67 _t
(denying)_S 67 _t
(or)_S 67 _t
(implying)_S 67 _t
(the)_S 67 _t
(existence)_S 1500 2781 _m
(of)_S 67 _t
(similar)_S 67 _t
(work)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(classified)_S 67 _t
(arena.)_S 134 _t
(A)_S 67 _t
(good)_S 67 _t
(unclassified)_S 67 _t
(tutorial)_S 67 _t
(on)_S 67 _t
(the)_S 1500 2432 _m
(fundamentals)_S 67 _t
(of)_S 67 _t
(naval)_S 67 _t
(submarine)_S 67 _t
(design)_S 67 _t
(is)_S 67 _t
(\(Jackson)_S 67 _t
(92\).)_S 134 _t
(Details)_S 67 _t
(on)_S 67 _t
(experimentally)_S 1500 2083 _m
(and)_S 67 _t
(analytically)_S 67 _t
(developing)_S 67 _t
(submarine)_S 67 _t
(hydrodynamics)_S 67 _t
(models)_S 67 _t
(are)_S 67 _t
(in)_S 67 _t
(\(Huang)_S 67 _t
(88\).)_S 67 _t
5000 1288 _m
(90)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(Unclassified)_S 67 _t
(overview)_S 67 _t
(descriptions)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(use)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(design)_S 1500 11506 _m
(and)_S 67 _t
(testing)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(ARPA/Navy)_S 67 _t
(Unmanned)_S 67 _t
(Underwater)_S 67 _t
(Vehicle)_S 67 _t
(\(UUV\))_S 67 _t
(are)_S 67 _t
(in)_S 1500 11157 _m
(\(Pappas)_S 67 _t
(91\))_S 67 _t
(and)_S 67 _t
(\(Brancart)_S 67 _t
(94\).)_S 134 _t
(Primary)_S 67 _t
(references)_S 67 _t
(for)_S 67 _t
(this)_S 67 _t
(dissertation)_S 67 _t
(are)_S 1500 10808 _m
(\(Healey)_S 67 _t
(92c,)_S 67 _t
(93\))_S 67 _t
(and)_S 67 _t
(\(Fossen)_S 67 _t
(94\).)_S 134 _t
(Finally,)_S 67 _t
(a)_S 67 _t
(large)_S 67 _t
(number)_S 67 _t
(of)_S 67 _t
(papers)_S 67 _t
(and)_S 67 _t
(theses)_S 67 _t
(have)_S 1500 10459 _m
(been)_S 67 _t
(written)_S 67 _t
(at)_S 67 _t
(the)_S 67 _t
(Naval)_S 67 _t
(Postgraduate)_S 67 _t
(School)_S 67 _t
(\(NPS\))_S 67 _t
(pertaining)_S 67 _t
(to)_S 67 _t
(hydrodynamics)_S 1500 10110 _m
(modeling)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV,)_S 67 _t
(and)_S 67 _t
(each)_S 67 _t
(contributed)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(theoretical)_S 67 _t
(and)_S 67 _t
(experimental)_S 1500 9761 _m
(knowledge)_S 67 _t
(presented)_S 67 _t
(here)_S 67 _t
(\(Papoulias)_S 67 _t
(89\))_S 67 _t
(\(Cristi)_S 67 _t
(89\))_S 67 _t
(\(Jurewicz)_S 67 _t
(90\))_S 67 _t
(\(Zyda)_S 67 _t
(90\))_S 1500 9412 _m
(\(Warner)_S 67 _t
(91\))_S 67 _t
(\(Bahrke)_S 67 _t
(92\))_S 67 _t
(\(Brutzman)_S 67 _t
(92a\))_S 67 _t
(\(Brutzman)_S 67 _t
(92c\))_S 67 _t
(\(Cooke)_S 67 _t
(92a,)_S 67 _t
(92b\))_S 67 _t
(\(Cody)_S 67 _t
(92\))_S 1500 9063 _m
(\(Brown)_S 67 _t
(93\))_S 67 _t
(\(Belton)_S 67 _t
(93\))_S 67 _t
(\(Haynes)_S 67 _t
(93\))_S 67 _t
(\(Zehner)_S 67 _t
(93\))_S 67 _t
(\(Cottle)_S 67 _t
(93\))_S 67 _t
(\(Torsiello)_S 67 _t
(94\))_S 67 _t
(and)_S 1500 8714 _m
(\(Marco)_S 67 _t
(95\).)_S 1980 8365 _m
(This)_S 67 _t
(chapter)_S 67 _t
(begins)_S 67 _t
(with)_S 67 _t
(a)_S 67 _t
(comparison)_S 67 _t
(of)_S 67 _t
(dynamics)_S 67 _t
(considerations)_S 67 _t
(for)_S 67 _t
(different)_S 1500 8016 _m
(vehicles)_S 67 _t
(and)_S 67 _t
(their)_S 67 _t
(respective)_S 67 _t
(environments.)_S 134 _t
(A)_S 67 _t
(description)_S 67 _t
(of)_S 67 _t
(world)_S 67 _t
(and)_S 67 _t
(body)_S 1500 7667 _m
(coordinate)_S 67 _t
(systems)_S 67 _t
(is)_S 67 _t
(used)_S 67 _t
(to)_S 67 _t
(derive)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(kinematics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion.)_S 134 _t
(A)_S 1500 7318 _m
(rigorous)_S 67 _t
(real-time)_S 67 _t
(six)_S 67 _t
(degree-of-freedom)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(is)_S 67 _t
(then)_S 67 _t
(derived)_S 67 _t
(based)_S 1500 6969 _m
(on)_S 67 _t
(the)_S 67 _t
(work)_S 67 _t
(of)_S 67 _t
(\(Healey)_S 67 _t
(92c,)_S 67 _t
(93\))_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 67 _t
(and)_S 67 _t
(others.)_S 134 _t
(Verified)_S 67 _t
(coefficient)_S 67 _t
(values)_S 1500 6618 _m
(for)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV)_S 67 _t
(II)_S 67 _t
/Times-ItalicR 600 _ff
(Phoenix)_S /Times-RomanR 600 _ff
67 _t
(vehicle)_S 67 _t
(are)_S 67 _t
(included)_S 67 _t
(and)_S 67 _t
(experimental)_S 67 _t
(model)_S 67 _t
(coefficient)_S 1500 6268 _m
(determination)_S 67 _t
(for)_S 67 _t
(other)_S 67 _t
(vehicles)_S 67 _t
(is)_S 67 _t
(considered.)_S 134 _t
(Different)_S 67 _t
(representations)_S 67 _t
(for)_S 1500 5919 _m
(calculating)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(compared)_S 67 _t
(using)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(or)_S 67 _t
(quaternion)_S 67 _t
(methods.)_S 67 _t
1500 5570 _m
(Network)_S 67 _t
(protocol)_S 67 _t
(considerations)_S 67 _t
(are)_S 67 _t
(then)_S 67 _t
(examined)_S 67 _t
(for)_S 67 _t
(integration)_S 67 _t
(of)_S 67 _t
(the)_S 1500 5221 _m
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(into)_S 67 _t
(a)_S 67 _t
(wide-scale)_S 67 _t
(distributed)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(using)_S 67 _t
(the)_S 67 _t
(Distributed)_S 1500 4872 _m
(Interactive)_S 67 _t
(Simulation)_S 67 _t
(\(DIS\))_S 67 _t
(protocol.)_S 134 _t
(A)_S 67 _t
(general)_S 67 _t
(object-oriented)_S 67 _t
(networked)_S 1500 4523 _m
(underwater)_S 67 _t
(rigid)_S 67 _t
(body)_S 67 _t
(class)_S 67 _t
(hierarchy)_S 67 _t
(is)_S 67 _t
(presented.)_S 134 _t
(Simulation)_S 67 _t
(of)_S 67 _t
(on-board)_S 67 _t
(sensors)_S 67 _t
(is)_S 1500 4174 _m
(considered,)_S 67 _t
(and)_S 67 _t
(the)_S 67 _t
(relationship)_S 67 _t
(of)_S 67 _t
(robust)_S 67 _t
(control)_S 67 _t
(system)_S 67 _t
(design)_S 67 _t
(to)_S 67 _t
(hydrodynamics)_S 1500 3825 _m
(modeling)_S 67 _t
(is)_S 67 _t
(briefly)_S 67 _t
(examined.)_S 134 _t
(Finally,)_S 67 _t
(future)_S 67 _t
(work)_S 67 _t
(is)_S 67 _t
(discussed)_S 67 _t
(concerning)_S 67 _t
(tether)_S 1500 3476 _m
(dynamics,)_S 67 _t
(ocean)_S 67 _t
(current)_S 67 _t
(modeling)_S 67 _t
(and)_S 67 _t
(collision)_S 67 _t
(detection.)_S 67 _t
(and)_S 67 _t
(addition)_S 67 _t
(of)_S 1500 3127 _m
(hydrodynamics)_S 67 _t
(models)_S 67 _t
(to)_S 67 _t
(on-board)_S 67 _t
(robot)_S 67 _t
(autopilots.)_S 5000 1288 _m
(91)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11705 _m
/Times-BoldR 600 _ff
(B.)_S 1980 11705 _m
(COMPARISON)_S 67 _t
(OF)_S 67 _t
(DYNAMICS)_S 67 _t
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(GROUND)_S 67 _t
(VEHICLES,)_S 67 _t
(AIR)_S 1980 11356 _m
(VEHICLES,)_S 67 _t
(SPACE)_S 67 _t
(VEHICLES,)_S 67 _t
(SURFACE)_S 67 _t
(SHIPS)_S 67 _t
(AND)_S 1980 11007 _m
(UNDERWATER)_S 67 _t
(VEHICLES)_S /Times-RomanR 600 _ff
1980 10658 _m
(Dynamics)_S 67 _t
(models)_S 67 _t
(are)_S 67 _t
(available)_S 67 _t
(for)_S 67 _t
(a)_S 67 _t
(wide)_S 67 _t
(variety)_S 67 _t
(of)_S 67 _t
(vehicles)_S 67 _t
(and)_S 67 _t
(articulated)_S 1500 10309 _m
(bodies)_S 67 _t
(\(Fu)_S 67 _t
(87\))_S 67 _t
(\(Greenwood)_S 67 _t
(88\))_S 67 _t
(\(Wilhelms)_S 67 _t
(91\))_S 67 _t
(\(Green)_S 67 _t
(91\))_S 67 _t
(\(Barzel)_S 67 _t
(92\))_S 67 _t
(\(Witkin)_S 67 _t
(93\).)_S 134 _t
(In)_S 1500 9960 _m
(every)_S 67 _t
(case)_S 67 _t
(it)_S 67 _t
(is)_S 67 _t
(desirable)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(physical)_S 67 _t
(laws)_S 67 _t
(governing)_S 67 _t
(vehicle)_S 67 _t
(interaction)_S 67 _t
(with)_S 67 _t
(its)_S 1500 9611 _m
(environment)_S 67 _t
(be)_S 67 _t
(specified)_S 67 _t
(as)_S 67 _t
(exactly)_S 67 _t
(and)_S 67 _t
(correctly)_S 67 _t
(as)_S 67 _t
(possible.)_S 134 _t
(Constraints)_S 67 _t
(on)_S 67 _t
(vehicle)_S 1500 9262 _m
(motions)_S 67 _t
(vary)_S 67 _t
(greatly)_S 67 _t
(during)_S 67 _t
(interaction)_S 67 _t
(with)_S 67 _t
(different)_S 67 _t
(environments.)_S 134 _t
(A)_S 67 _t
(brief)_S 1500 8913 _m
(examination)_S 67 _t
(of)_S 67 _t
(each)_S 67 _t
(basic)_S 67 _t
(type)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(environment)_S 67 _t
(and)_S 67 _t
(the)_S 67 _t
(physics)_S 67 _t
(associated)_S 67 _t
(with)_S 1500 8564 _m
(those)_S 67 _t
(environments)_S 67 _t
(is)_S 67 _t
(useful)_S 67 _t
(in)_S 67 _t
(understanding)_S 67 _t
(the)_S 67 _t
(nature)_S 67 _t
(of)_S 67 _t
(hydrodynamics)_S 67 _t
(modeling.)_S 1980 8215 _m
(One)_S 67 _t
(well-specified)_S 67 _t
(objective)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(is)_S 67 _t
(to)_S 67 _t
(repeatedly)_S 1500 7866 _m
(determine)_S 67 _t
(system)_S 67 _t
(state,)_S 67 _t
(defined)_S 67 _t
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(follows:)_S 1980 7282 _m
(The)_S 67 _t
/Times-ItalicR 600 _ff
(state)_S /Times-RomanR 600 _ff
67 _t
(of)_S 67 _t
(a)_S 67 _t
(system)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(mathematical)_S 67 _t
(structure)_S 67 _t
(containing)_S 67 _t
(a)_S 67 _t
(set)_S 67 _t
(of)_S 67 _t
/Times-ItalicR 600 _ff
(n)_S /Times-RomanR 600 _ff
1740 7047 _m
(variables)_S 67 _t
/Times-ItalicR 600 _ff
(x)_S /Times-ItalicR 360 _ff
2618 7003 _m
(1)_S 2678 7003 _m
/Times-ItalicR 600 _ff
2678 7047 _m
(\(t\),x)_S /Times-ItalicR 360 _ff
3005 7003 _m
(2)_S 3065 7003 _m
/Times-ItalicR 600 _ff
3065 7047 _m
(\(t\),...,x)_S /Times-ItalicR 360 _ff
3593 7003 _m
(i)_S 3626 7003 _m
/Times-ItalicR 600 _ff
3626 7047 _m
(\(t\),...,x)_S /Times-ItalicR 360 _ff
4154 7003 _m
(n)_S 4214 7003 _m
/Times-ItalicR 600 _ff
4214 7047 _m
(\(t\))_S /Times-RomanR 600 _ff
(,)_S 67 _t
(called)_S 67 _t
(the)_S 67 _t
/Times-ItalicR 600 _ff
(state)_S 67 _t
(variables)_S /Times-RomanR 600 _ff
(,)_S 67 _t
(such)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(initial)_S 1740 6812 _m
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/Times-ItalicR 600 _ff
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5614 6812 _m
(\(t\))_S /Times-RomanR 600 _ff
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67 _t
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5518 6533 _m
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/Times-RomanR 600 _ff
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67 _t
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1840 6063 _m
(1)_S 1900 6063 _m
/Times-ItalicR 600 _ff
1900 6107 _m
(\(t\),u)_S /Times-ItalicR 360 _ff
2239 6063 _m
(2)_S 2299 6063 _m
/Times-ItalicR 600 _ff
2299 6107 _m
(\(t\),...,u)_S /Times-ItalicR 360 _ff
2838 6063 _m
(i)_S 2871 6063 _m
/Times-ItalicR 600 _ff
2871 6107 _m
(\(t\),...,u)_S /Times-ItalicR 360 _ff
3410 6063 _m
(n)_S 3470 6063 _m
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3470 6107 _m
(\(t\))_S /Times-RomanR 600 _ff
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67 _t
(t)_S /Times-ItalicR 360 _ff
3329 5828 _m
(0)_S 3389 5828 _m
/Times-RomanR 600 _ff
3389 5872 _m
(.)_S 134 _t
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(the)_S 1500 4941 _m
(position,)_S 67 _t
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(Unique)_S 67 _t
(descriptions)_S 67 _t
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(vehicle)_S 67 _t
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(also)_S 67 _t
(require)_S 67 _t
(inclusion)_S 67 _t
(of)_S 67 _t
(an)_S 1500 4243 _m
(accompanying)_S 67 _t
(dynamics)_S 67 _t
(model,)_S 67 _t
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(an)_S 67 _t
(equal)_S 67 _t
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(equations)_S 67 _t
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(state)_S 67 _t
(variables)_S 67 _t
(expressed)_S 67 _t
(in)_S 67 _t
(list)_S 67 _t
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(One)_S 67 _t
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(clarification)_S 67 _t
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(the)_S 67 _t
(quoted)_S 67 _t
(definition)_S 67 _t
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(not)_S 67 _t
(be)_S 1500 3196 _m
(deterministic)_S 67 _t
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(can)_S 67 _t
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(stochastic.)_S 1980 2847 _m
(A)_S 67 _t
(key)_S 67 _t
(characterization)_S 67 _t
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(any)_S 67 _t
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(dynamics)_S 67 _t
(laws)_S 67 _t
(is)_S 67 _t
(whether)_S 67 _t
(the)_S 67 _t
(system)_S 67 _t
(is)_S 1500 2498 _m
(holonomic)_S 67 _t
(or)_S 67 _t
(nonholonomic.)_S 134 _t
(These)_S 67 _t
(two)_S 67 _t
(terms)_S 67 _t
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(merit)_S 1500 2147 _m
(definition)_S 67 _t
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/Times-ItalicR 600 _ff
(Holonomic)_S /Times-RomanR 600 _ff
67 _t
(describes)_S 67 _t
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(92)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(of)_S 67 _t
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(a)_S 67 _t
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(body;)_S 67 _t
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("whole.")_S 67 _t
1500 11506 _m
(Ordinarily,)_S 67 _t
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(a)_S 67 _t
(single)_S 67 _t
(rigid)_S 67 _t
(body,)_S 67 _t
(twelve)_S 67 _t
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(holonomic)_S 67 _t
(motion,)_S 1500 11157 _m
(corresponding)_S 67 _t
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(six)_S 67 _t
(physical)_S 67 _t
(degrees)_S 67 _t
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(freedom.)_S 134 _t
(Specifically)_S 67 _t
(these)_S 67 _t
(twelve)_S 67 _t
(state)_S 1500 10808 _m
(variables)_S 67 _t
(include)_S 67 _t
(six)_S 67 _t
(values)_S 67 _t
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(linear)_S 67 _t
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(velocities,)_S 67 _t
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(six)_S 67 _t
(values)_S 67 _t
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(position)_S 67 _t
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(\(i.e.)_S 67 _t
(posture\).)_S 134 _t
/Times-ItalicR 600 _ff
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67 _t
(motion)_S 67 _t
(indicates)_S 67 _t
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(interdependent)_S 67 _t
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(rigid)_S 67 _t
(body)_S 67 _t
(motion,)_S 67 _t
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(variation)_S 67 _t
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(one)_S 67 _t
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(more)_S 67 _t
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(these)_S 67 _t
(state)_S 67 _t
(variables)_S 67 _t
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(constrained)_S 67 _t
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(other)_S 67 _t
(state)_S 67 _t
(variables.)_S 67 _t
1500 9409 _m
(Nonholonomic)_S 67 _t
(constraints)_S 67 _t
(prevent)_S 67 _t
(direct)_S 67 _t
(integration)_S 67 _t
(of)_S 67 _t
(accelerations)_S 67 _t
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(velocities)_S 67 _t
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(posture.)_S 134 _t
(Examples)_S 67 _t
(of)_S 67 _t
(nonholonomic)_S 67 _t
(motion)_S 67 _t
(constraints)_S 67 _t
(include)_S 67 _t
(a)_S 67 _t
(rolling)_S 67 _t
(ball)_S 67 _t
(that)_S 67 _t
(can)_S 1500 8711 _m
(not)_S 67 _t
(slip)_S 67 _t
(\(i.e.)_S 67 _t
(lose)_S 67 _t
(traction\))_S 67 _t
(relative)_S 67 _t
(to)_S 67 _t
(a)_S 67 _t
(surface,)_S 67 _t
(or)_S 67 _t
(parallel)_S 67 _t
(parking)_S 67 _t
(an)_S 67 _t
(automobile)_S 1500 8362 _m
(where)_S 67 _t
(no)_S 67 _t
(sideslip)_S 67 _t
(is)_S 67 _t
(allowed.)_S 134 _t
(Another)_S 67 _t
(example)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(falling)_S 67 _t
(cat)_S 67 _t
(as)_S 67 _t
(it)_S 67 _t
(moves)_S 67 _t
(in)_S 67 _t
(midair,)_S 1500 8013 _m
(which)_S 67 _t
(must)_S 67 _t
(obey)_S 67 _t
(the)_S 67 _t
(conservation)_S 67 _t
(law)_S 67 _t
(for)_S 67 _t
(angular)_S 67 _t
(momentum.)_S 134 _t
(In)_S 67 _t
(each)_S 67 _t
(case,)_S 1500 7664 _m
(nonholonomic)_S 67 _t
(constraints)_S 67 _t
(limit)_S 67 _t
(the)_S 67 _t
(freedom)_S 67 _t
(of)_S 67 _t
(motion.)_S 201 _t
(Further)_S 67 _t
(descriptions)_S 67 _t
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(recent)_S 67 _t
(research)_S 67 _t
(in)_S 67 _t
(nonholonomic)_S 67 _t
(motion)_S 67 _t
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(examined)_S 67 _t
(in)_S 67 _t
(\(Greenwood)_S 67 _t
(88\),)_S 1500 6966 _m
(\(Latombe)_S 67 _t
(91\))_S 67 _t
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(\(Li,)_S 67 _t
(Canny)_S 67 _t
(93\).)_S 1980 6544 _m
/Times-BoldR 600 _ff
(1.)_S 2400 6544 _m
(Ground)_S 67 _t
(Vehicles)_S /Times-RomanR 600 _ff
2400 6195 _m
(Ground)_S 67 _t
(vehicles)_S 67 _t
(are)_S 67 _t
(constrained)_S 67 _t
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(contact)_S 67 _t
(with)_S 67 _t
(a)_S 67 _t
(surface)_S 67 _t
(that)_S 67 _t
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(normal)_S 67 _t
(and)_S 67 _t
(frictional)_S 67 _t
(forces)_S 67 _t
(between)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(terrain.)_S 134 _t
(On)_S 67 _t
(a)_S 67 _t
(surface)_S 67 _t
(that)_S 67 _t
(is)_S 1500 5497 _m
(predominantly)_S 67 _t
(planar,)_S 67 _t
(high)_S 67 _t
(frequency)_S 67 _t
(vertical)_S 67 _t
(components)_S 67 _t
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(motion)_S 67 _t
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(horizontal)_S 67 _t
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(mechanical)_S 67 _t
(devices)_S 67 _t
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(shock)_S 67 _t
(absorbers,)_S 67 _t
(tire)_S 1500 4450 _m
(wheels,)_S 67 _t
(suspension)_S 67 _t
(systems)_S 67 _t
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(flexible)_S 67 _t
(legs.)_S 134 _t
(Vertical)_S 67 _t
(forces)_S 67 _t
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(displace)_S 67 _t
(the)_S 1500 4101 _m
(vehicle)_S 67 _t
(a)_S 67 _t
(small)_S 67 _t
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(independent)_S 67 _t
(amount)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(vertical)_S 67 _t
(direction)_S 67 _t
(with)_S 67 _t
(little)_S 67 _t
(effect)_S 67 _t
(on)_S 1500 3752 _m
(horizontal)_S 67 _t
(velocity.)_S 134 _t
(Travel)_S 67 _t
(up)_S 67 _t
(and)_S 67 _t
(down)_S 67 _t
(hills)_S 67 _t
(can)_S 67 _t
(add)_S 67 _t
(a)_S 67 _t
(vertical)_S 67 _t
(component)_S 67 _t
(to)_S 67 _t
(the)_S 1500 3403 _m
(direction)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(but)_S 67 _t
(does)_S 67 _t
(not)_S 67 _t
(fundamentally)_S 67 _t
(change)_S 67 _t
(the)_S 67 _t
(two-dimensional)_S 67 _t
(nature)_S 67 _t
(of)_S 1500 3054 _m
(vehicle)_S 67 _t
(travel)_S 67 _t
(relative)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(surface.)_S 134 _t
(Often)_S 67 _t
(simple)_S 67 _t
(kinematic)_S 67 _t
(models)_S 67 _t
(suffice)_S 67 _t
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(wheeled)_S 67 _t
(robots)_S 67 _t
(\(Alexander)_S 67 _t
(90\),)_S 67 _t
(especially)_S 67 _t
(when)_S 67 _t
(surface)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(slow)_S 67 _t
(and)_S 1500 2356 _m
(constrained)_S 67 _t
(to)_S 67 _t
(follow)_S 67 _t
(roads)_S 67 _t
(and)_S 67 _t
(tracks)_S 67 _t
(when)_S 67 _t
(outside)_S 67 _t
(or)_S 67 _t
(flat)_S 67 _t
(floor)_S 67 _t
(surfaces)_S 67 _t
(when)_S 5000 1288 _m
(93)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(indoors.)_S 134 _t
(Legged)_S 67 _t
(robot)_S 67 _t
(interactions)_S 67 _t
(with)_S 67 _t
(surfaces)_S 67 _t
(are)_S 67 _t
(complex)_S 67 _t
(and)_S 67 _t
(require)_S 67 _t
(dynamics)_S 1500 11506 _m
(models)_S 67 _t
(\(Frank)_S 67 _t
(69\))_S 67 _t
(\(McGhee)_S 67 _t
(79\))_S 67 _t
(\(Raibert)_S 67 _t
(86\).)_S 2400 11157 _m
(Ground)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(complicated)_S 67 _t
(by)_S 67 _t
(operation)_S 67 _t
(at)_S 67 _t
(the)_S 67 _t
(interface)_S 67 _t
(between)_S 1500 10808 _m
(two)_S 67 _t
(media:)_S 134 _t
(ground)_S 67 _t
(and)_S 67 _t
(atmosphere.)_S 134 _t
(Aerodynamics)_S 67 _t
(loading)_S 67 _t
(is)_S 67 _t
(usually)_S 67 _t
(secondary,)_S 67 _t
(but)_S 1500 10459 _m
(must)_S 67 _t
(be)_S 67 _t
(considered)_S 67 _t
(during)_S 67 _t
(high)_S 67 _t
(wind)_S 67 _t
(conditions)_S 67 _t
(or)_S 67 _t
(in)_S 67 _t
(conjunction)_S 67 _t
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(the)_S 67 _t
(response)_S 67 _t
(at)_S 1500 10110 _m
(high)_S 67 _t
(relative)_S 67 _t
(speeds)_S 67 _t
(between)_S 67 _t
(robot)_S 67 _t
(and)_S 67 _t
(ground.)_S 134 _t
(Detailed)_S 67 _t
(analysis)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(mechanisms)_S 1500 9761 _m
(governing)_S 67 _t
(vehicle)_S 67 _t
(interaction)_S 67 _t
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(various)_S 67 _t
(surface)_S 67 _t
(types)_S 67 _t
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(traversal)_S 67 _t
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(rough)_S 67 _t
(terrain)_S 67 _t
(by)_S 67 _t
(off-road)_S 67 _t
(vehicles)_S 67 _t
(\(Bekker)_S 67 _t
(56\))_S 1500 9063 _m
(\(Bekker)_S 67 _t
(69\).)_S 134 _t
(Fortunately)_S 67 _t
(for)_S 67 _t
(most)_S 67 _t
(robot)_S 67 _t
(operations,)_S 67 _t
(however,)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(of)_S 1500 8714 _m
(ground-vehicle)_S 67 _t
(interaction)_S 67 _t
(rarely)_S 67 _t
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(vehicle)_S 67 _t
(stability,)_S 67 _t
(reliability,)_S 1500 8365 _m
(navigation)_S 67 _t
(or)_S 67 _t
(higher-level)_S 67 _t
(control)_S 67 _t
(functions.)_S 134 _t
(Ground)_S 67 _t
(robots)_S 67 _t
(may)_S 67 _t
(further)_S 67 _t
(attempt)_S 67 _t
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(advantage)_S 67 _t
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(ground)_S 67 _t
(contact)_S 67 _t
(for)_S 67 _t
(navigational)_S 67 _t
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(measuring)_S 67 _t
(wheel)_S 1500 7667 _m
(rotation,)_S 67 _t
(frictional)_S 67 _t
(contact)_S 67 _t
(or)_S 67 _t
(leg)_S 67 _t
(motion)_S 67 _t
(\(MacPherson)_S 67 _t
(93\).)_S 134 _t
(In)_S 67 _t
(this)_S 67 _t
(overall)_S 67 _t
(robotics)_S 1500 7318 _m
(context,)_S 67 _t
(regardless)_S 67 _t
(of)_S 67 _t
(how)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(estimated,)_S 67 _t
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(vehicle)_S 67 _t
(dynamic)_S 67 _t
(behavior)_S 67 _t
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(often)_S 67 _t
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(approximated)_S 67 _t
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(kinematic)_S 67 _t
(models,)_S 67 _t
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(dynamics)_S 67 _t
(considerations)_S 67 _t
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(only)_S 67 _t
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(effects)_S 67 _t
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(robot)_S 67 _t
(control)_S 67 _t
(logic.)_S 134 _t
(Ground)_S 67 _t
(vehicles)_S 67 _t
(remain)_S 67 _t
(highly)_S 1500 6271 _m
(constrained)_S 67 _t
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(the)_S 67 _t
(nonholonomic)_S 67 _t
(nature)_S 67 _t
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(contact)_S 67 _t
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(environment.)_S 1980 5849 _m
/Times-BoldR 600 _ff
(2.)_S 2400 5849 _m
(Air)_S 67 _t
(Vehicles)_S /Times-RomanR 600 _ff
2400 5500 _m
(Air)_S 67 _t
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(differ)_S 67 _t
(from)_S 67 _t
(ground)_S 67 _t
(vehicles)_S 67 _t
(in)_S 67 _t
(that)_S 67 _t
(vertical)_S 67 _t
(components)_S 67 _t
(of)_S 1500 5151 _m
(motion)_S 67 _t
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(coupled)_S 67 _t
(to)_S 67 _t
(interactions)_S 67 _t
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(the)_S 67 _t
(local)_S 67 _t
(horizontal)_S 67 _t
(plane.)_S 134 _t
(Interactions)_S 67 _t
(with)_S 67 _t
(the)_S 1500 4802 _m
(atmosphere)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(aerodynamic)_S 67 _t
(forces)_S 67 _t
(have)_S 67 _t
(a)_S 67 _t
(significant)_S 67 _t
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(vehicle)_S 67 _t
(motion.)_S 67 _t
1500 4453 _m
(There)_S 67 _t
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(no)_S 67 _t
(direct)_S 67 _t
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(air)_S 67 _t
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(contact,)_S 67 _t
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(aircraft)_S 67 _t
(flight)_S 67 _t
(dynamics)_S 67 _t
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(holonomic.)_S 134 _t
(Fixed)_S 67 _t
(wing)_S 67 _t
(air)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(are)_S 67 _t
(typically)_S 1500 3755 _m
(dominated)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(high)_S 67 _t
(speed)_S 67 _t
(forward)_S 67 _t
(motion)_S 67 _t
(which)_S 67 _t
(is)_S 67 _t
(necessary)_S 67 _t
(to)_S 67 _t
(generate)_S 67 _t
(sufficient)_S 1500 3406 _m
(lift)_S 67 _t
(to)_S 67 _t
(carry)_S 67 _t
(vehicle)_S 67 _t
(weight.)_S 134 _t
(The)_S 67 _t
(density)_S 67 _t
(of)_S 67 _t
(air)_S 67 _t
(is)_S 67 _t
(low,)_S 67 _t
(and)_S 67 _t
(thus)_S 67 _t
(vehicle)_S 67 _t
(accelerations)_S 1500 3057 _m
(do)_S 67 _t
(not)_S 67 _t
(produce)_S 67 _t
(significant)_S 67 _t
(acceleration-related)_S 67 _t
(aerodynamic)_S 67 _t
(forces.)_S 134 _t
(This)_S 67 _t
(means)_S 67 _t
(that)_S 1500 2708 _m
(the)_S 67 _t
(atmosphere)_S 67 _t
(does)_S 67 _t
(not)_S 67 _t
(induce)_S 67 _t
(significant)_S 67 _t
("added)_S 67 _t
(mass")_S 67 _t
(effects)_S 67 _t
(\(Yuh)_S 67 _t
(90\).)_S 2400 2359 _m
(Helicopters)_S 67 _t
(differ)_S 67 _t
(in)_S 67 _t
(many)_S 67 _t
(respects)_S 67 _t
(from)_S 67 _t
(fixed)_S 67 _t
(wing)_S 67 _t
(aircraft.)_S 134 _t
(Helicopter)_S 1500 2010 _m
(rotors)_S 67 _t
(have)_S 67 _t
(high)_S 67 _t
(degrees)_S 67 _t
(of)_S 67 _t
(freedom)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(multiple)_S 67 _t
(rotor)_S 67 _t
(blades,)_S 67 _t
(each)_S 67 _t
(of)_S 67 _t
(which)_S 67 _t
(have)_S 5000 1288 _m
(94)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(individual)_S 67 _t
(mechanical)_S 67 _t
(articulations)_S 67 _t
(for)_S 67 _t
(twist)_S 67 _t
(and)_S 67 _t
(lag.)_S 134 _t
(Additional)_S 67 _t
(degrees)_S 67 _t
(of)_S 67 _t
(freedom)_S 1500 11506 _m
(occur)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(many)_S 67 _t
(factors,)_S 67 _t
(including)_S 67 _t
(flexible)_S 67 _t
(rotational)_S 67 _t
(twist)_S 67 _t
(of)_S 67 _t
(individual)_S 67 _t
(blades,)_S 67 _t
(tail)_S 1500 11157 _m
(rotors,)_S 67 _t
(optional)_S 67 _t
(jet)_S 67 _t
(assist,)_S 67 _t
(and)_S 67 _t
(airstream)_S 67 _t
(interactions)_S 67 _t
(during)_S 67 _t
(phenomena)_S 67 _t
(such)_S 67 _t
(as)_S 1500 10808 _m
(turbulence)_S 67 _t
(and)_S 67 _t
(ground)_S 67 _t
(effects.)_S 134 _t
(Despite)_S 67 _t
(this)_S 67 _t
(high)_S 67 _t
(degree)_S 67 _t
(of)_S 67 _t
(complexity,)_S 67 _t
(helicopter)_S 1500 10459 _m
(dynamics)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(well)_S 67 _t
(specified)_S 67 _t
(\(Saunders)_S 67 _t
(75\),)_S 67 _t
(modeled)_S 67 _t
(in)_S 67 _t
(real)_S 67 _t
(time)_S 67 _t
(\(Williams)_S 67 _t
(85\))_S 1500 10110 _m
(\(Offenbeck)_S 67 _t
(85\))_S 67 _t
(and)_S 67 _t
(visually)_S 67 _t
(verified)_S 67 _t
(during)_S 67 _t
(repeated)_S 67 _t
(testing.)_S 2400 9761 _m
(In)_S 67 _t
(fixed-wing)_S 67 _t
(aircraft,)_S 67 _t
(wings)_S 67 _t
(support)_S 67 _t
(the)_S 67 _t
(weight)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(also)_S 1500 9412 _m
(support)_S 67 _t
(control)_S 67 _t
(surfaces.)_S 134 _t
(Although)_S 67 _t
(aircraft)_S 67 _t
(weight)_S 67 _t
(and)_S 67 _t
(balance)_S 67 _t
(variations)_S 67 _t
(can)_S 67 _t
(produce)_S 1500 9063 _m
(large)_S 67 _t
(effects,)_S 67 _t
(they)_S 67 _t
(are)_S 67 _t
(ordinarily)_S 67 _t
(maintained)_S 67 _t
(within)_S 67 _t
(carefully)_S 67 _t
(specified)_S 67 _t
(ranges)_S 67 _t
(that)_S 67 _t
(the)_S 1500 8714 _m
(wings)_S 67 _t
(and)_S 67 _t
(control)_S 67 _t
(surfaces)_S 67 _t
(can)_S 67 _t
(accommodate.)_S 134 _t
(Wing)_S 67 _t
(aerodynamics)_S 67 _t
(have)_S 67 _t
(been)_S 1500 8365 _m
(extensively)_S 67 _t
(studied)_S 67 _t
(under)_S 67 _t
(steady)_S 67 _t
(motion)_S 67 _t
(conditions)_S 67 _t
(and)_S 67 _t
(are)_S 67 _t
(easily)_S 67 _t
(generalizable.)_S 134 _t
(Thus)_S 1500 8016 _m
(the)_S 67 _t
(overall)_S 67 _t
(lift)_S 67 _t
(and)_S 67 _t
(drag)_S 67 _t
(behavior)_S 67 _t
(of)_S 67 _t
(most)_S 67 _t
(air)_S 67 _t
(vehicles)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(predicted)_S 67 _t
(with)_S 67 _t
(reasonable)_S 1500 7667 _m
(accuracy)_S 67 _t
(and)_S 67 _t
(in)_S 67 _t
(real)_S 67 _t
(time)_S 67 _t
(using)_S 67 _t
(simultaneous)_S 67 _t
(differential)_S 67 _t
(equation)_S 67 _t
(solutions)_S 1500 7318 _m
(\(Cooke)_S 67 _t
(92a,)_S 67 _t
(92b\))_S 67 _t
(\(Rolfe)_S 67 _t
(86\).)_S 134 _t
(Nevertheless)_S 67 _t
(precise)_S 67 _t
(localized)_S 67 _t
(modeling)_S 67 _t
(of)_S 1500 6969 _m
(high-performance)_S 67 _t
(aircraft)_S 67 _t
(dynamics)_S 67 _t
(for)_S 67 _t
(design)_S 67 _t
(purposes)_S 67 _t
(does)_S 67 _t
(not)_S 67 _t
(permit)_S 67 _t
(general)_S 1500 6620 _m
(closed-form)_S 67 _t
(solutions.)_S 134 _t
(Feasible)_S 67 _t
(solutions)_S 67 _t
(for)_S 67 _t
(precision)_S 67 _t
(design)_S 67 _t
(include)_S 67 _t
(massive)_S 67 _t
(finite)_S 1500 6271 _m
(element)_S 67 _t
(analysis,)_S 67 _t
(a)_S 67 _t
(large-scale)_S 67 _t
(computational)_S 67 _t
(fluid)_S 67 _t
(dynamics)_S 67 _t
(\(CFD\))_S 67 _t
(approach,)_S 67 _t
(and)_S 1500 5922 _m
(wind)_S 67 _t
(tunnel)_S 67 _t
(testing.)_S 134 _t
(These)_S 67 _t
(approaches)_S 67 _t
(do)_S 67 _t
(not)_S 67 _t
(suit)_S 67 _t
(real-time)_S 67 _t
(application)_S 67 _t
(since)_S 1500 5573 _m
(large-scale)_S 67 _t
(finite)_S 67 _t
(element)_S 67 _t
(analysis)_S 67 _t
(and)_S 67 _t
(CFD)_S 67 _t
(are)_S 67 _t
(considered)_S 67 _t
(computational)_S 1500 5224 _m
("grand)_S 67 _t
(challenges")_S 67 _t
(\(Draper)_S 67 _t
(94\).)_S 134 _t
(Scientific)_S 67 _t
(visualization)_S 67 _t
(and)_S 67 _t
(virtual)_S 67 _t
(reality)_S 67 _t
(techniques)_S 1500 4875 _m
(have)_S 67 _t
(also)_S 67 _t
(been)_S 67 _t
(applied)_S 67 _t
(with)_S 67 _t
(some)_S 67 _t
(success)_S 67 _t
(in)_S 67 _t
(advanced)_S 67 _t
(aircraft)_S 67 _t
(design)_S 67 _t
(\(Bryson)_S 67 _t
(91\).)_S 67 _t
1500 4526 _m
(These)_S 67 _t
(complex)_S 67 _t
(advanced)_S 67 _t
(techniques)_S 67 _t
(are)_S 67 _t
(special)_S 67 _t
(cases,)_S 67 _t
(however,)_S 67 _t
(compared)_S 67 _t
(to)_S 67 _t
(the)_S 1500 4177 _m
(general)_S 67 _t
(state)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(art)_S 67 _t
(in)_S 67 _t
(aircraft)_S 67 _t
(design.)_S 134 _t
(Aircraft)_S 67 _t
(dynamics)_S 67 _t
(are)_S 67 _t
(typically)_S 67 _t
(well)_S 67 _t
(defined,)_S 1500 3828 _m
(well)_S 67 _t
(understood,)_S 67 _t
(and)_S 67 _t
(directly)_S 67 _t
(verifiable)_S 67 _t
(through)_S 67 _t
(visual)_S 67 _t
(examination)_S 67 _t
(during)_S 67 _t
(in-flight)_S 1500 3479 _m
(tests)_S 67 _t
(and)_S 67 _t
(wind)_S 67 _t
(tunnel)_S 67 _t
(experiments.)_S 1980 3057 _m
/Times-BoldR 600 _ff
(3.)_S 2400 3057 _m
(Space)_S 67 _t
(Vehicles)_S /Times-RomanR 600 _ff
2400 2708 _m
(Space)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(are)_S 67 _t
(principally)_S 67 _t
(determined)_S 67 _t
(by)_S 67 _t
(orbital)_S 67 _t
(mechanics.)_S 67 _t
1500 2359 _m
(Friction)_S 67 _t
(between)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(environment)_S 67 _t
(is)_S 67 _t
(almost)_S 67 _t
(non-existent,)_S 67 _t
(and)_S 67 _t
(thus)_S 67 _t
(the)_S 1500 2010 _m
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(include)_S 67 _t
(only)_S 67 _t
(gravitational,)_S 67 _t
(inertial)_S 67 _t
(and)_S 67 _t
(thrust)_S 67 _t
(effects.)_S 134 _t
(There)_S 67 _t
(are)_S 5000 1288 _m
(95)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(few)_S 67 _t
(\(if)_S 67 _t
(any\))_S 67 _t
(uncertain)_S 67 _t
(vehicle)_S 67 _t
(parameters,)_S 67 _t
(and)_S 67 _t
(vehicle)_S 67 _t
(postures)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(tracked)_S 67 _t
(both)_S 1500 11506 _m
(locally)_S 67 _t
(and)_S 67 _t
(remotely)_S 67 _t
(with)_S 67 _t
(great)_S 67 _t
(precision.)_S 134 _t
(Interestingly,)_S 67 _t
(ballistic)_S 67 _t
(missiles)_S 67 _t
(can)_S 67 _t
(be)_S 1500 11157 _m
(considered)_S 67 _t
(a)_S 67 _t
(special)_S 67 _t
(class)_S 67 _t
(of)_S 67 _t
(orbital)_S 67 _t
(vehicle)_S 67 _t
(whose)_S 67 _t
(path)_S 67 _t
(intersects)_S 67 _t
(the)_S 67 _t
(Earth's)_S 1500 10808 _m
(surface)_S 67 _t
(\(Bate)_S 67 _t
(71\).)_S 134 _t
(Many)_S 67 _t
(summaries)_S 67 _t
(of)_S 67 _t
(spacecraft)_S 67 _t
(dynamics)_S 67 _t
(are)_S 67 _t
(available,)_S 67 _t
(including)_S 1500 10459 _m
(\(Larson)_S 67 _t
(92\))_S 67 _t
(\(Bate)_S 67 _t
(71\))_S 67 _t
(\(Allen)_S 67 _t
(91\).)_S 134 _t
(Translation)_S 67 _t
(and)_S 67 _t
(angular)_S 67 _t
(movements)_S 67 _t
(for)_S 67 _t
(orbital)_S 1500 10110 _m
(vehicles)_S 67 _t
(may)_S 67 _t
(be)_S 67 _t
(counterintuitive)_S 67 _t
(from)_S 67 _t
(an)_S 67 _t
(everyday)_S 67 _t
(perspective)_S 67 _t
(but)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(calculated)_S 1500 9761 _m
(exactly.)_S 134 _t
(Under)_S 67 _t
(some)_S 67 _t
(conditions)_S 67 _t
(this)_S 67 _t
(motion)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(nonholonomic,)_S 67 _t
(since)_S 67 _t
(six)_S 1500 9412 _m
(degree-of-freedom)_S 67 _t
(space)_S 67 _t
(vehicles)_S 67 _t
(controlled)_S 67 _t
(by)_S 67 _t
(internal)_S 67 _t
(motors)_S 67 _t
(must)_S 67 _t
(still)_S 67 _t
(conserve)_S 1500 9063 _m
(angular)_S 67 _t
(momentum.)_S 134 _t
(If)_S 67 _t
(thrusters)_S 67 _t
(are)_S 67 _t
(used,)_S 67 _t
(spacecraft)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(holonomic.)_S 67 _t
1500 8714 _m
(Additionally)_S 67 _t
(some)_S 67 _t
(orbital)_S 67 _t
(vehicles)_S 67 _t
(\(such)_S 67 _t
(as)_S 67 _t
(an)_S 67 _t
(astronaut)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(space)_S 67 _t
(suit\))_S 67 _t
(have)_S 67 _t
(a)_S 1500 8365 _m
(variable)_S 67 _t
(mass)_S 67 _t
(distribution)_S 67 _t
(and)_S 67 _t
(may)_S 67 _t
(not)_S 67 _t
(strictly)_S 67 _t
(behave)_S 67 _t
(as)_S 67 _t
(rigid)_S 67 _t
(bodies.)_S 134 _t
(Other)_S 67 _t
(motions)_S 1500 8016 _m
(at)_S 67 _t
(higher)_S 67 _t
(frequencies)_S 67 _t
(may)_S 67 _t
(exist)_S 67 _t
(if)_S 67 _t
(vehicle)_S 67 _t
(components)_S 67 _t
(are)_S 67 _t
(flexible,)_S 67 _t
(in)_S 67 _t
(which)_S 67 _t
(case)_S 1500 7667 _m
(detailed)_S 67 _t
(partial)_S 67 _t
(differential)_S 67 _t
(equation)_S 67 _t
(solutions)_S 67 _t
(are)_S 67 _t
(required)_S 67 _t
(for)_S 67 _t
(twist,)_S 67 _t
(bending,)_S 67 _t
(shear)_S 67 _t
(and)_S 1500 7318 _m
(axial)_S 67 _t
(deformation.)_S 134 _t
(Nevertheless,)_S 67 _t
(in)_S 67 _t
(many)_S 67 _t
(respects)_S 67 _t
(the)_S 67 _t
(mathematical)_S 67 _t
(and)_S 67 _t
(empirical)_S 1500 6969 _m
(foundations)_S 67 _t
(of)_S 67 _t
(equations)_S 67 _t
(predicting)_S 67 _t
(spacecraft)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(the)_S 67 _t
(best)_S 67 _t
(defined,)_S 67 _t
(best)_S 1500 6620 _m
(understood)_S 67 _t
(and)_S 67 _t
(most)_S 67 _t
(directly)_S 67 _t
(verifiable)_S 67 _t
(of)_S 67 _t
(any)_S 67 _t
(vehicle)_S 67 _t
(type.)_S 1980 6198 _m
/Times-BoldR 600 _ff
(4.)_S 2400 6198 _m
(Surface)_S 67 _t
(Ships)_S /Times-RomanR 600 _ff
2400 5849 _m
(Surface)_S 67 _t
(ship)_S 67 _t
(dynamics)_S 67 _t
(are)_S 67 _t
(unconstrained)_S 67 _t
(in)_S 67 _t
(six)_S 67 _t
(degrees)_S 67 _t
(of)_S 67 _t
(freedom)_S 67 _t
(and)_S 67 _t
(are)_S 1500 5500 _m
(holonomic.)_S 134 _t
(The)_S 67 _t
(vertical)_S 67 _t
(component)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(primarily)_S 67 _t
(determined)_S 67 _t
(by)_S 67 _t
(very)_S 67 _t
(large)_S 1500 5151 _m
(counterbalancing)_S 67 _t
(values)_S 67 _t
(of)_S 67 _t
(weight)_S 67 _t
(and)_S 67 _t
(displacement)_S 67 _t
(which)_S 67 _t
(keep)_S 67 _t
(the)_S 67 _t
(ship)_S 67 _t
(at)_S 67 _t
(the)_S 67 _t
(surface)_S 1500 4802 _m
(of)_S 67 _t
(the)_S 67 _t
(ocean.)_S 134 _t
(Vertical)_S 67 _t
(posture)_S 67 _t
(changes)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(roll)_S 67 _t
(variations)_S 67 _t
(normally)_S 1500 4453 _m
(average)_S 67 _t
(to)_S 67 _t
(zero)_S 67 _t
(over)_S 67 _t
(long)_S 67 _t
(time)_S 67 _t
(scales,)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(hydrostatic)_S 67 _t
(righting)_S 67 _t
(moments)_S 1500 4104 _m
(produced)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(current)_S 67 _t
(location)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(buoyancy)_S 67 _t
(relative)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(center)_S 67 _t
(of)_S 1500 3755 _m
(gravity.)_S 134 _t
(Equipment,)_S 67 _t
(personnel)_S 67 _t
(and)_S 67 _t
(overall)_S 67 _t
(ship)_S 67 _t
(trajectory)_S 67 _t
(are)_S 67 _t
(typically)_S 67 _t
(unaffected)_S 67 _t
(by)_S 1500 3406 _m
(the)_S 67 _t
(time)_S 67 _t
(rates)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(components)_S 67 _t
(of)_S 67 _t
(motion,)_S 67 _t
(either)_S 67 _t
(by)_S 67 _t
(design)_S 67 _t
(or)_S 67 _t
(seafaring)_S 1500 3057 _m
(practice.)_S 134 _t
(Changes)_S 67 _t
(in)_S 67 _t
(vertical)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(strongly)_S 67 _t
(affected)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(changing)_S 67 _t
(buoyancy)_S 1500 2708 _m
(of)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(which)_S 67 _t
(varies)_S 67 _t
(as)_S 67 _t
(water)_S 67 _t
(displacement)_S 67 _t
(changes.)_S 134 _t
(As)_S 67 _t
(a)_S 67 _t
(result,)_S 67 _t
(a)_S 67 _t
(paramount)_S 1500 2359 _m
(criterion)_S 67 _t
(in)_S 67 _t
(ship)_S 67 _t
(design)_S 67 _t
(is)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(be)_S 67 _t
(reliably)_S 67 _t
(stable)_S 67 _t
(and)_S 67 _t
(self-righting,)_S 67 _t
(under)_S 1500 2010 _m
(both)_S 67 _t
(normal)_S 67 _t
(and)_S 67 _t
(damaged)_S 67 _t
(conditions.)_S 134 _t
(Interactions)_S 67 _t
(of)_S 67 _t
(greatest)_S 67 _t
(interest)_S 67 _t
(between)_S 67 _t
(vehicle)_S 5000 1288 _m
(96)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(and)_S 67 _t
(environment)_S 67 _t
(usually)_S 67 _t
(pertain)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(travel)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(ship)_S 67 _t
(along)_S 67 _t
(the)_S 67 _t
(horizontal)_S 67 _t
(ocean)_S 1500 11506 _m
(surface.)_S 134 _t
(Nevertheless)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(greatly)_S 67 _t
(complicated)_S 67 _t
(by)_S 67 _t
(vehicle)_S 67 _t
(operation)_S 67 _t
(at)_S 67 _t
(the)_S 1500 11157 _m
(interface)_S 67 _t
(between)_S 67 _t
(two)_S 67 _t
(media:)_S 134 _t
(ocean)_S 67 _t
(and)_S 67 _t
(atmosphere.)_S 134 _t
(Except)_S 67 _t
(for)_S 67 _t
(sailing)_S 67 _t
(vessels)_S 67 _t
(and)_S 1500 10808 _m
(ships)_S 67 _t
(with)_S 67 _t
(low)_S 67 _t
(headway,)_S 67 _t
(aerodynamic)_S 67 _t
(forces)_S 67 _t
(tend)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(weaker)_S 67 _t
(than)_S 67 _t
(hydrodynamic)_S 1500 10459 _m
(forces.)_S 134 _t
(Regardless)_S 67 _t
(of)_S 67 _t
(surface)_S 67 _t
(ship)_S 67 _t
(type,)_S 67 _t
(both)_S 67 _t
(sets)_S 67 _t
(of)_S 67 _t
(forces)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(significant)_S 67 _t
(and)_S 67 _t
(both)_S 1500 10110 _m
(must)_S 67 _t
(be)_S 67 _t
(considered)_S 67 _t
(simultaneously.)_S 2400 9761 _m
(Hydrodynamics)_S 67 _t
(and)_S 67 _t
(navigation)_S 67 _t
(of)_S 67 _t
(surface)_S 67 _t
(vessels)_S 67 _t
(are)_S 67 _t
(complex)_S 67 _t
(subjects)_S 67 _t
(but)_S 1500 9412 _m
(have)_S 67 _t
(been)_S 67 _t
(extensively)_S 67 _t
(studied,)_S 67 _t
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(a)_S 67 _t
(comprehensive)_S 67 _t
(compendium)_S 67 _t
(of)_S 67 _t
(knowledge)_S 67 _t
(in)_S 1500 9063 _m
(\(Lewis)_S 67 _t
(88\))_S 67 _t
(and)_S 67 _t
(more)_S 67 _t
(examples)_S 67 _t
(in)_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 67 _t
(\(Covington)_S 67 _t
(94\))_S 67 _t
(\(Maloney)_S 67 _t
(85\).)_S 67 _t
1500 8714 _m
(Predictable)_S 67 _t
(courses,)_S 67 _t
(predictable)_S 67 _t
(speeds,)_S 67 _t
(sideslip)_S 67 _t
(\(lateral)_S 67 _t
(motion)_S 67 _t
(due)_S 67 _t
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(momentum)_S 1500 8365 _m
(during)_S 67 _t
(turns\))_S 67 _t
(and)_S 67 _t
(gradual)_S 67 _t
(smooth)_S 67 _t
(changes)_S 67 _t
(in)_S 67 _t
(vehicle)_S 67 _t
(velocity)_S 67 _t
(are)_S 67 _t
(all)_S 67 _t
(typical)_S 67 _t
(of)_S 67 _t
(surface)_S 1500 8016 _m
(ship)_S 67 _t
(behavior.)_S 134 _t
(Behavior)_S 67 _t
(of)_S 67 _t
(surface)_S 67 _t
(vehicle)_S 67 _t
(dynamic)_S 67 _t
(response)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(tested)_S 67 _t
(and)_S 1500 7667 _m
(verified)_S 67 _t
(visually.)_S 134 _t
(Tow)_S 67 _t
(tank)_S 67 _t
(verification)_S 67 _t
(is)_S 67 _t
(also)_S 67 _t
(possible,)_S 67 _t
(but)_S 67 _t
(tow)_S 67 _t
(tank)_S 67 _t
(testing)_S 67 _t
(is)_S 1500 7318 _m
(expensive)_S 67 _t
(and)_S 67 _t
(is)_S 67 _t
(limited)_S 67 _t
(by)_S 67 _t
(two)_S 67 _t
(competing)_S 67 _t
(requirements.)_S 134 _t
(Test)_S 67 _t
(tank)_S 67 _t
(model)_S 67 _t
(designers)_S 1500 6969 _m
(attempt)_S 67 _t
(to)_S 67 _t
(maintain)_S 67 _t
(inverse)_S 67 _t
(proportionality)_S 67 _t
(constraints)_S 67 _t
(between)_S 67 _t
(the)_S 67 _t
(square)_S 67 _t
(root)_S 67 _t
(of)_S 1500 6620 _m
(model)_S 67 _t
(scale)_S 67 _t
(and)_S 67 _t
(maximum)_S 67 _t
(water)_S 67 _t
(speed)_S 67 _t
(\(Froude)_S 67 _t
(number\),)_S 67 _t
(along)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(concurrent)_S 1500 6271 _m
(desirability)_S 67 _t
(of)_S 67 _t
(simultaneously)_S 67 _t
(maintaining)_S 67 _t
(drag)_S 67 _t
(coefficient)_S 67 _t
(\(Reynolds)_S 67 _t
(number\))_S 1500 5922 _m
(similarity.)_S 134 _t
(Tradeoffs)_S 67 _t
(between)_S 67 _t
(these)_S 67 _t
(competing)_S 67 _t
(requirements)_S 67 _t
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(necessary)_S 67 _t
(when)_S 1500 5573 _m
(building)_S 67 _t
(and)_S 67 _t
(testing)_S 67 _t
(scale)_S 67 _t
(models.)_S 134 _t
(Wind)_S 67 _t
(and)_S 67 _t
(wave)_S 67 _t
(models)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(represented)_S 67 _t
(by)_S 1500 5224 _m
(complex)_S 67 _t
(spectral)_S 67 _t
(functions)_S 67 _t
(that)_S 67 _t
(are)_S 67 _t
(computationally)_S 67 _t
(expensive)_S 67 _t
(and)_S 67 _t
(difficult)_S 67 _t
(to)_S 67 _t
(specify)_S 1500 4875 _m
(\(Fossen)_S 67 _t
(94\).)_S 134 _t
(Nevertheless)_S 67 _t
(environmental)_S 67 _t
(disturbances)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(separately)_S 67 _t
(computed)_S 67 _t
(and)_S 1500 4526 _m
(independently)_S 67 _t
(added)_S 67 _t
(to)_S 67 _t
(hydrodynamic)_S 67 _t
(forces)_S 67 _t
(based)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(principle)_S 67 _t
(of)_S 67 _t
(superposition)_S 1500 4177 _m
(\(Lewis)_S 67 _t
(88\))_S 67 _t
(\(Fossen)_S 67 _t
(94\).)_S 134 _t
(Additionally,)_S 67 _t
(linear)_S 67 _t
(models)_S 67 _t
(are)_S 67 _t
(available)_S 67 _t
(for)_S 67 _t
(wind)_S 67 _t
(and)_S 67 _t
(wave)_S 1500 3828 _m
(behavior)_S 67 _t
(which)_S 67 _t
(permit)_S 67 _t
(reasonably)_S 67 _t
(accurate)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 1500 3479 _m
(\(Covington)_S 67 _t
(94\).)_S 134 _t
(Models)_S 67 _t
(of)_S 67 _t
(similar)_S 67 _t
(or)_S 67 _t
(lesser)_S 67 _t
(complexity)_S 67 _t
(are)_S 67 _t
(also)_S 67 _t
(available)_S 67 _t
(for)_S 1500 3130 _m
(hovercraft)_S 67 _t
(vehicles)_S 67 _t
(\(Amyot)_S 67 _t
(89\).)_S 134 _t
(In)_S 67 _t
(summary,)_S 67 _t
(modeling)_S 67 _t
(of)_S 67 _t
(surface)_S 67 _t
(ship)_S 67 _t
(dynamics)_S 67 _t
(is)_S 1500 2781 _m
(reasonably)_S 67 _t
(well)_S 67 _t
(defined,)_S 67 _t
(well)_S 67 _t
(studied)_S 67 _t
(and)_S 67 _t
(directly)_S 67 _t
(verifiable)_S 67 _t
(during)_S 67 _t
(testing.)_S 5000 1288 _m
(97)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1980 11735 _m
/Times-BoldR 600 _ff
(5.)_S 2400 11735 _m
(Underwater)_S 67 _t
(Vehicles)_S /Times-RomanR 600 _ff
2400 11386 _m
(Underwater)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(may)_S 67 _t
(be)_S 67 _t
(as)_S 67 _t
(complex)_S 67 _t
(and)_S 67 _t
(difficult)_S 67 _t
(to)_S 67 _t
(model)_S 67 _t
(as)_S 1500 11037 _m
(any)_S 67 _t
(of)_S 67 _t
(these)_S 67 _t
(regimes,)_S 67 _t
(principally)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(difficulties)_S 67 _t
(in)_S 67 _t
(observing)_S 67 _t
(and)_S 67 _t
(measuring)_S 67 _t
(actual)_S 1500 10688 _m
(underwater)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(response.)_S 134 _t
(Submerged)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(not)_S 1500 10339 _m
(constrained)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(vertical)_S 67 _t
(direction.)_S 134 _t
(For)_S 67 _t
(some)_S 67 _t
(unmanned)_S 67 _t
(vehicles,)_S 67 _t
(posture)_S 67 _t
(must)_S 67 _t
(be)_S 1500 9990 _m
(restricted)_S 67 _t
(to)_S 67 _t
(only)_S 67 _t
(reach)_S 67 _t
(moderate)_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(roll)_S 67 _t
(angles.)_S 134 _t
(This)_S 67 _t
(constraint)_S 67 _t
(is)_S 67 _t
(imposed)_S 1500 9641 _m
(since)_S 67 _t
(pointing)_S 67 _t
(vertically)_S 67 _t
(or)_S 67 _t
(inverting)_S 67 _t
(can)_S 67 _t
(cause)_S 67 _t
(equipment)_S 67 _t
(damage)_S 67 _t
(or)_S 67 _t
(dangerous)_S 1500 9292 _m
(control)_S 67 _t
(response.)_S 134 _t
(Very)_S 67 _t
(large)_S 67 _t
(angles)_S 67 _t
(of)_S 67 _t
(attack)_S 67 _t
(between)_S 67 _t
(vehicle)_S 67 _t
(orientation)_S 67 _t
(and)_S 67 _t
(vehicle)_S 1500 8943 _m
(direction)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(possible.)_S 134 _t
(The)_S 67 _t
(effects)_S 67 _t
(of)_S 67 _t
(forces)_S 67 _t
(and)_S 67 _t
(moments)_S 67 _t
(can)_S 67 _t
(all)_S 67 _t
(be)_S 1500 8594 _m
(cross-coupled)_S 67 _t
(between)_S 67 _t
(vertical,)_S 67 _t
(lateral)_S 67 _t
(and)_S 67 _t
(horizontal)_S 67 _t
(directions.)_S 134 _t
(Motion)_S 67 _t
(in)_S 67 _t
(world)_S 1500 8245 _m
(coordinates)_S 67 _t
(is)_S 67 _t
(only)_S 67 _t
(calculable)_S 67 _t
(after)_S 67 _t
(all)_S 67 _t
(effects)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(system)_S 67 _t
(are)_S 1500 7896 _m
(comprehensively)_S 67 _t
(predicted.)_S 134 _t
(Actual)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(watched)_S 67 _t
(remotely)_S 67 _t
(only)_S 67 _t
(with)_S 1500 7547 _m
(very)_S 67 _t
(low)_S 67 _t
(precision)_S 67 _t
(or)_S 67 _t
(\(more)_S 67 _t
(often\))_S 67 _t
(not)_S 67 _t
(at)_S 67 _t
(all.)_S 134 _t
(Tow)_S 67 _t
(tank)_S 67 _t
(testing)_S 67 _t
(imposes)_S 67 _t
(unrealistic)_S 1500 7198 _m
(external)_S 67 _t
(force)_S 67 _t
(constraints)_S 67 _t
(which)_S 67 _t
(are)_S 67 _t
(otherwise)_S 67 _t
(not)_S 67 _t
(present.)_S 134 _t
(The)_S 67 _t
(effects)_S 67 _t
(of)_S 67 _t
(the)_S 1500 6849 _m
(surrounding)_S 67 _t
(environment)_S 67 _t
(are)_S 67 _t
(relatively)_S 67 _t
(large)_S 67 _t
(and)_S 67 _t
(significant,)_S 67 _t
(so)_S 67 _t
(much)_S 67 _t
(so)_S 67 _t
(that)_S 67 _t
(the)_S 1500 6500 _m
(adjacent)_S 67 _t
(water)_S 67 _t
(tends)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(accelerated)_S 67 _t
(along)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(thought)_S 67 _t
(of)_S 67 _t
(as)_S 1500 6151 _m
(an)_S 67 _t
("added)_S 67 _t
(mass.")_S 134 _t
(Together)_S 67 _t
(these)_S 67 _t
(challenges)_S 67 _t
(make)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(physical)_S 1500 5802 _m
(response,)_S 67 _t
(guidance)_S 67 _t
(and)_S 67 _t
(control)_S 67 _t
(an)_S 67 _t
(extremely)_S 67 _t
(difficult)_S 67 _t
(dynamics)_S 67 _t
(problem.)_S 2400 5453 _m
(There)_S 67 _t
(are)_S 67 _t
(over)_S 67 _t
(one)_S 67 _t
(hundred)_S 67 _t
(pertinent)_S 67 _t
(coefficients)_S 67 _t
(and)_S 67 _t
(variables)_S 67 _t
(relating)_S 67 _t
(to)_S 1500 5104 _m
(the)_S 67 _t
(linear)_S 67 _t
(and)_S 67 _t
(non-linear)_S 67 _t
(coupled)_S 67 _t
(effects)_S 67 _t
(of)_S 67 _t
(lift,)_S 67 _t
(drag,)_S 67 _t
(added)_S 67 _t
(mass)_S 67 _t
(and)_S 67 _t
(propulsion)_S 67 _t
(in)_S 1500 4755 _m
(the)_S 67 _t
(model)_S 67 _t
(of)_S 67 _t
(this)_S 67 _t
(dissertation.)_S 134 _t
(Although)_S 67 _t
(a)_S 67 _t
(number)_S 67 _t
(of)_S 67 _t
(these)_S 67 _t
(coefficients)_S 67 _t
(are)_S 67 _t
(of)_S 1500 4406 _m
(second-order)_S 67 _t
(effect)_S 67 _t
(or)_S 67 _t
(negligible)_S 67 _t
(importance,)_S 67 _t
(determination)_S 67 _t
(of)_S 67 _t
(primary)_S 67 _t
(coefficient)_S 1500 4057 _m
(values)_S 67 _t
(is)_S 67 _t
(very)_S 67 _t
(difficult)_S 67 _t
(and)_S 67 _t
(expensive.)_S 134 _t
(These)_S 67 _t
(problems)_S 67 _t
(are)_S 67 _t
(frequently)_S 67 _t
(compounded)_S 1500 3708 _m
(when)_S 67 _t
(the)_S 67 _t
(subject)_S 67 _t
(vehicle)_S 67 _t
(has)_S 67 _t
(an)_S 67 _t
(open)_S 67 _t
(frame)_S 67 _t
(with)_S 67 _t
(irregular)_S 67 _t
(surfaces,)_S 67 _t
(or)_S 67 _t
(when)_S 67 _t
(a)_S 67 _t
(towed)_S 1500 3359 _m
(tether)_S 67 _t
(is)_S 67 _t
(attached.)_S 2400 3010 _m
(It)_S 67 _t
(is)_S 67 _t
(conceivable)_S 67 _t
(that)_S 67 _t
(an)_S 67 _t
(even)_S 67 _t
(more)_S 67 _t
(complex)_S 67 _t
(and)_S 67 _t
(fundamental)_S 67 _t
(model)_S 67 _t
(to)_S 1500 2661 _m
(calculate)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(might)_S 67 _t
(be)_S 67 _t
(derived)_S 67 _t
(than)_S 67 _t
(is)_S 67 _t
(presented)_S 67 _t
(here.)_S 67 _t
1500 2312 _m
(Specifically,)_S 67 _t
(the)_S 67 _t
(Navier-Stokes)_S 67 _t
(fluid)_S 67 _t
(flow)_S 67 _t
(differential)_S 67 _t
(equations)_S 67 _t
(might)_S 67 _t
(be)_S 67 _t
(applied)_S 67 _t
(in)_S 67 _t
(a)_S 1500 1963 _m
(CFD)_S 67 _t
(vehicle-fluid)_S 67 _t
(coupled)_S 67 _t
(interaction)_S 67 _t
(model)_S 67 _t
(\(Ren)_S 67 _t
(93\).)_S 134 _t
(Closed-form)_S 67 _t
(solutions)_S 67 _t
(for)_S 67 _t
(this)_S 5000 1288 _m
(98)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(approach)_S 67 _t
(do)_S 67 _t
(not)_S 67 _t
(exist,)_S 67 _t
(and)_S 67 _t
(numerical)_S 67 _t
(methods)_S 67 _t
(attempting)_S 67 _t
(to)_S 67 _t
(solve)_S 67 _t
(the)_S 67 _t
(Navier-Stokes)_S 1500 11506 _m
(partial)_S 67 _t
(differential)_S 67 _t
(equations)_S 67 _t
(in)_S 67 _t
(this)_S 67 _t
(domain)_S 67 _t
(tend)_S 67 _t
(to)_S 67 _t
(introduce)_S 67 _t
(more)_S 67 _t
(unknown)_S 1500 11157 _m
(parameters)_S 67 _t
(than)_S 67 _t
(they)_S 67 _t
(eliminate.)_S 134 _t
(This)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(particular)_S 67 _t
(problem)_S 67 _t
(for)_S 67 _t
(UUVs)_S 67 _t
(which)_S 67 _t
(often)_S 1500 10808 _m
(have)_S 67 _t
(irregular)_S 67 _t
(shapes.)_S 134 _t
(Additionally,)_S 67 _t
(CFD)_S 67 _t
(problems)_S 67 _t
(are)_S 67 _t
(among)_S 67 _t
(those)_S 67 _t
(currently)_S 1500 10459 _m
(considered)_S 67 _t
(as)_S 67 _t
(computational)_S 67 _t
("grand)_S 67 _t
(challenges")_S 67 _t
(\(Draper)_S 67 _t
(94\).)_S 134 _t
(Thus)_S 67 _t
(CFD)_S 67 _t
(methods)_S 67 _t
(are)_S 1500 10110 _m
(not)_S 67 _t
(currently)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(of)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics.)_S 2400 9761 _m
(Many)_S 67 _t
(models)_S 67 _t
(exist)_S 67 _t
(for)_S 67 _t
(ground)_S 67 _t
(vehicles,)_S 67 _t
(air)_S 67 _t
(vehicles,)_S 67 _t
(space)_S 67 _t
(vehicles,)_S 67 _t
(and)_S 1500 9412 _m
(surface)_S 67 _t
(ships)_S 67 _t
(that)_S 67 _t
(appear)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(use)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(virtual)_S 67 _t
(world.)_S 134 _t
(No)_S 67 _t
(complete)_S 1500 9063 _m
(analogous)_S 67 _t
(model)_S 67 _t
(for)_S 67 _t
(underwater)_S 67 _t
(vehicles)_S 67 _t
(was)_S 67 _t
(encountered)_S 67 _t
(during)_S 67 _t
(this)_S 67 _t
(research.)_S 134 _t
(A)_S 1500 8714 _m
(great)_S 67 _t
(many)_S 67 _t
(partial)_S 67 _t
(models)_S 67 _t
(of)_S 67 _t
(underwater)_S 67 _t
(dynamics)_S 67 _t
(exist,)_S 67 _t
(but)_S 67 _t
(all)_S 67 _t
(were)_S 67 _t
(found)_S 67 _t
(to)_S 67 _t
(suffer)_S 1500 8365 _m
(from)_S 67 _t
(incompleteness,)_S 67 _t
(confused)_S 67 _t
(nomenclature,)_S 67 _t
(oversimplification,)_S 67 _t
(or)_S 67 _t
(a)_S 67 _t
(formulation)_S 1500 8016 _m
(unsuitable)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(simulation.)_S 134 _t
(No)_S 67 _t
(other)_S 67 _t
(models)_S 67 _t
(were)_S 67 _t
(found)_S 67 _t
(which)_S 67 _t
(combined)_S 1500 7667 _m
(cruise)_S 67 _t
(mode)_S 67 _t
(hydrodynamics)_S 67 _t
(\(propellers,)_S 67 _t
(fins)_S 67 _t
(and)_S 67 _t
(predominantly)_S 67 _t
(forward)_S 67 _t
(velocity\))_S 67 _t
(with)_S 1500 7318 _m
(hovering)_S 67 _t
(mode)_S 67 _t
(hydrodynamics)_S 67 _t
(\(thrusters,)_S 67 _t
(station-keeping,)_S 67 _t
(low)_S 67 _t
(forward)_S 67 _t
(motion)_S 67 _t
(and)_S 1500 6967 _m
(large)_S 67 _t
(angle)_S 67 _t
(of)_S 67 _t
(attack\).)_S 134 _t
/Times-ItalicR 600 _ff
(No)_S 67 _t
(rigorous)_S 67 _t
(general)_S 67 _t
(model)_S 67 _t
(was)_S 67 _t
(previously)_S 67 _t
(available)_S 67 _t
(from)_S 67 _t
(a)_S 1500 6615 _m
(single)_S 67 _t
(source)_S 67 _t
(which)_S 67 _t
(is)_S 67 _t
(computationally)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(of)_S 67 _t
(submerged)_S 1500 6266 _m
(vehicle)_S 67 _t
(hydrodynamics)_S /Times-RomanR 600 _ff
(.)_S 1980 5843 _m
/Times-BoldR 600 _ff
(6.)_S 2400 5843 _m
(Comparison)_S 67 _t
(Summary)_S /Times-RomanR 600 _ff
2400 5494 _m
(Examination)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(salient)_S 67 _t
(characteristics)_S 67 _t
(of)_S 67 _t
(dynamics)_S 67 _t
(models)_S 67 _t
(in)_S 67 _t
(these)_S 1500 5145 _m
(many)_S 67 _t
(different)_S 67 _t
(robot)_S 67 _t
(environments)_S 67 _t
(reveals)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(underwater)_S 67 _t
(case)_S 67 _t
(is)_S 67 _t
(very)_S 67 _t
(difficult)_S 67 _t
(to)_S 1500 4796 _m
(accurately)_S 67 _t
(specify,)_S 67 _t
(most)_S 67 _t
(difficult)_S 67 _t
(to)_S 67 _t
(verify)_S 67 _t
(and)_S 67 _t
(most)_S 67 _t
(critical)_S 67 _t
(for)_S 67 _t
(preventing)_S 67 _t
(catastrophic)_S 1500 4447 _m
(vehicle)_S 67 _t
(loss.)_S 134 _t
(Failure)_S 67 _t
(to)_S 67 _t
(properly)_S 67 _t
(predict)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(of)_S 67 _t
(ground)_S 67 _t
(vehicles,)_S 67 _t
(orbital)_S 67 _t
(space)_S 1500 4098 _m
(vehicles)_S 67 _t
(or)_S 67 _t
(surface)_S 67 _t
(ships)_S 67 _t
(at)_S 67 _t
(worst)_S 67 _t
(may)_S 67 _t
(result)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(vehicle)_S 67 _t
(which)_S 67 _t
(stays)_S 67 _t
(in)_S 67 _t
(place)_S 67 _t
(and)_S 67 _t
(can)_S 1500 3749 _m
(be)_S 67 _t
(safely)_S 67 _t
(commanded.)_S 134 _t
(Failure)_S 67 _t
(of)_S 67 _t
(aircraft)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(improper)_S 67 _t
(prediction)_S 67 _t
(of)_S 67 _t
(aerodynamics)_S 1500 3400 _m
(can)_S 67 _t
(be)_S 67 _t
(mitigated)_S 67 _t
(through)_S 67 _t
(well-developed)_S 67 _t
(analytic)_S 67 _t
(techniques,)_S 67 _t
(wind)_S 67 _t
(tunnel)_S 67 _t
(testing)_S 67 _t
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(human)_S 67 _t
(supervisory)_S 67 _t
(control.)_S 134 _t
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(to)_S 67 _t
(properly)_S 67 _t
(predict)_S 67 _t
(the)_S 67 _t
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(lead)_S 67 _t
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(failure)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(any)_S 67 _t
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(faults)_S 67 _t
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(control,)_S 67 _t
(sensing,)_S 67 _t
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(power)_S 67 _t
(consumption.)_S 134 _t
(This)_S 1500 2004 _m
(critical)_S 67 _t
(vulnerability)_S 67 _t
(in)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(design)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(contributing)_S 67 _t
(cause)_S 67 _t
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(99)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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(rarity)_S 67 _t
(of)_S 67 _t
(working)_S 67 _t
(underwater)_S 67 _t
(robots.)_S 134 _t
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(the)_S 67 _t
(rigorous)_S 67 _t
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(nearly)_S 67 _t
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(\(Healey)_S 67 _t
(93\))_S 67 _t
(hydrodynamics)_S 67 _t
(model,)_S 67 _t
(which)_S 67 _t
(is)_S 67 _t
(compatibly)_S 67 _t
(described)_S 67 _t
(in)_S 67 _t
(\(Fossen)_S 67 _t
(94\),)_S 67 _t
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(been)_S 67 _t
(fully)_S 67 _t
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(implemented)_S 67 _t
(here.)_S 134 _t
(This)_S 67 _t
(revised)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(now)_S 1500 10808 _m
(fills)_S 67 _t
(a)_S 67 _t
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(robotics)_S 67 _t
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(the)_S 67 _t
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(of)_S 67 _t
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(a)_S 67 _t
(fluid)_S 67 _t
(medium.)_S 134 _t
(There)_S 67 _t
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(two)_S 67 _t
(coordinate)_S 67 _t
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(each)_S 67 _t
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/Times-ItalicR 600 _ff
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67 _t
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(now)_S 67 _t
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(The)_S 67 _t
(world)_S 67 _t
(coordinate)_S 1500 7511 _m
(system)_S 67 _t
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(model)_S 67 _t
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(by)_S 67 _t
(three)_S 67 _t
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(originating)_S 67 _t
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(point)_S 67 _t
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(computer)_S 67 _t
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(aircraft)_S 1500 5760 _m
(aerodynamics,)_S 67 _t
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(Simulation)_S 67 _t
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(87\))_S 67 _t
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(90\))_S 67 _t
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(85\))_S 67 _t
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(93,)_S 67 _t
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(94b\).)_S 134 _t
(Conversions)_S 67 _t
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(a)_S 67 _t
(topocentric)_S 67 _t
(local)_S 1500 4713 _m
(earth)_S 67 _t
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1500 3314 _m
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_s [] 0 _d 2 _lc 0 g _s 375 1800 _m
_sp 2174 1800 2174 1803 375 1803 3 _pl _pf _np _s _s 2171 1800 _m
_sp 2174 1800 2174 2999 2171 2999 3 _pl _pf _np _s _s 375 2996 _m
_sp 2174 2996 2174 2999 375 2999 3 _pl _pf _np _s _s 375 1800 _m
_sp 378 1800 378 2999 375 2999 3 _pl _pf _np 
_s 0 g 1131 1731 409 1834 _cw 
_s 
_s 0 g _s 959 2762 _m
_sp 939 2700 959 2714 980 2700 3 _pl _pf _np 
_s 15 _w 0 g 959 2714 _m
959 2119 _l _s 
_s 1 _w 0 g _s 1602 2119 _m
_sp 1540 2140 1554 2119 1540 2099 3 _pl _pf _np 
_s 15 _w 0 g 959 2119 _m
1554 2119 _l _s 
_s 1 _w 255 g _s 1000 2125 _m
_sp 1000 2125 1000 2129 999 2133 998 2137 997 2140 995 2144 993 2147 991 2150 988 2153 985 2156 982 2158 979 2160 975 2162 972 2163 968 2164 
964 2165 960 2165 956 2165 952 2164 948 2163 944 2162 941 2160 937 2158 934 2156 931 2153 929 2150 927 2147 925 2144 923 2140 921 2137 
920 2133 920 2129 920 2125 920 2121 920 2117 921 2113 923 2109 925 2106 927 2102 929 2099 931 2097 934 2094 937 2092 941 2090 944 2088 
948 2086 952 2085 956 2085 960 2085 964 2085 968 2085 972 2086 975 2088 979 2090 982 2092 985 2094 988 2097 991 2099 993 2102 995 2106 
997 2109 998 2113 999 2117 1000 2121 1000 2125 65 _pl _pf 
13 _w 0 g _cp _s 
_s 12 _w 0 g 932 2151 _m
987 2096 _l 933 2094 _m
986 2154 _l _s 
1 _w 0 g 881 2025 _m
_sp 881 2025 908 2025 909 2035 908 2035 907 2032 906 2030 903 2028 900 2028 890 2028 909 2057 884 2057 884 2048 885 2048 886 2051 887 2053 
889 2054 891 2054 900 2054 18 _pl _cp 
0 g _f _s _s 
0 g 914 2044 _m
_sp 914 2044 914 2040 932 2040 932 2044 4 _pl _cp 
0 g _f _s _s 
0 g 954 2046 _m
_sp 954 2046 950 2044 946 2043 943 2042 941 2040 939 2039 938 2037 938 2036 937 2034 937 2032 938 2029 939 2027 941 2026 944 2025 946 2025 
949 2026 951 2027 954 2029 955 2027 956 2026 957 2025 959 2025 961 2025 962 2026 964 2027 965 2028 965 2030 964 2029 962 2028 961 2029 
960 2032 960 2047 960 2048 960 2049 960 2051 960 2052 958 2055 956 2057 953 2058 949 2058 945 2057 941 2056 939 2053 938 2050 939 2048 
941 2047 943 2048 944 2050 944 2050 944 2050 944 2052 944 2053 944 2053 944 2054 945 2055 947 2056 949 2056 951 2056 953 2054 954 2052 
954 2048 61 _pl _cp 954 2044 _m
_sp 954 2044 950 2042 947 2040 945 2038 944 2036 943 2034 943 2032 944 2030 946 2029 948 2029 950 2029 951 2030 953 2031 954 2032 14 _pl _cp 
0 g _f _s _s 
0 g 981 2042 _m
_sp 981 2042 975 2032 973 2030 971 2028 969 2027 967 2027 967 2025 979 2025 979 2027 977 2027 976 2028 976 2029 978 2032 983 2039 987 2032 
989 2029 989 2028 988 2027 986 2027 986 2025 1001 2025 1001 2027 999 2027 998 2028 996 2030 994 2032 986 2044 990 2050 992 2052 994 2054 
995 2055 998 2056 998 2057 986 2057 986 2056 987 2056 988 2055 989 2054 989 2053 987 2050 985 2047 983 2050 980 2053 980 2054 981 2055 
983 2056 983 2056 983 2057 968 2057 968 2056 971 2055 972 2054 974 2052 975 2050 54 _pl _cp 
0 g _f _s _s 
0 g 1015 2059 _m
_sp 1015 2059 1014 2059 1003 2055 1003 2053 1004 2053 1006 2053 1008 2052 1008 2050 1008 2048 1008 2032 1008 2030 1008 2028 1006 2027 1004 2027 1003 2027 
1003 2025 1020 2025 1020 2027 1019 2027 1017 2027 1016 2028 1015 2030 1015 2032 23 _pl _cp 1007 2070 _m
_sp 1007 2070 1008 2067 1011 2066 1014 2067 1015 2070 1015 2072 1014 2074 1013 2075 1011 2075 1010 2075 1008 2074 1007 2072 12 _pl _cp 
0 g _f _s _s 
0 g 1023 2025 _m
_sp 1023 2025 1025 2025 1026 2026 1026 2026 1028 2026 1030 2025 1032 2025 1033 2025 1035 2025 1036 2025 1040 2026 1044 2027 1046 2030 1047 2034 1047 2036 
1046 2037 1046 2039 1045 2040 1043 2041 1041 2042 1039 2043 1035 2045 1032 2047 1030 2048 1028 2050 1028 2051 1029 2053 1030 2055 1032 2056 1035 2056 
1038 2055 1040 2054 1042 2051 1044 2047 1045 2047 1045 2057 1044 2057 1043 2057 1042 2057 1042 2057 1041 2057 1038 2057 1036 2058 1034 2058 1030 2057 
1026 2055 1024 2053 1023 2049 1024 2046 1025 2044 1028 2042 1032 2040 1037 2037 1039 2036 1041 2035 1042 2033 1042 2032 1041 2030 1040 2028 1038 2027 
1036 2027 1034 2027 1033 2027 1031 2028 1029 2029 1028 2030 1027 2031 1026 2033 1025 2036 1023 2036 70 _pl _cp 
0 g _f _s _s 
0 g 879 1997 _m
_sp 879 1997 879 1995 879 1995 882 1995 884 1994 885 1992 885 1988 885 1959 885 1955 884 1953 882 1952 879 1952 879 1952 879 1950 898 1950 
904 1950 909 1951 913 1952 916 1954 919 1957 922 1960 924 1963 925 1966 926 1969 926 1973 926 1977 925 1981 923 1984 921 1987 919 1990 
916 1992 913 1994 909 1995 905 1996 900 1997 894 1997 36 _pl _cp 892 1959 _m
_sp 892 1959 892 1955 893 1953 896 1953 899 1953 902 1954 905 1954 907 1955 910 1957 913 1960 915 1963 916 1968 917 1973 917 1977 916 1981 
914 1985 912 1988 910 1990 907 1992 904 1993 901 1994 897 1994 896 1994 894 1994 893 1993 892 1992 892 1988 27 _pl _cp 
0 g _f _s _s 
0 g 936 1969 _m
_sp 936 1969 958 1969 957 1973 955 1977 952 1980 949 1981 945 1982 941 1981 938 1980 934 1977 932 1974 931 1970 930 1965 931 1960 933 1955 
936 1952 939 1950 944 1949 948 1949 951 1951 954 1953 957 1957 959 1961 958 1962 957 1960 956 1959 955 1957 954 1956 952 1955 951 1954 
949 1953 947 1953 944 1954 940 1956 938 1959 937 1964 936 1969 936 1969 38 _pl _cp 950 1972 _m
_sp 950 1972 950 1975 948 1978 946 1979 943 1980 940 1979 938 1978 937 1975 936 1972 9 _pl _cp 
0 g _f _s _s 
0 g 972 1978 _m
_sp 972 1978 972 1983 971 1983 960 1979 960 1978 962 1978 964 1978 965 1977 966 1975 966 1972 966 1942 966 1940 965 1938 963 1937 961 1937 
960 1937 960 1935 978 1935 978 1937 976 1937 974 1937 973 1938 972 1940 972 1942 972 1952 974 1951 976 1950 977 1949 979 1949 983 1950 
986 1951 989 1954 992 1958 993 1962 994 1967 993 1972 992 1976 989 1979 986 1981 982 1982 979 1982 977 1981 974 1980 43 _pl _cp 972 1974 _m
_sp 972 1974 972 1956 974 1954 975 1953 977 1952 979 1952 982 1953 985 1956 986 1960 987 1965 986 1970 985 1975 982 1977 979 1978 977 1978 
975 1977 974 1976 17 _pl _cp 
0 g _f _s _s 
0 g 996 1981 _m
_sp 996 1981 996 1979 1000 1979 1000 1959 1001 1954 1002 1951 1004 1950 1007 1949 1009 1949 1011 1950 1013 1952 1015 1955 1014 1956 1012 1954 1010 1953 
1009 1953 1008 1954 1007 1956 1007 1958 1007 1979 1013 1979 1013 1982 1007 1982 1007 1991 1005 1991 1004 1989 1003 1987 1001 1985 1000 1984 998 1982 
30 _pl _cp 
0 g _f _s _s 
0 g 1027 1999 _m
_sp 1027 1999 1026 1999 1015 1996 1015 1994 1016 1994 1018 1994 1020 1993 1021 1991 1021 1989 1021 1957 1021 1954 1020 1952 1018 1951 1016 1951 1015 1951 
1015 1950 1032 1950 1032 1951 1031 1951 1029 1951 1028 1952 1027 1954 1027 1957 1027 1974 1029 1976 1031 1978 1032 1979 1034 1979 1036 1979 1038 1977 
1039 1974 1039 1969 1039 1957 1039 1954 1039 1952 1037 1951 1035 1951 1035 1951 1035 1950 1051 1950 1051 1951 1050 1951 1048 1951 1047 1952 1046 1954 
1046 1957 1046 1971 1045 1976 1044 1980 1041 1981 1037 1982 1034 1982 1032 1981 1030 1980 1027 1977 55 _pl _cp 
0 g _f _s _s 
0 g 828 1923 _m
_sp 828 1923 824 1920 821 1918 819 1916 817 1913 814 1909 813 1906 812 1901 811 1897 811 1892 811 1887 812 1883 813 1879 814 1876 817 1872 
819 1869 821 1867 824 1865 828 1862 829 1863 827 1865 826 1866 824 1868 823 1869 822 1871 821 1873 820 1875 819 1877 818 1880 818 1884 
817 1888 817 1892 817 1895 817 1899 818 1902 818 1905 819 1908 820 1910 821 1912 822 1913 823 1915 824 1917 826 1918 827 1920 829 1921 
45 _pl _cp 
0 g _f _s _s 
0 g 843 1908 _m
_sp 843 1908 842 1908 832 1904 832 1902 833 1902 835 1902 836 1901 837 1899 837 1897 837 1882 837 1879 836 1877 835 1876 833 1876 832 1876 
832 1875 849 1875 849 1876 847 1876 845 1876 844 1877 843 1879 843 1882 23 _pl _cp 836 1920 _m
_sp 836 1920 836 1918 837 1916 839 1915 840 1915 841 1915 843 1916 844 1918 844 1920 843 1923 840 1924 837 1923 12 _pl _cp 
0 g _f _s _s 
0 g 861 1908 _m
_sp 861 1908 861 1908 850 1904 850 1902 851 1902 853 1902 854 1901 855 1899 855 1897 855 1882 855 1879 855 1877 853 1876 851 1876 850 1876 
850 1875 866 1875 866 1876 866 1876 864 1876 862 1877 861 1879 861 1882 861 1898 864 1901 866 1903 867 1904 869 1904 871 1903 873 1902 
874 1898 874 1893 874 1882 874 1879 873 1877 872 1876 870 1876 869 1876 869 1875 886 1875 886 1876 884 1876 882 1876 881 1877 880 1879 
880 1882 880 1897 879 1901 878 1904 875 1906 872 1907 869 1907 867 1906 864 1904 861 1902 55 _pl _cp 
0 g _f _s _s 
0 g 886 1905 _m
_sp 886 1905 886 1903 890 1903 890 1883 890 1879 892 1876 894 1875 897 1874 899 1874 901 1875 903 1877 905 1879 904 1880 902 1878 900 1877 
899 1877 897 1879 896 1880 896 1883 896 1903 903 1903 903 1906 896 1906 896 1916 895 1916 894 1913 893 1911 891 1910 890 1908 888 1907 
30 _pl _cp 
0 g _f _s _s 
0 g 907 1890 _m
_sp 907 1890 908 1886 909 1882 912 1879 915 1876 919 1875 923 1874 927 1874 931 1876 934 1879 937 1882 938 1886 939 1891 938 1896 936 1901 
933 1904 929 1906 924 1907 919 1906 915 1905 912 1902 909 1899 908 1895 23 _pl _cp 914 1893 _m
_sp 914 1893 914 1887 916 1883 918 1879 921 1877 924 1876 927 1877 930 1880 931 1884 932 1889 931 1894 930 1898 928 1902 925 1904 922 1905 
919 1904 916 1902 915 1898 914 1893 914 1893 20 _pl _cp 
0 g _f _s _s 
0 g 976 1902 _m
_sp 976 1902 976 1908 975 1908 965 1904 965 1902 966 1902 968 1902 969 1901 970 1899 970 1897 970 1867 970 1864 969 1862 968 1861 966 1861 
965 1861 965 1860 982 1860 982 1861 980 1861 978 1861 977 1862 976 1864 976 1867 976 1876 978 1875 980 1874 981 1874 983 1874 987 1875 
990 1876 993 1879 996 1883 997 1887 998 1892 997 1897 996 1901 993 1904 990 1906 986 1907 984 1907 981 1906 978 1904 43 _pl _cp 976 1899 _m
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907 2869 907 2868 907 2867 905 2866 905 2865 919 2865 919 2866 917 2867 916 2868 914 2870 912 2872 905 2883 909 2888 911 2890 913 2892 
914 2893 916 2893 916 2895 905 2895 905 2893 905 2893 907 2893 907 2892 907 2891 905 2888 903 2885 901 2888 899 2891 899 2892 900 2893 
902 2893 902 2893 902 2895 888 2895 888 2893 890 2893 892 2892 893 2890 895 2888 54 _pl _cp 
0 g _f _s _s 
0 g 922 2883 _m
_sp 922 2883 922 2879 939 2879 939 2883 4 _pl _cp 
0 g _f _s _s 
0 g 960 2885 _m
_sp 960 2885 956 2883 953 2882 950 2880 948 2879 946 2877 945 2876 944 2875 943 2873 943 2871 944 2868 946 2866 948 2865 951 2864 953 2864 
955 2865 957 2867 960 2869 961 2867 962 2865 963 2864 964 2864 966 2864 968 2865 969 2866 971 2867 971 2869 969 2868 968 2867 966 2868 
966 2871 966 2885 966 2887 966 2888 966 2889 965 2890 964 2893 962 2895 959 2896 956 2896 952 2895 948 2894 946 2891 945 2888 946 2886 
948 2885 950 2886 951 2888 951 2888 951 2888 951 2890 951 2891 951 2891 952 2893 955 2894 957 2894 959 2892 960 2890 960 2886 59 _pl _cp 960 2882 _m
_sp 960 2882 957 2881 954 2879 952 2877 950 2875 950 2873 950 2871 951 2869 952 2868 954 2868 956 2868 957 2869 959 2870 960 2871 14 _pl _cp 
0 g _f _s _s 
0 g 986 2880 _m
_sp 986 2880 980 2872 978 2869 976 2868 974 2867 972 2866 972 2865 983 2865 983 2866 982 2867 981 2868 981 2869 983 2872 987 2878 991 2872 
993 2869 993 2868 992 2867 990 2866 990 2865 1004 2865 1004 2866 1002 2867 1001 2868 999 2870 998 2872 990 2883 994 2888 996 2890 998 2892 
999 2893 1001 2893 1001 2895 990 2895 990 2893 991 2893 992 2893 993 2892 993 2891 991 2888 989 2885 987 2888 985 2891 985 2892 986 2893 
987 2893 988 2893 988 2895 974 2895 974 2893 976 2893 977 2892 978 2890 980 2888 54 _pl _cp 
0 g _f _s _s 
0 g 1017 2897 _m
_sp 1017 2897 1016 2897 1006 2892 1006 2891 1008 2891 1010 2891 1011 2890 1011 2888 1011 2886 1011 2872 1011 2869 1011 2867 1009 2866 1007 2866 1006 2866 
1006 2865 1022 2865 1022 2866 1021 2866 1019 2866 1018 2867 1017 2869 1017 2872 23 _pl _cp 1010 2907 _m
_sp 1010 2907 1011 2904 1014 2903 1017 2904 1018 2907 1017 2910 1014 2911 1011 2910 8 _pl _cp 
0 g _f _s _s 
0 g 1025 2865 _m
_sp 1025 2865 1027 2865 1028 2865 1028 2865 1029 2865 1031 2865 1033 2865 1035 2865 1036 2864 1037 2864 1041 2865 1045 2867 1047 2869 1048 2873 1048 2875 
1047 2876 1046 2878 1045 2879 1044 2880 1042 2881 1040 2882 1037 2883 1034 2885 1032 2886 1030 2888 1030 2889 1030 2891 1032 2893 1033 2894 1036 2894 
1039 2893 1041 2892 1043 2889 1045 2886 1046 2886 1046 2895 1045 2895 1044 2894 1043 2894 1043 2894 1042 2895 1039 2895 1038 2896 1036 2896 1032 2895 
1028 2893 1026 2891 1025 2887 1026 2885 1027 2883 1030 2881 1033 2879 1038 2876 1040 2875 1042 2874 1043 2872 1043 2871 1043 2869 1042 2867 1040 2866 
1037 2866 1036 2866 1034 2867 1033 2867 1031 2868 1030 2869 1029 2871 1028 2873 1027 2875 1025 2875 70 _pl _cp 
0 g _f _s _s 
0 g 927 2806 _m
_sp 927 2806 902 2838 891 2838 891 2836 892 2836 894 2836 896 2835 897 2833 897 2830 897 2803 897 2799 896 2797 894 2796 892 2796 891 2796 
891 2794 906 2794 906 2796 905 2796 903 2796 901 2797 900 2799 900 2803 900 2828 929 2793 931 2793 931 2830 931 2833 932 2835 934 2836 
936 2836 937 2836 937 2838 921 2838 921 2836 922 2836 924 2836 926 2835 927 2833 927 2830 40 _pl _cp 
0 g _f _s _s 
0 g 940 2808 _m
_sp 940 2808 941 2803 943 2799 946 2796 949 2794 954 2793 958 2793 962 2795 965 2798 968 2801 969 2805 970 2810 969 2815 967 2819 964 2822 
960 2824 955 2825 951 2824 947 2823 944 2820 942 2817 940 2813 22 _pl _cp 946 2811 _m
_sp 946 2811 946 2805 948 2801 950 2798 952 2796 955 2795 959 2796 961 2798 963 2802 964 2807 963 2812 962 2816 960 2819 957 2821 954 2822 
951 2821 948 2819 947 2816 946 2811 946 2811 20 _pl _cp 
0 g _f _s _s 
0 g 982 2825 _m
_sp 982 2825 982 2825 972 2821 972 2820 973 2820 975 2820 976 2819 976 2817 976 2815 976 2800 976 2798 976 2796 975 2795 973 2795 972 2795 
972 2794 988 2794 988 2795 986 2795 984 2795 983 2796 982 2798 982 2800 982 2815 983 2817 984 2819 985 2820 986 2820 987 2820 988 2819 
990 2818 991 2818 993 2819 994 2821 993 2824 990 2825 988 2825 986 2824 984 2822 982 2819 40 _pl _cp 
0 g _f _s _s 
0 g 994 2823 _m
_sp 994 2823 994 2821 998 2821 998 2802 998 2798 1000 2795 1001 2794 1004 2793 1006 2793 1008 2794 1010 2796 1012 2798 1011 2799 1009 2797 1007 2796 
1006 2796 1005 2798 1004 2799 1004 2802 1004 2821 1010 2821 1010 2824 1004 2824 1004 2833 1003 2833 1002 2830 1001 2828 999 2827 998 2826 996 2824 
30 _pl _cp 
0 g _f _s _s 
0 g 1023 2840 _m
_sp 1023 2840 1022 2840 1012 2837 1012 2836 1013 2836 1015 2836 1016 2835 1017 2833 1017 2830 1017 2800 1017 2798 1017 2796 1015 2795 1013 2795 1012 2795 
1012 2794 1028 2794 1028 2795 1027 2795 1025 2795 1024 2796 1023 2798 1023 2800 1023 2817 1026 2819 1027 2820 1029 2821 1030 2821 1032 2821 1034 2819 
1035 2816 1035 2812 1035 2800 1035 2798 1034 2796 1033 2795 1031 2795 1030 2795 1030 2794 1046 2794 1046 2795 1045 2795 1043 2795 1042 2796 1041 2798 
1041 2800 1041 2814 1040 2819 1039 2822 1036 2824 1033 2825 1030 2825 1028 2824 1026 2822 1023 2820 55 _pl _cp 
0 g _f _s _s 
_s 255 g _s 1656 2591 _m
_sp 1644 2648 1642 2651 1641 2654 1639 2657 1637 2660 1636 2663 1634 2665 1632 2668 1630 2671 1628 2674 1626 2676 1624 2679 1622 2681 1619 2684 1617 2686 
1615 2689 1613 2691 1610 2694 1607 2696 1605 2698 1602 2700 1600 2702 1597 2704 1594 2706 1591 2708 1589 2710 1586 2711 1583 2713 1580 2715 1577 2716 
1574 2718 1571 2719 1567 2720 1564 2722 1561 2723 1558 2724 1555 2725 1551 2726 1548 2727 1545 2727 1541 2728 1538 2729 1534 2729 1531 2729 1527 2730 
1524 2730 1520 2730 1517 2730 1513 2730 1510 2730 1506 2730 1503 2729 1499 2729 1496 2729 1492 2728 1489 2727 1486 2727 1482 2726 1479 2725 1476 2724 
1472 2723 1469 2722 1466 2720 1463 2719 1460 2718 1457 2716 1454 2715 1451 2713 1448 2711 1445 2710 1442 2708 1439 2706 1437 2704 1434 2702 1431 2700 
1428 2698 1426 2696 1423 2694 1421 2691 1419 2689 1416 2686 1414 2684 1412 2681 1409 2679 1407 2676 1405 2674 1403 2671 1401 2668 1400 2665 1398 2663 
1396 2660 1394 2657 1393 2654 1391 2651 1390 2648 1388 2644 1387 2641 1386 2638 1385 2635 1384 2632 1383 2629 1382 2625 1381 2622 1380 2618 1379 2615 
1379 2612 1378 2608 1378 2605 1378 2601 1377 2598 1377 2594 1377 2591 1377 2587 1377 2583 1378 2580 1378 2577 1378 2573 1379 2570 1379 2566 1380 2563 
1381 2559 1382 2556 1383 2553 1384 2549 1385 2546 1386 2543 1387 2540 1388 2537 1390 2534 1391 2531 1393 2528 1394 2525 1396 2522 1398 2519 1400 2516 
1401 2513 1403 2510 1405 2508 1407 2505 1409 2502 1412 2500 1414 2497 1416 2495 1419 2492 1421 2490 1423 2488 1426 2485 1428 2483 1431 2481 1434 2479 
1437 2477 1439 2475 1442 2473 1445 2472 1448 2470 1451 2468 1454 2467 1457 2465 1460 2464 1463 2462 1466 2461 1469 2460 1472 2459 1476 2457 1479 2457 
1482 2456 1486 2455 1489 2454 1492 2453 1496 2453 1499 2452 1503 2452 1506 2452 1510 2451 1513 2451 1517 2451 1520 2451 1524 2451 1527 2452 1531 2452 
1534 2452 1538 2453 1541 2453 1545 2454 1548 2455 1551 2456 1555 2457 1558 2457 1561 2459 1564 2460 1567 2461 1571 2462 1574 2464 1577 2465 1580 2467 
1583 2468 1586 2470 1589 2472 1591 2473 1594 2475 1597 2477 1600 2479 1602 2481 1605 2483 1607 2485 1610 2488 1613 2490 1615 2492 1617 2495 1619 2497 
1622 2500 1624 2502 1626 2505 1628 2508 1630 2510 1632 2513 1634 2516 1636 2519 1637 2522 1639 2525 1641 2528 1642 2531 1644 2534 1645 2537 1646 2540 
1648 2543 1649 2546 1650 2549 1651 2553 1652 2556 1653 2559 1653 2563 1654 2566 1655 2570 1655 2573 1655 2577 1656 2580 1656 2583 1656 2587 1656 2591 
240 _pl 1656 2591 1656 2594 1656 2598 1656 2601 1655 2605 1655 2608 1655 2612 1654 2615 1653 2618 1653 2622 1652 2625 1651 2629 1650 2632 1649 2635 1648 2638 
1646 2641 1645 2644 17 _pl _pf 
0 g _cp _s 1356 2591 _m
1677 2591 _l 1517 2752 _m
1517 2430 _l _s 
_s 255 g _s 1645 2591 _m
_sp 1634 2643 1633 2646 1631 2649 1630 2652 1628 2654 1627 2657 1625 2660 1623 2662 1621 2665 1620 2667 1618 2670 1616 2672 1614 2675 1612 2677 1610 2679 
1607 2681 1605 2684 1603 2686 1601 2688 1598 2690 1596 2692 1593 2694 1591 2695 1588 2697 1586 2699 1583 2701 1580 2702 1578 2704 1575 2705 1572 2707 
1569 2708 1566 2709 1563 2710 1561 2711 1558 2712 1555 2713 1552 2714 1549 2715 1546 2716 1542 2717 1539 2717 1536 2718 1533 2718 1530 2719 1527 2719 
1523 2719 1520 2719 1517 2719 1513 2719 1510 2719 1507 2719 1504 2719 1501 2718 1497 2718 1494 2717 1491 2717 1488 2716 1485 2715 1482 2714 1479 2713 
1476 2712 1473 2711 1470 2710 1467 2709 1464 2708 1461 2707 1459 2705 1456 2704 1453 2702 1450 2701 1448 2699 1445 2697 1443 2695 1440 2694 1438 2692 
1435 2690 1433 2688 1431 2686 1428 2684 1426 2681 1424 2679 1422 2677 1420 2675 1418 2672 1416 2670 1414 2667 1412 2665 1410 2662 1409 2660 1407 2657 
1405 2654 1404 2652 1402 2649 1401 2646 1400 2643 1398 2640 1397 2637 1396 2634 1395 2632 1394 2629 1393 2625 1392 2622 1391 2619 1391 2616 1390 2613 
1389 2610 1389 2607 1389 2604 1388 2600 1388 2597 1388 2594 1388 2591 1388 2587 1388 2584 1388 2581 1389 2578 1389 2574 1389 2571 1390 2568 1391 2565 
1391 2562 1392 2559 1393 2556 1394 2553 1395 2550 1396 2547 1397 2544 1398 2541 1400 2538 1401 2535 1402 2532 1404 2530 1405 2527 1407 2524 1409 2522 
1410 2519 1412 2516 1414 2514 1416 2512 1418 2509 1420 2507 1422 2504 1424 2502 1426 2500 1428 2498 1431 2496 1433 2494 1435 2492 1438 2490 1440 2488 
1443 2486 1445 2484 1448 2482 1450 2481 1453 2479 1456 2478 1459 2476 1461 2475 1464 2473 1467 2472 1470 2471 1473 2470 1476 2469 1479 2468 1482 2467 
1485 2466 1488 2465 1491 2464 1494 2464 1497 2463 1501 2463 1504 2463 1507 2462 1510 2462 1513 2462 1517 2462 1520 2462 1523 2462 1527 2462 1530 2463 
1533 2463 1536 2463 1539 2464 1542 2464 1546 2465 1549 2466 1552 2467 1555 2468 1558 2469 1561 2470 1563 2471 1566 2472 1569 2473 1572 2475 1575 2476 
1578 2478 1580 2479 1583 2481 1586 2482 1588 2484 1591 2486 1593 2488 1596 2490 1598 2492 1601 2494 1603 2496 1605 2498 1607 2500 1610 2502 1612 2504 
1614 2507 1616 2509 1618 2512 1620 2514 1621 2516 1623 2519 1625 2522 1627 2524 1628 2527 1630 2530 1631 2532 1633 2535 1634 2538 1635 2541 1636 2544 
1637 2547 1639 2550 1640 2553 1640 2556 1641 2559 1642 2562 1643 2565 1643 2568 1644 2571 1644 2574 1645 2578 1645 2581 1645 2584 1645 2587 1645 2591 
240 _pl 1645 2591 1645 2594 1645 2597 1645 2600 1645 2604 1644 2607 1644 2610 1643 2613 1643 2616 1642 2619 1641 2622 1640 2625 1640 2629 1639 2632 1637 2634 
1636 2637 1635 2640 17 _pl _pf 
0 g _cp _s _s _s 1460 2627 _m
_sp 1460 2627 1456 2615 1397 2639 3 _pl _pf _np _s 
_s 255 g _s 1398 2638 _m
_sp 1398 2638 1454 2615 1451 2603 3 _pl _pf 
0 g _cp _s _s _s 1388 2591 _m
_sp 1388 2591 1450 2591 1450 2603 3 _pl _pf _np _s 
_s 255 g _s 1426 2682 _m
_sp 1426 2682 1470 2638 1460 2627 3 _pl _pf 
0 g _cp _s _s _s 1426 2682 _m
_sp 1426 2682 1470 2637 1479 2646 3 _pl _pf _np _s 
_s 255 g _s 1467 2709 _m
_sp 1467 2709 1492 2652 1480 2647 3 _pl _pf 
0 g _cp _s _s _s 1467 2710 _m
_sp 1467 2710 1491 2653 1503 2657 3 _pl _pf _np _s 
_s 255 g _s 1517 2720 _m
_sp 1517 2720 1517 2657 1504 2657 3 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1574 2627 _m
_sp 1574 2627 1578 2615 1636 2639 3 _pl _pf 
0 g _cp _s _s _s 1636 2638 _m
_sp 1636 2638 1579 2615 1583 2603 3 _pl _pf _np _s 
_s 255 g _s 1645 2591 _m
_sp 1645 2591 1583 2591 1583 2603 3 _pl _pf 
0 g _cp _s _s _s 1608 2682 _m
_sp 1608 2682 1564 2638 1573 2627 3 _pl _pf _np _s 
_s 255 g _s 1608 2682 _m
_sp 1608 2682 1564 2637 1554 2646 3 _pl _pf 
0 g _cp _s _s _s 1566 2709 _m
_sp 1566 2709 1542 2652 1554 2647 3 _pl _pf _np _s 
_s 255 g _s 1566 2710 _m
_sp 1566 2710 1542 2653 1531 2657 3 _pl _pf 
0 g _cp _s _s _s 1517 2720 _m
_sp 1517 2720 1517 2657 1530 2657 3 _pl _pf _np _s _s 1574 2555 _m
_sp 1574 2555 1578 2567 1636 2543 3 _pl _pf _np _s 
_s 255 g _s 1636 2543 _m
_sp 1636 2543 1579 2566 1583 2579 3 _pl _pf 
0 g _cp _s _s _s 1645 2591 _m
_sp 1645 2591 1583 2591 1583 2579 3 _pl _pf _np _s 
_s 255 g _s 1608 2500 _m
_sp 1608 2500 1564 2543 1573 2554 3 _pl _pf 
0 g _cp _s _s _s 1608 2500 _m
_sp 1608 2500 1564 2544 1554 2535 3 _pl _pf _np _s 
_s 255 g _s 1566 2472 _m
_sp 1566 2472 1542 2530 1554 2535 3 _pl _pf 
0 g _cp _s _s _s 1566 2472 _m
_sp 1566 2472 1542 2529 1531 2525 3 _pl _pf _np _s 
_s 255 g _s 1517 2462 _m
_sp 1517 2462 1517 2524 1530 2525 3 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1459 2555 _m
_sp 1459 2555 1455 2567 1397 2543 3 _pl _pf 
0 g _cp _s _s _s 1397 2543 _m
_sp 1397 2543 1454 2566 1450 2579 3 _pl _pf _np _s 
_s 255 g _s 1388 2591 _m
_sp 1388 2591 1450 2591 1450 2579 3 _pl _pf 
0 g _cp _s _s _s 1425 2500 _m
_sp 1425 2500 1469 2543 1460 2554 3 _pl _pf _np _s 
_s 255 g _s 1425 2500 _m
_sp 1425 2500 1470 2544 1479 2535 3 _pl _pf 
0 g _cp _s _s _s 1467 2472 _m
_sp 1467 2472 1491 2530 1479 2535 3 _pl _pf _np _s 
_s 255 g _s 1467 2472 _m
_sp 1467 2472 1491 2529 1502 2525 3 _pl _pf 
0 g _cp _s _s _s 1516 2462 _m
_sp 1516 2462 1516 2524 1503 2525 3 _pl _pf _np _s 
_s 255 g _s 1584 2591 _m
_sp 1578 2618 1578 2620 1577 2621 1576 2623 1575 2624 1574 2625 1573 2627 1573 2628 1572 2630 1571 2631 1570 2632 1569 2633 1568 2635 1567 2636 1565 2637 
1564 2638 1563 2639 1562 2641 1561 2642 1559 2643 1558 2644 1557 2645 1556 2646 1554 2647 1553 2647 1552 2648 1550 2649 1549 2650 1547 2651 1546 2652 
1544 2652 1543 2653 1541 2653 1540 2654 1538 2655 1537 2655 1535 2656 1533 2656 1532 2656 1530 2657 1529 2657 1527 2657 1525 2658 1524 2658 1522 2658 
1520 2658 1518 2658 1517 2658 1515 2658 1513 2658 1512 2658 1510 2658 1508 2658 1507 2657 1505 2657 1503 2657 1502 2656 1500 2656 1498 2656 1497 2655 
1495 2655 1494 2654 1492 2653 1491 2653 1489 2652 1488 2652 1486 2651 1485 2650 1483 2649 1482 2648 1481 2647 1479 2647 1478 2646 1477 2645 1475 2644 
1474 2643 1473 2642 1472 2641 1470 2639 1469 2638 1468 2637 1467 2636 1466 2635 1465 2633 1464 2632 1463 2631 1462 2630 1461 2628 1460 2627 1459 2625 
1458 2624 1458 2623 1457 2621 1456 2620 1455 2618 1455 2617 1454 2615 1453 2614 1453 2612 1452 2611 1452 2609 1451 2607 1451 2606 1451 2604 1450 2602 
1450 2601 1450 2599 1450 2598 1449 2596 1449 2594 1449 2592 1449 2591 1449 2589 1449 2587 1449 2586 1450 2584 1450 2582 1450 2580 1450 2579 1451 2577 
1451 2576 1451 2574 1452 2572 1452 2571 1453 2569 1453 2568 1454 2566 1455 2565 1455 2563 1456 2562 1457 2560 1458 2559 1458 2557 1459 2556 1460 2554 
1461 2553 1462 2552 1463 2550 1464 2549 1465 2548 1466 2547 1467 2545 1468 2544 1469 2543 1470 2542 1472 2541 1473 2540 1474 2539 1475 2538 1477 2537 
1478 2536 1479 2535 1481 2534 1482 2533 1483 2532 1485 2531 1486 2531 1488 2530 1489 2529 1491 2528 1492 2528 1494 2527 1495 2527 1497 2526 1498 2526 
1500 2525 1502 2525 1503 2525 1505 2524 1507 2524 1508 2524 1510 2524 1512 2523 1513 2523 1515 2523 1517 2523 1518 2523 1520 2523 1522 2523 1524 2524 
1525 2524 1527 2524 1529 2524 1530 2525 1532 2525 1533 2525 1535 2526 1537 2526 1538 2527 1540 2527 1541 2528 1543 2528 1544 2529 1546 2530 1547 2531 
1549 2531 1550 2532 1552 2533 1553 2534 1554 2535 1556 2536 1557 2537 1558 2538 1559 2539 1561 2540 1562 2541 1563 2542 1564 2543 1565 2544 1567 2545 
1568 2547 1569 2548 1570 2549 1571 2550 1572 2552 1573 2553 1573 2554 1574 2556 1575 2557 1576 2559 1577 2560 1578 2562 1578 2563 1579 2565 1580 2566 
1580 2568 1581 2569 1581 2571 1582 2572 1582 2574 1582 2576 1583 2577 1583 2579 1583 2580 1584 2582 1584 2584 1584 2586 1584 2587 1584 2589 1584 2591 
240 _pl 1584 2591 1584 2592 1584 2594 1584 2596 1584 2598 1584 2599 1583 2601 1583 2602 1583 2604 1582 2606 1582 2607 1582 2609 1581 2611 1581 2612 1580 2614 
1580 2615 1579 2617 17 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1575 2591 _m
_sp 1575 2591 1575 2594 1575 2597 1575 2599 1574 2602 1573 2605 1573 2608 1572 2610 1571 2613 1570 2615 1568 2618 1567 2620 1565 2623 1564 2625 1562 2627 
1560 2629 1558 2631 1556 2633 1554 2635 1552 2637 1550 2638 1547 2640 1545 2641 1542 2643 1540 2644 1537 2645 1535 2646 1532 2647 1529 2647 1526 2648 
1524 2648 1520 2648 1518 2648 1515 2648 1512 2648 1509 2648 1506 2647 1503 2647 1501 2646 1498 2645 1495 2644 1493 2643 1490 2641 1488 2640 1485 2638 
1483 2637 1481 2635 1479 2633 1477 2631 1475 2629 1473 2627 1472 2625 1470 2623 1468 2620 1467 2618 1466 2615 1464 2613 1463 2610 1463 2608 1462 2605 
1461 2602 1461 2599 1460 2597 1460 2594 1460 2591 1460 2588 1460 2585 1461 2582 1461 2579 1462 2576 1463 2574 1463 2571 1464 2568 1466 2566 1467 2563 
1468 2561 1470 2559 1472 2556 1473 2554 1475 2552 1477 2550 1479 2548 1481 2546 1483 2545 1485 2543 1488 2541 1490 2540 1493 2539 1495 2537 1498 2536 
1501 2536 1503 2535 1506 2534 1509 2534 1512 2533 1515 2533 1518 2533 1520 2533 1524 2533 1526 2534 1529 2534 1532 2535 1535 2536 1537 2536 1540 2537 
1542 2539 1545 2540 1547 2541 1550 2543 1552 2545 1554 2546 1556 2548 1558 2550 1560 2552 1562 2554 1564 2556 1565 2559 1567 2561 1568 2563 1570 2566 
1571 2568 1572 2571 1573 2574 1573 2576 1574 2579 1575 2582 1575 2585 1575 2588 1575 2591 129 _pl _pf 
0 g _cp _s 1584 2591 _m
1449 2591 _l 1469 2638 _m
1564 2543 _l 1491 2654 _m
1542 2529 _l 1579 2566 _m
1454 2615 _l 1517 2659 _m
1517 2523 _l 1543 2654 _m
1491 2529 _l 1449 2591 _m
1584 2591 _l 1469 2543 _m
1564 2638 _l 1579 2615 _m
1454 2566 _l _s 
_s 255 g _s 1545 2591 _m
_sp 1545 2591 1545 2592 1544 2593 1544 2595 1544 2596 1544 2597 1543 2599 1543 2600 1542 2601 1542 2602 1541 2603 1541 2604 1540 2606 1539 2607 1538 2608 
1537 2609 1537 2610 1536 2611 1535 2611 1534 2612 1533 2613 1531 2614 1530 2614 1529 2615 1528 2615 1527 2616 1526 2616 1524 2617 1523 2617 1522 2617 
1520 2618 1519 2618 1518 2618 1516 2618 1515 2618 1514 2617 1512 2617 1511 2617 1510 2616 1508 2616 1507 2615 1506 2615 1505 2614 1504 2614 1503 2613 
1502 2612 1501 2611 1500 2611 1499 2610 1498 2609 1497 2608 1496 2607 1495 2606 1495 2604 1494 2603 1493 2602 1493 2601 1492 2600 1492 2599 1492 2597 
1491 2596 1491 2595 1491 2593 1491 2592 1491 2591 1491 2589 1491 2588 1491 2587 1491 2585 1492 2584 1492 2583 1492 2581 1493 2580 1493 2579 1494 2578 
1495 2577 1495 2576 1496 2575 1497 2574 1498 2573 1499 2572 1500 2571 1501 2570 1502 2569 1503 2568 1504 2568 1505 2567 1506 2566 1507 2566 1508 2565 
1510 2565 1511 2565 1512 2564 1514 2564 1515 2564 1516 2564 1518 2564 1519 2564 1520 2564 1522 2564 1523 2564 1524 2565 1526 2565 1527 2565 1528 2566 
1529 2566 1530 2567 1531 2568 1533 2568 1534 2569 1535 2570 1536 2571 1537 2572 1537 2573 1538 2574 1539 2575 1540 2576 1541 2577 1541 2578 1542 2579 
1542 2580 1543 2581 1543 2583 1544 2584 1544 2585 1544 2587 1544 2588 1545 2589 1545 2591 129 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1538 2591 _m
_sp 1538 2591 1538 2592 1538 2593 1538 2594 1537 2595 1537 2596 1537 2597 1537 2598 1536 2598 1536 2599 1535 2600 1535 2601 1534 2602 1534 2603 1533 2603 
1532 2604 1532 2605 1531 2606 1530 2606 1530 2607 1529 2607 1528 2608 1527 2608 1526 2609 1525 2609 1525 2610 1524 2610 1523 2610 1522 2610 1521 2611 
1520 2611 1519 2611 1518 2611 1517 2611 1516 2611 1515 2611 1514 2610 1513 2610 1512 2610 1511 2610 1510 2609 1509 2609 1508 2608 1507 2608 1506 2607 
1506 2607 1505 2606 1504 2606 1503 2605 1503 2604 1502 2603 1502 2603 1501 2602 1500 2601 1500 2600 1499 2599 1499 2598 1499 2598 1498 2597 1498 2596 
1498 2595 1498 2594 1497 2593 1497 2592 1497 2591 1497 2590 1497 2589 1498 2588 1498 2587 1498 2586 1498 2585 1499 2584 1499 2583 1499 2582 1500 2581 
1500 2580 1501 2579 1502 2579 1502 2578 1503 2577 1503 2576 1504 2576 1505 2575 1506 2575 1506 2574 1507 2573 1508 2573 1509 2572 1510 2572 1511 2572 
1512 2571 1513 2571 1514 2571 1515 2571 1516 2570 1517 2570 1518 2570 1519 2570 1520 2570 1521 2571 1522 2571 1523 2571 1524 2571 1525 2572 1525 2572 
1526 2572 1527 2573 1528 2573 1529 2574 1530 2575 1530 2575 1531 2576 1532 2576 1532 2577 1533 2578 1534 2579 1534 2579 1535 2580 1535 2581 1536 2582 
1536 2583 1537 2584 1537 2585 1537 2586 1537 2587 1538 2588 1538 2589 1538 2590 1538 2591 129 _pl _pf 
0 g _cp _s _s _s 1517 2790 _m
_sp 1517 2790 1517 2731 1522 2731 1523 2748 1529 2770 5 _pl _pf _np _s 
_s 255 g _s 1517 2790 _m
_sp 1517 2790 1517 2731 1511 2731 1510 2748 1505 2770 5 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1512 2731 _m
_sp 1512 2731 1510 2740 1509 2744 1508 2746 1507 2749 1507 2750 1505 2751 1504 2752 1502 2750 1501 2749 1499 2749 1497 2749 1495 2751 1495 2753 1495 2755 
1496 2756 1498 2757 1500 2758 1503 2758 1504 2757 1506 2756 1507 2754 1508 2753 1510 2750 1511 2748 1512 2744 1512 2741 27 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1521 2731 _m
_sp 1521 2731 1523 2740 1524 2744 1525 2746 1526 2749 1527 2750 1528 2751 1530 2752 1531 2750 1532 2749 1535 2749 1537 2749 1538 2751 1539 2753 1538 2755 
1538 2756 1536 2757 1534 2758 1531 2758 1529 2757 1528 2756 1526 2754 1525 2753 1524 2750 1523 2748 1522 2744 1522 2741 27 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1524 2736 _m
_sp 1524 2736 1524 2737 1524 2737 1524 2738 1523 2738 1523 2738 1522 2738 1522 2738 1521 2739 1520 2738 1520 2738 1519 2738 1519 2738 1519 2738 1518 2737 
1518 2737 1518 2736 1518 2736 1518 2736 1519 2735 1519 2735 1519 2735 1520 2735 1520 2734 1521 2734 1522 2734 1522 2735 1523 2735 1523 2735 1524 2735 
1524 2736 1524 2736 1524 2736 33 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1526 2733 _m
_sp 1526 2733 1526 2733 1526 2733 1525 2734 1525 2734 1524 2734 1524 2735 1523 2735 1523 2735 1522 2735 1521 2735 1521 2734 1520 2734 1520 2734 1519 2733 
1519 2733 1519 2733 1519 2732 1519 2732 1520 2731 1520 2731 1521 2731 1521 2730 1522 2730 1523 2730 1523 2730 1524 2730 1524 2731 1525 2731 1525 2731 
1526 2732 1526 2732 1526 2733 33 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1515 2736 _m
_sp 1515 2736 1515 2737 1515 2737 1515 2738 1514 2738 1514 2738 1513 2738 1513 2738 1512 2739 1512 2738 1511 2738 1511 2738 1510 2738 1510 2738 1509 2737 
1509 2737 1509 2736 1509 2736 1509 2736 1510 2735 1510 2735 1511 2735 1511 2735 1512 2734 1512 2734 1513 2734 1513 2735 1514 2735 1514 2735 1515 2735 
1515 2736 1515 2736 1515 2736 33 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1514 2733 _m
_sp 1514 2733 1514 2733 1514 2733 1514 2734 1513 2734 1513 2734 1512 2735 1511 2735 1511 2735 1510 2735 1509 2735 1509 2734 1508 2734 1508 2734 1508 2733 
1507 2733 1507 2733 1507 2732 1508 2732 1508 2731 1508 2731 1509 2731 1509 2730 1510 2730 1511 2730 1511 2730 1512 2730 1513 2731 1513 2731 1514 2731 
1514 2732 1514 2732 1514 2733 33 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1521 2733 _m
_sp 1521 2733 1521 2733 1521 2734 1521 2734 1520 2734 1520 2735 1520 2735 1520 2735 1520 2735 1519 2736 1518 2736 1517 2736 1516 2736 1516 2736 1515 2736 
1514 2736 1513 2735 1513 2735 1513 2735 1513 2735 1513 2734 1512 2734 1512 2734 1512 2733 1512 2733 1512 2733 1512 2733 1512 2732 1513 2732 1513 2732 
1513 2732 1513 2731 1513 2731 1514 2731 1515 2731 1516 2730 1516 2730 1517 2730 1518 2731 1519 2731 1520 2731 1520 2731 1520 2732 1520 2732 1520 2732 
1521 2732 1521 2733 1521 2733 1521 2733 49 _pl _pf 
0 g _cp _s _s _s 1677 2603 _m
_sp 1677 2603 1698 2603 1698 2596 1697 2598 1696 2600 1694 2601 1693 2601 1691 2602 1690 2602 1688 2602 1687 2602 1687 2601 1686 2601 1686 2592 1689 2592 
1690 2593 1691 2594 1692 2595 1692 2597 1692 2585 1692 2587 1691 2589 1690 2590 1689 2590 1686 2590 1686 2582 1687 2581 1687 2580 1688 2580 1690 2580 
1692 2580 1694 2581 1695 2581 1696 2582 1697 2583 1698 2584 1700 2586 1698 2579 1677 2579 1678 2579 1679 2580 1680 2581 1680 2582 1680 2600 1680 2601 
1680 2602 1679 2602 47 _pl _pf _np _s _s 1524 2425 _m
_sp 1524 2425 1524 2417 1523 2419 1522 2420 1521 2422 1519 2423 1517 2423 1516 2423 1514 2423 1513 2422 1512 2421 1512 2419 1513 2418 1514 2417 1521 2413 
1522 2412 1523 2411 1524 2410 1525 2409 1525 2407 1525 2406 1524 2404 1524 2403 1523 2402 1521 2400 1520 2400 1518 2400 1516 2399 1514 2400 1512 2400 
1510 2401 1510 2401 1509 2401 1509 2401 1508 2399 1508 2408 1509 2405 1510 2404 1511 2403 1513 2402 1514 2401 1516 2401 1517 2401 1518 2401 1520 2402 
1521 2403 1521 2405 1520 2406 1520 2407 1518 2408 1512 2411 1511 2412 1509 2414 1509 2415 1508 2417 1508 2418 1509 2420 1509 2421 1510 2422 1511 2424 
1513 2424 1515 2425 1517 2425 1519 2424 1522 2423 1523 2423 1523 2423 67 _pl _pf _np _s _s 1321 2603 _m
_sp 1321 2603 1331 2603 1330 2602 1329 2602 1329 2601 1329 2600 1333 2586 1338 2597 1336 2600 1335 2601 1335 2602 1334 2603 1333 2603 1345 2603 1344 2602 
1343 2602 1343 2601 1343 2600 1347 2586 1351 2600 1351 2601 1351 2602 1350 2602 1348 2603 1355 2603 1354 2602 1353 2602 1353 2600 1345 2577 1338 2596 
1331 2577 1322 2601 1322 2602 33 _pl _pf _np _s _s 1505 2817 _m
_sp 1505 2817 1512 2817 1525 2802 1525 2814 1525 2815 1524 2816 1523 2817 1521 2817 1530 2817 1528 2817 1527 2816 1527 2815 1526 2814 1526 2792 1509 2812 
1509 2796 1510 2795 1511 2794 1512 2793 1513 2793 1505 2793 1506 2793 1507 2794 1508 2795 1508 2796 1508 2814 1508 2815 1507 2816 1506 2817 29 _pl _pf _np _s 
0 g 806 2226 _m
_sp 806 2226 805 2226 796 2223 796 2221 797 2221 800 2221 800 2217 800 2188 800 2186 800 2184 799 2183 797 2183 796 2183 796 2182 811 2182 
811 2183 810 2183 808 2183 807 2184 806 2186 806 2188 21 _pl _cp 
0 g _f _s _s 
0 g 813 2196 _m
_sp 813 2196 814 2191 816 2187 819 2184 823 2182 828 2181 832 2182 836 2184 839 2187 841 2192 842 2197 841 2201 839 2205 836 2208 832 2210 
828 2211 823 2210 819 2208 816 2205 814 2201 20 _pl _cp 819 2198 _m
_sp 819 2198 820 2193 821 2189 823 2186 825 2184 828 2184 831 2185 834 2187 835 2190 836 2195 836 2199 834 2203 832 2206 830 2208 827 2209 
824 2208 821 2206 820 2203 819 2199 819 2198 20 _pl _cp 
0 g _f _s _s 
0 g 869 2192 _m
_sp 869 2192 867 2189 865 2188 863 2186 860 2186 856 2187 853 2189 851 2193 850 2198 851 2202 853 2206 855 2208 859 2209 861 2208 862 2205 
864 2203 866 2202 868 2203 869 2204 868 2207 866 2209 863 2210 859 2211 854 2210 851 2208 848 2205 846 2201 845 2196 846 2191 847 2187 
850 2184 854 2182 858 2181 860 2181 862 2182 864 2184 866 2185 867 2186 868 2187 869 2189 870 2191 41 _pl _cp 
0 g _f _s _s 
0 g 889 2200 _m
_sp 889 2200 885 2199 882 2198 879 2197 878 2195 876 2194 875 2193 874 2191 873 2190 873 2188 874 2185 875 2183 877 2182 880 2181 882 2181 
884 2182 886 2184 889 2186 889 2184 890 2182 891 2181 893 2181 895 2181 896 2182 898 2183 899 2184 899 2186 897 2185 896 2184 895 2185 
894 2188 894 2201 894 2202 894 2203 894 2205 894 2206 893 2208 891 2210 888 2211 885 2211 881 2210 877 2209 875 2207 874 2204 875 2202 
877 2201 879 2202 880 2204 880 2204 880 2204 880 2206 880 2206 880 2206 881 2208 884 2209 886 2209 888 2207 889 2205 889 2202 59 _pl _cp 889 2198 _m
_sp 889 2198 885 2197 882 2195 881 2194 879 2192 879 2190 879 2188 880 2186 882 2185 883 2185 885 2185 886 2186 888 2187 889 2188 14 _pl _cp 
0 g _f _s _s 
0 g 911 2226 _m
_sp 911 2226 910 2226 901 2223 901 2221 902 2221 905 2221 906 2217 906 2188 906 2186 905 2184 904 2183 902 2183 901 2183 901 2182 916 2182 
916 2183 915 2183 913 2183 912 2184 911 2186 911 2188 21 _pl _cp 
0 g _f _s _s 
0 g 1003 2196 _m
_sp 1003 2196 1004 2191 1006 2187 1009 2184 1012 2182 1017 2181 1022 2182 1026 2184 1029 2187 1031 2192 1032 2197 1031 2201 1029 2205 1026 2208 1022 2210 
1018 2211 1013 2210 1009 2208 1006 2205 1004 2201 20 _pl _cp 1009 2198 _m
_sp 1009 2198 1009 2193 1011 2189 1013 2186 1015 2184 1018 2184 1021 2185 1024 2187 1025 2190 1026 2195 1025 2199 1024 2203 1022 2206 1020 2208 1017 2209 
1014 2208 1011 2206 1010 2203 1009 2199 1009 2198 20 _pl _cp 
0 g _f _s _s 
0 g 1044 2212 _m
_sp 1044 2212 1043 2212 1033 2208 1033 2207 1034 2207 1036 2207 1037 2206 1038 2204 1038 2202 1038 2188 1038 2186 1037 2184 1036 2183 1034 2183 1033 2183 
1033 2182 1049 2182 1049 2183 1047 2183 1045 2183 1044 2184 1044 2186 1044 2188 1044 2202 1045 2204 1046 2206 1046 2207 1047 2207 1048 2207 1049 2206 
1051 2205 1052 2204 1053 2205 1054 2207 1053 2210 1050 2211 1049 2211 1047 2210 1046 2208 1044 2206 40 _pl _cp 
0 g _f _s _s 
0 g 1066 2212 _m
_sp 1066 2212 1065 2212 1056 2208 1056 2207 1057 2207 1059 2207 1060 2206 1060 2204 1060 2202 1060 2188 1060 2186 1060 2184 1059 2183 1057 2183 1056 2183 
1056 2182 1071 2182 1071 2183 1070 2183 1068 2183 1067 2184 1066 2186 1066 2188 23 _pl _cp 1059 2222 _m
_sp 1059 2222 1060 2219 1063 2218 1065 2219 1066 2222 1065 2225 1063 2226 1060 2225 8 _pl _cp 
0 g _f _s _s 
0 g 1080 2182 _m
_sp 1080 2182 1077 2179 1074 2177 1074 2175 1075 2172 1077 2170 1080 2169 1084 2168 1088 2168 1091 2169 1094 2170 1097 2172 1099 2174 1101 2176 1101 2179 
1100 2182 1099 2184 1096 2185 1093 2186 1087 2186 1084 2186 1082 2187 1081 2187 1081 2188 1082 2190 1084 2192 1086 2191 1088 2191 1092 2192 1095 2194 
1097 2197 1098 2201 1098 2203 1097 2206 1102 2206 1102 2209 1097 2209 1096 2209 1094 2210 1094 2210 1093 2210 1092 2211 1090 2211 1089 2211 1087 2211 
1083 2210 1079 2208 1077 2205 1076 2201 1076 2198 1078 2196 1079 2194 1082 2192 1081 2192 1081 2191 1079 2189 1078 2188 1077 2186 1077 2185 1077 2184 
60 _pl _cp 1081 2182 _m
_sp 1081 2182 1080 2180 1079 2179 1078 2177 1078 2176 1079 2174 1081 2173 1084 2172 1088 2172 1092 2172 1096 2174 1098 2175 1099 2178 1098 2180 1095 2181 
1086 2181 1085 2181 1083 2181 1082 2181 19 _pl _cp 1082 2203 _m
_sp 1082 2203 1082 2199 1084 2196 1085 2194 1088 2193 1090 2193 1092 2195 1093 2196 1093 2199 1092 2203 1091 2206 1089 2208 1086 2209 1084 2209 1083 2208 
1082 2206 1082 2203 1082 2203 18 _pl _cp 
0 g _f _s _s 
0 g 1115 2212 _m
_sp 1115 2212 1114 2212 1105 2208 1105 2207 1106 2207 1108 2207 1109 2206 1110 2204 1110 2202 1110 2188 1110 2186 1109 2184 1108 2183 1106 2183 1105 2183 
1105 2182 1120 2182 1120 2183 1119 2183 1117 2183 1116 2184 1115 2186 1115 2188 23 _pl _cp 1109 2222 _m
_sp 1109 2222 1110 2219 1112 2218 1115 2219 1116 2222 1115 2225 1112 2226 1110 2225 8 _pl _cp 
0 g _f _s _s 
0 g 1131 2212 _m
_sp 1131 2212 1131 2212 1121 2208 1121 2207 1122 2207 1124 2207 1125 2206 1126 2204 1126 2202 1126 2188 1126 2186 1125 2184 1124 2183 1122 2183 1121 2183 
1121 2182 1136 2182 1136 2183 1135 2183 1133 2183 1132 2184 1131 2186 1131 2188 1131 2203 1133 2205 1135 2207 1136 2208 1138 2208 1140 2208 1142 2206 
1143 2203 1143 2199 1143 2188 1143 2186 1142 2184 1141 2183 1139 2183 1138 2183 1138 2182 1153 2182 1153 2183 1152 2183 1150 2183 1149 2184 1148 2186 
1148 2188 1148 2202 1147 2206 1146 2209 1143 2210 1140 2211 1138 2211 1136 2210 1134 2208 1131 2206 55 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 3519 6778 _m
/Times-BoldR 600 _ff
(Figure)_S 67 _t
(6.1)_S /Times-RomanR 600 _ff
(.)_S 134 _t
(World)_S 67 _t
(coordinate)_S 67 _t
(system.)_S 1500 5911 _m
(volumetric)_S 67 _t
(displacement)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(submerged)_S 67 _t
(vehicle.)_S 134 _t
(A)_S 67 _t
(related)_S 67 _t
(location)_S 67 _t
(is)_S 67 _t
(the)_S 1500 5560 _m
/Times-ItalicR 600 _ff
(center)_S 67 _t
(of)_S 67 _t
(gravity)_S /Times-RomanR 600 _ff
67 _t
(\()_S /Times-BoldItalicR 600 _ff
(CG)_S /Times-RomanR 600 _ff
(\),)_S 67 _t
(which)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(first)_S 67 _t
(moment)_S 67 _t
(centroid)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(mass.)_S 134 _t
(Ordinarily)_S 1500 5210 _m
(the)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(gravity)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(rigid)_S 67 _t
(body)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(point)_S 67 _t
(at)_S 67 _t
(which)_S 67 _t
(net)_S 67 _t
(forces)_S 67 _t
(and)_S 67 _t
(moments)_S 67 _t
(are)_S 1500 4861 _m
(assumed)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(applied.)_S 134 _t
(The)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(gravity)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(ship)_S 67 _t
(or)_S 67 _t
(submarine)_S 67 _t
(is)_S 67 _t
(always)_S 1500 4512 _m
(designed)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(below)_S 67 _t
(the)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(buoyancy)_S 67 _t
(to)_S 67 _t
(ensure)_S 67 _t
(static)_S 67 _t
(vehicle)_S 67 _t
(stability.)_S 134 _t
(The)_S 1500 4162 _m
(torque)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(any)_S 67 _t
(vertical)_S 67 _t
(difference)_S 67 _t
(between)_S 67 _t
(the)_S 67 _t
(two)_S 67 _t
(centers)_S 67 _t
/Times-BoldItalicR 600 _ff
(CB)_S /Times-RomanR 600 _ff
67 _t
(and)_S 67 _t
/Times-BoldItalicR 600 _ff
(CG)_S /Times-RomanR 600 _ff
67 _t
(is)_S 67 _t
(called)_S 67 _t
(the)_S 1500 3810 _m
/Times-ItalicR 600 _ff
(righting)_S 67 _t
(moment)_S /Times-RomanR 600 _ff
(.)_S 134 _t
(A)_S 67 _t
(nonzero)_S 67 _t
(righting)_S 67 _t
(moment)_S 67 _t
(results)_S 67 _t
(when)_S 67 _t
(the)_S 67 _t
(centers)_S 67 _t
(of)_S 67 _t
(buoyancy)_S 1500 3460 _m
(and)_S 67 _t
(gravity)_S 67 _t
(are)_S 67 _t
(not)_S 67 _t
(aligned)_S 67 _t
(vertically,)_S 67 _t
(tending)_S 67 _t
(to)_S 67 _t
(bring)_S 67 _t
(the)_S 67 _t
(submerged)_S 67 _t
(vehicle)_S 67 _t
(back)_S 67 _t
(to)_S 67 _t
(a)_S 1500 3111 _m
(neutral)_S 67 _t
(\(typically)_S 67 _t
(level\))_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(roll)_S 67 _t
(posture.)_S 134 _t
(Any)_S 67 _t
(submerged)_S 67 _t
(vehicle)_S 67 _t
(that)_S 67 _t
(instead)_S 1500 2762 _m
(has)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(gravity)_S 67 _t
(above)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(buoyancy)_S 67 _t
(is)_S 67 _t
(inherently)_S 67 _t
(unstable)_S 67 _t
(and)_S 67 _t
(will)_S 67 _t
(tend)_S 67 _t
(to)_S 1500 2413 _m
(invert,)_S 67 _t
(even)_S 67 _t
(under)_S 67 _t
(static)_S 67 _t
(conditions.)_S 4950 1288 _m
(101)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1980 11855 _m
(Underwater)_S 67 _t
(vehicles)_S 67 _t
(often)_S 67 _t
(include)_S 67 _t
(free-flood)_S 67 _t
(spaces)_S 67 _t
(which)_S 67 _t
(can)_S 67 _t
(equalize)_S 67 _t
(with)_S 1500 11506 _m
(ocean)_S 67 _t
(pressure)_S 67 _t
(through)_S 67 _t
(small)_S 67 _t
(openings,)_S 67 _t
(all)_S 67 _t
(while)_S 67 _t
(remaining)_S 67 _t
(essentially)_S 67 _t
(contained)_S 67 _t
(by)_S 1500 11157 _m
(the)_S 67 _t
(hull.)_S 134 _t
(The)_S 67 _t
(water)_S 67 _t
(enclosed)_S 67 _t
(in)_S 67 _t
(these)_S 67 _t
(free-flood)_S 67 _t
(spaces)_S 67 _t
(directly)_S 67 _t
(contributes)_S 67 _t
(both)_S 67 _t
(to)_S 1500 10808 _m
(volumetric)_S 67 _t
(displacement)_S 67 _t
(and)_S 67 _t
(vehicle)_S 67 _t
(mass.)_S 134 _t
(Thus)_S 67 _t
(free-flood)_S 67 _t
(spaces)_S 67 _t
(affect)_S 67 _t
(buoyancy,)_S 1500 10459 _m
(mass,)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(buoyancy,)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(mass)_S 67 _t
(and)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(response.)_S 134 _t
(While)_S 1500 10110 _m
(submerged)_S 67 _t
(these)_S 67 _t
(effects)_S 67 _t
(are)_S 67 _t
(ordinarily)_S 67 _t
(static)_S 67 _t
(and)_S 67 _t
(not)_S 67 _t
(time-varying.)_S 1980 9761 _m
(Interactions)_S 67 _t
(between)_S 67 _t
(a)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(the)_S 67 _t
(ocean)_S 67 _t
(environment)_S 67 _t
(are)_S 67 _t
(defined)_S 67 _t
(from)_S 67 _t
(the)_S 1500 9412 _m
(perspective)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(vehicle,)_S 67 _t
(i.e.)_S 67 _t
(within)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(system.)_S 134 _t
(This)_S 67 _t
(is)_S 67 _t
(because)_S 67 _t
(all)_S 1500 9063 _m
(actions)_S 67 _t
(and)_S 67 _t
(reactions)_S 67 _t
(between)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(environment)_S 67 _t
(are)_S 67 _t
(dependent)_S 67 _t
(on)_S 67 _t
(the)_S 1500 8714 _m
(orientation,)_S 67 _t
(shape,)_S 67 _t
(velocity)_S 67 _t
(and)_S 67 _t
(acceleration)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(body,)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(sole)_S 1500 8365 _m
(exceptions)_S 67 _t
(of)_S 67 _t
(gravity)_S 67 _t
(and)_S 67 _t
(ocean)_S 67 _t
(current.)_S 134 _t
(The)_S 67 _t
(direction)_S 67 _t
(of)_S 67 _t
(gravity)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(sensed)_S 67 _t
(or)_S 1500 8016 _m
(estimated)_S 67 _t
(and)_S 67 _t
(is)_S 67 _t
(thus)_S 67 _t
(directly)_S 67 _t
(usable)_S 67 _t
(within)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(of)_S 67 _t
(reference.)_S 67 _t
1500 7667 _m
(Ocean)_S 67 _t
(current)_S 67 _t
(is)_S 67 _t
(reasonably)_S 67 _t
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(the)_S 67 _t
(entire)_S 67 _t
(vehicle)_S 67 _t
(body.)_S 67 _t
1500 7318 _m
(Therefore)_S 67 _t
(all)_S 67 _t
(vehicle-environment)_S 67 _t
(interactions)_S 67 _t
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(Wind)_S 67 _t
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(zero)_S 67 _t
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(an)_S 67 _t
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(model)_S 67 _t
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(coordinates)_S 67 _t
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(kinematics)_S 67 _t
(equations)_S 67 _t
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(system)_S 67 _t
(diagram)_S 67 _t
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(coordinate)_S 67 _t
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(in)_S 67 _t
(Figure)_S 67 _t
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(The)_S 67 _t
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(coordinate)_S 67 _t
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(Euler)_S 67 _t
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(that)_S 67 _t
(these)_S 67 _t
(rotations)_S 67 _t
(be)_S 67 _t
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(order.)_S 67 _t
1500 11151 _m
(Robotics)_S 67 _t
(conventions)_S 67 _t
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(specify)_S 67 _t
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(Results)_S 67 _t
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(Figure)_S 67 _t
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(world)_S 67 _t
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(temporal)_S 67 _t
(order)_S 67 _t
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1500 7653 _m
(Consistency)_S 67 _t
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(converting)_S 67 _t
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1980 6257 _m
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(angle)_S 67 _t
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(103)_S _ep
_bp /Times-RomanR 600 _ff
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_s [] 0 _d 2 _lc 0 g _s 375 2066 _m
_sp 2174 2066 2174 2069 375 2069 3 _pl _pf _np _s _s 2171 2066 _m
_sp 2174 2066 2174 2999 2171 2999 3 _pl _pf _np _s _s 375 2996 _m
_sp 2174 2996 2174 2999 375 2999 3 _pl _pf _np _s _s 375 2066 _m
_sp 378 2066 378 2999 375 2999 3 _pl _pf _np 
_s 0 g 865 1731 409 2100 _cw 

_s 0 g 511 2476 _m
786 2613 _l 786 2613 _m
837 2578 _l 837 2578 _m
563 2442 _l 563 2442 _m
511 2476 _l 563 2441 _m
563 2389 _l 563 2389 _m
838 2526 _l 838 2526 _m
838 2577 _l 512 2474 _m
442 2411 _l 442 2411 _m
476 2388 _l 476 2388 _m
563 2440 _l 563 2440 _m
563 2388 _l 563 2388 _m
476 2388 _l 837 2523 _m
904 2593 _l 904 2593 _m
901 2615 _l 901 2615 _m
880 2619 _l 880 2619 _m
873 2622 _l 873 2622 _m
826 2619 _l 826 2619 _m
823 2615 _l 823 2615 _m
791 2611 _l 791 2611 _m
784 2611 _l 833 2576 _m
851 2579 _l 851 2579 _m
901 2608 _l 901 2608 _m
887 2619 _l 887 2619 _m
869 2619 _l 869 2619 _m
869 2619 _l _s _s 443 2410 _m
_sp 443 2410 443 2406 439 2410 436 2431 446 2434 450 2420 6 _pl _pf _np _s _s 443 2410 _m
_sp 443 2410 443 2410 446 2410 439 2406 436 2392 439 2384 446 2381 450 2399 8 _pl _pf _np _s _s 471 2388 _m
_sp 471 2388 471 2388 475 2388 467 2392 464 2406 467 2413 475 2417 478 2399 8 _pl _pf _np _s _s 475 2388 _m
_sp 475 2388 471 2388 471 2388 467 2367 478 2364 482 2377 6 _pl _pf _np _s _s 683 2345 _m
_sp 691 2367 683 2362 676 2367 3 _pl _pf _np 683 2447 _m
683 2362 _l _s _s 804 2418 _m
_sp 789 2437 789 2428 781 2425 3 _pl _pf _np 708 2484 _m
789 2428 _l _s _s 977 2646 _m
_sp 953 2644 961 2639 959 2630 3 _pl _pf _np 907 2612 _m
961 2639 _l _s 
_s 255 g _s 1887 2644 _m
_sp 1887 2644 1888 2646 1889 2647 1890 2649 1890 2651 1890 2653 1890 2655 1890 2657 1889 2659 1888 2661 1887 2663 1886 2666 1885 2667 1883 2670 1881 2672 
1879 2673 1877 2675 1875 2676 1873 2678 1870 2679 1868 2680 1866 2681 1864 2682 1861 2682 1859 2682 1857 2682 1855 2682 1853 2682 1851 2681 1849 2680 
1848 2680 1846 2678 1845 2677 1844 2675 1843 2673 1843 2672 1842 2670 1842 2668 1843 2666 1843 2664 1843 2662 1844 2660 1845 2657 1846 2655 1847 2653 
1849 2651 1850 2649 1853 2647 1855 2646 1857 2645 1859 2643 1861 2642 1864 2641 1866 2640 1868 2639 1870 2639 1873 2639 1875 2639 1877 2639 1879 2639 
1881 2640 1883 2641 1884 2641 1885 2643 1887 2644 65 _pl _pf 
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_sp 1866 2646 1853 2648 1861 2636 3 _pl _pf _np _s 
_s 255 g _s 1842 2664 _m
_sp 1842 2664 1839 2651 1849 2649 1852 2662 4 _pl _pf _np _s 
_s 0 g _s 1870 2660 _m
_sp 1870 2660 1869 2661 1869 2661 1869 2662 1869 2662 1868 2663 1867 2663 1866 2663 1866 2663 1865 2663 1864 2663 1864 2663 1864 2662 1863 2662 1863 2661 
1863 2661 1863 2660 1863 2659 1863 2659 1863 2658 1864 2657 1864 2657 1864 2656 1865 2656 1866 2656 1866 2656 1867 2656 1868 2657 1869 2657 1869 2658 
1869 2659 1869 2659 1870 2660 33 _pl _pf _np 1368 2471 _m
1642 2608 _l 1642 2608 _m
1694 2574 _l 1694 2574 _m
1419 2437 _l 1419 2437 _m
1368 2471 _l 1420 2436 _m
1420 2384 _l 1420 2384 _m
1695 2521 _l 1695 2521 _m
1695 2573 _l 1368 2470 _m
1299 2406 _l 1299 2406 _m
1333 2384 _l 1333 2384 _m
1420 2436 _l 1420 2436 _m
1420 2384 _l 1420 2384 _m
1333 2384 _l 1692 2519 _m
1711 2533 _l 1711 2533 _m
1728 2548 _l 1728 2548 _m
1753 2576 _l 1753 2576 _m
1756 2583 _l 1756 2583 _m
1764 2593 _l 1764 2593 _m
1760 2608 _l 1760 2608 _m
1749 2611 _l 1749 2611 _m
1742 2615 _l 1742 2615 _m
1668 2611 _l 1668 2611 _m
1654 2608 _l 1654 2608 _m
1646 2608 _l 1646 2608 _m
1639 2604 _l 1692 2569 _m
1703 2576 _l 1703 2576 _m
1718 2579 _l 1718 2579 _m
1756 2604 _l 1756 2604 _m
1742 2615 _l 1742 2615 _m
1725 2615 _l 1725 2615 _m
1725 2615 _l _s _s 1298 2402 _m
_sp 1298 2402 1295 2399 1298 2395 1291 2406 1288 2424 1291 2431 1302 2434 1305 2413 8 _pl _pf _np _s _s 1298 2399 _m
_sp 1298 2399 1298 2402 1302 2402 1295 2399 1291 2371 1302 2367 1305 2395 7 _pl _pf _np _s _s 1327 2381 _m
_sp 1327 2381 1327 2381 1327 2377 1323 2384 1320 2388 1316 2402 1320 2410 1323 2417 1334 2410 1337 2395 10 _pl _pf _np _s _s 1327 2381 _m
_sp 1327 2381 1327 2381 1327 2381 1323 2349 1330 2346 1334 2377 6 _pl _pf _np 1566 2477 _m
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1659 2413 _l 1539 2443 _m
1539 2339 _l 1539 2339 _m
1539 2339 _l 1833 2641 _m
1762 2606 _l _s 
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1534 2302 1537 2302 1541 2302 1545 2303 1548 2303 1551 2303 1554 2304 1557 2304 1560 2305 1562 2305 1565 2306 1567 2307 1569 2308 1570 2309 1571 2309 
1572 2310 1573 2311 1573 2312 1573 2313 1572 2314 1571 2315 1570 2316 1569 2317 1567 2318 1565 2319 1562 2320 1560 2320 1557 2321 1554 2321 1551 2322 
1548 2322 1545 2322 1541 2323 1537 2323 1534 2323 1530 2322 1527 2322 1524 2322 1521 2321 1518 2321 1515 2320 1513 2320 1510 2319 1508 2318 1506 2317 
1505 2316 1503 2315 1502 2314 1502 2313 1502 2312 65 _pl _pf 
0 g _cp _s _s _s 1520 2315 _m
_sp 1520 2315 1539 2323 1520 2329 3 _pl _pf _np _s 
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_sp 1557 2320 1557 2324 1539 2324 1539 2320 4 _pl _pf _np _s 
_s 0 g _s 1544 2314 _m
_sp 1544 2314 1544 2314 1544 2313 1544 2312 1543 2312 1543 2311 1542 2311 1542 2311 1541 2311 1540 2311 1539 2311 1539 2311 1538 2312 1538 2312 1537 2313 
1537 2314 1537 2314 1537 2315 1537 2316 1538 2316 1538 2317 1539 2317 1539 2318 1540 2318 1541 2318 1542 2318 1542 2318 1543 2317 1543 2317 1544 2316 
1544 2316 1544 2315 1544 2314 33 _pl _pf _np _s 
_s 255 g _s 1649 2381 _m
_sp 1649 2381 1649 2382 1649 2384 1649 2385 1649 2387 1650 2388 1651 2390 1652 2392 1653 2394 1655 2396 1657 2398 1659 2399 1661 2402 1663 2404 1666 2406 
1669 2408 1672 2409 1675 2411 1677 2413 1681 2414 1683 2415 1686 2417 1689 2418 1691 2419 1694 2419 1696 2420 1698 2420 1700 2420 1702 2420 1704 2420 
1705 2419 1706 2419 1707 2418 1707 2416 1708 2415 1707 2414 1707 2412 1706 2410 1705 2409 1704 2407 1703 2405 1701 2403 1699 2401 1697 2399 1695 2397 
1692 2395 1690 2393 1687 2391 1684 2389 1681 2388 1678 2386 1675 2384 1672 2383 1670 2382 1667 2381 1665 2380 1662 2379 1660 2379 1658 2379 1656 2379 
1654 2379 1653 2379 1651 2379 1650 2380 1649 2381 65 _pl _pf 
0 g _cp _s _s _s 1663 2388 _m
_sp 1663 2388 1683 2390 1669 2376 3 _pl _pf _np _s 
_s 255 g _s 1691 2406 _m
_sp 1691 2406 1699 2401 1690 2384 1681 2390 4 _pl _pf _np _s 
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60 _pl _cp 
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45 _pl _cp 
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15 _pl _cp 
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1158 2610 1157 2613 17 _pl _cp 1153 2638 _m
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45 _pl _cp 
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924 2372 924 2375 17 _pl _cp 919 2400 _m
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15 _pl _cp 
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763 2253 762 2256 17 _pl _cp 758 2281 _m
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30 _pl _cp 851 2257 _m
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906 2243 904 2243 903 2246 903 2252 905 2252 907 2251 911 2252 914 2254 916 2258 917 2263 916 2267 915 2269 912 2271 909 2272 908 2272 
906 2272 905 2271 32 _pl _cp 903 2267 _m
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905 2269 904 2268 17 _pl _cp 
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927 2254 926 2257 926 2270 930 2270 930 2272 926 2272 926 2278 925 2278 924 2276 923 2275 922 2274 921 2273 920 2272 28 _pl _cp 
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45 _pl _cp 
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688 2221 16 _pl _cp 
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725 2217 727 2216 728 2217 729 2218 728 2220 727 2222 725 2223 722 2223 718 2222 714 2220 712 2216 711 2212 712 2208 714 2204 717 2202 
721 2201 722 2201 724 2202 725 2203 726 2204 727 2205 728 2206 729 2207 730 2209 39 _pl _cp 
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735 2220 733 2216 17 _pl _cp 736 2214 _m
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736 2217 736 2214 736 2214 18 _pl _cp 
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758 2220 756 2216 17 _pl _cp 759 2214 _m
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760 2217 759 2214 759 2214 18 _pl _cp 
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785 2204 785 2206 785 2216 786 2219 787 2220 788 2220 789 2219 790 2218 791 2218 792 2219 793 2220 792 2222 790 2223 789 2223 787 2222 
786 2221 785 2219 32 _pl _cp 
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797 2204 799 2202 803 2201 804 2201 806 2202 807 2203 808 2204 808 2201 809 2201 816 2204 816 2205 815 2205 813 2205 812 2208 29 _pl _cp 808 2206 _m
_sp 808 2206 808 2215 808 2218 807 2220 806 2221 804 2221 801 2220 800 2219 798 2216 798 2213 799 2209 800 2207 802 2205 805 2204 807 2204 
15 _pl _cp 
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825 2204 824 2206 17 _pl _cp 820 2231 _m
_sp 820 2231 820 2230 822 2229 824 2230 825 2231 824 2233 822 2234 820 2233 8 _pl _cp 
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837 2204 836 2206 836 2217 837 2219 839 2220 840 2221 841 2221 842 2221 844 2219 845 2217 845 2214 845 2206 844 2204 842 2203 841 2203 
841 2202 852 2202 852 2203 851 2203 849 2204 848 2206 848 2217 848 2219 847 2221 845 2222 843 2223 841 2223 840 2222 838 2221 836 2219 
45 _pl _cp 
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865 2205 866 2202 868 2201 870 2202 872 2204 872 2205 871 2204 870 2204 869 2204 869 2206 869 2216 869 2217 869 2217 868 2218 868 2219 
867 2221 866 2222 864 2223 861 2223 858 2223 856 2222 855 2220 854 2218 855 2217 856 2216 857 2216 858 2218 858 2218 858 2218 858 2219 
858 2219 858 2220 859 2221 861 2222 863 2222 864 2221 865 2219 865 2216 53 _pl _cp 865 2214 _m
_sp 865 2214 862 2213 860 2212 858 2211 857 2209 857 2208 858 2205 860 2204 863 2205 865 2206 10 _pl _cp 
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880 2205 880 2207 880 2221 884 2221 884 2222 880 2222 880 2229 879 2229 878 2227 877 2226 876 2225 875 2224 874 2223 28 _pl _cp 
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901 2203 903 2206 905 2209 904 2210 903 2208 901 2206 899 2205 897 2204 894 2205 892 2207 891 2210 890 2214 890 2214 28 _pl _cp 899 2216 _m
_sp 899 2216 899 2218 898 2220 897 2221 895 2221 893 2221 891 2220 890 2218 890 2216 9 _pl _cp 
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1858 2579 1856 2579 1856 2582 1856 2588 1858 2587 1860 2587 1864 2588 1866 2590 1868 2594 1869 2599 1868 2603 1867 2605 1865 2607 1862 2608 1861 2608 
1859 2607 1858 2606 32 _pl _cp 1856 2603 _m
_sp 1856 2603 1856 2591 1858 2589 1860 2588 1862 2589 1864 2591 1865 2593 1865 2597 1865 2601 1864 2603 1862 2605 1860 2606 1858 2605 13 _pl _cp 
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1877 2589 1876 2592 1876 2603 1878 2605 1879 2606 1880 2606 1881 2606 1882 2606 1883 2605 1884 2603 1884 2599 1884 2592 1884 2589 1882 2588 1881 2588 
1881 2587 1891 2587 1891 2588 1890 2588 1888 2589 1888 2592 1888 2601 1888 2604 1887 2606 1885 2608 1883 2608 1881 2608 1880 2608 1878 2607 1876 2605 
45 _pl _cp 
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1899 2589 1898 2592 17 _pl _cp 1894 2617 _m
_sp 1894 2617 1895 2615 1896 2614 1898 2615 1899 2617 1898 2618 1896 2619 1895 2618 8 _pl _cp 
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1928 2609 1926 2608 1924 2608 1922 2607 1921 2606 1920 2604 1919 2602 1918 2600 1918 2598 1919 2593 1921 2590 1924 2588 1928 2587 1928 2579 1931 2579 
1931 2587 1935 2588 1938 2590 1940 2594 1941 2598 1940 2603 1938 2606 1935 2608 38 _pl _cp 1928 2607 _m
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_sp 1931 2608 1934 2607 1936 2605 1937 2602 1937 2598 1937 2594 1936 2592 1934 2589 1931 2588 9 _pl _cp 
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1856 2539 1856 2542 1856 2552 1857 2555 1858 2556 1859 2556 1859 2555 1860 2554 1861 2554 1862 2555 1863 2556 1862 2558 1860 2559 1858 2558 1856 2555 
30 _pl _cp 
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_sp 1864 2548 1865 2544 1867 2540 1869 2538 1873 2537 1877 2538 1880 2540 1882 2544 1883 2549 1882 2553 1880 2556 1878 2558 1874 2559 1870 2558 1867 2556 
1865 2552 16 _pl _cp 1868 2550 _m
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1868 2553 1868 2550 1868 2550 18 _pl _cp 
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1892 2539 1891 2542 17 _pl _cp 
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1903 2539 1903 2542 17 _pl _cp 
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1925 2562 1925 2544 1925 2542 1925 2540 1924 2539 1922 2539 1922 2539 1922 2538 1944 2538 1946 2546 1945 2546 1944 2544 1943 2542 1941 2541 1940 2541 
1938 2540 1936 2540 1932 2540 1930 2540 1930 2542 1930 2552 1936 2552 1939 2552 1940 2549 1942 2549 1942 2559 1940 2559 1939 2556 1936 2555 44 _pl _cp 
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1960 2537 1961 2537 1967 2539 1967 2540 1964 2541 1964 2544 1964 2558 1957 2558 1957 2557 1958 2557 1960 2557 1960 2554 1960 2542 1958 2540 1956 2539 
1955 2539 1954 2541 1953 2542 1953 2545 34 _pl _cp 
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1975 2539 1975 2542 17 _pl _cp 
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1993 2539 1995 2542 1997 2545 1996 2546 1995 2544 1994 2542 1992 2541 1990 2540 1987 2541 1985 2543 1984 2546 1983 2550 1983 2550 28 _pl _cp 1992 2552 _m
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2005 2539 2004 2542 2004 2552 2006 2555 2007 2556 2007 2556 2008 2555 2009 2554 2010 2554 2011 2555 2011 2556 2010 2558 2009 2559 2008 2559 2007 2558 
2005 2557 2004 2555 32 _pl _cp 
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2037 2540 2038 2538 2039 2537 2041 2538 2043 2539 2043 2541 2042 2540 2042 2539 2040 2540 2040 2542 2040 2552 2040 2553 2040 2553 2040 2554 2040 2555 
2039 2557 2038 2558 2036 2559 2034 2559 2031 2559 2029 2558 2028 2556 2027 2554 2028 2552 2029 2552 2030 2552 2031 2554 2031 2554 2031 2554 2031 2555 
2031 2555 2031 2556 2032 2557 2034 2558 2035 2558 2036 2557 2037 2555 2037 2552 53 _pl _cp 2037 2550 _m
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2051 2539 2050 2542 2050 2553 2051 2555 2053 2556 2054 2557 2055 2557 2056 2557 2057 2555 2058 2553 2058 2550 2058 2542 2057 2539 2055 2539 2055 2539 
2055 2538 2064 2538 2064 2539 2064 2539 2062 2539 2061 2542 2061 2552 2061 2555 2060 2557 2058 2558 2056 2559 2055 2559 2053 2558 2052 2557 2050 2555 
45 _pl _cp 
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2083 2539 2081 2540 2078 2541 2075 2541 2071 2541 2070 2542 2071 2543 2072 2545 2074 2545 2075 2545 2078 2546 2080 2547 2081 2549 2082 2552 2082 2553 
2081 2556 2084 2556 2084 2558 2081 2558 2080 2558 2079 2558 2079 2558 2079 2558 2077 2559 2075 2559 2072 2558 2069 2557 2068 2555 2067 2552 2067 2550 
2068 2548 2069 2547 2071 2545 2071 2545 2070 2545 2068 2542 2068 2540 2068 2539 53 _pl _cp 2071 2538 _m
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2072 2537 2072 2538 17 _pl _cp 2071 2553 _m
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2071 2553 16 _pl _cp 
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2094 2539 2093 2542 17 _pl _cp 
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2111 2539 2113 2542 2115 2545 2114 2546 2113 2544 2112 2542 2110 2541 2108 2540 2105 2541 2103 2543 2102 2546 2101 2550 2101 2550 28 _pl _cp 2110 2552 _m
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1722 2361 1722 2364 1722 2377 1726 2377 1726 2379 1722 2379 1722 2385 1721 2385 1720 2384 1719 2383 1718 2381 1717 2380 1716 2379 28 _pl _cp 
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1735 2360 1735 2363 1735 2374 1737 2377 1739 2377 1741 2377 1742 2376 1743 2374 1743 2371 1743 2363 1742 2360 1740 2359 1740 2359 1740 2359 1750 2359 
1750 2359 1749 2359 1748 2360 1747 2363 1747 2372 1747 2375 1746 2377 1744 2379 1741 2379 1740 2379 1738 2379 1737 2378 1735 2376 43 _pl _cp 
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1766 2360 1768 2363 1770 2366 1769 2366 1768 2364 1767 2363 1765 2361 1762 2361 1759 2362 1757 2364 1756 2367 1755 2371 1755 2371 28 _pl _cp 1764 2372 _m
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1779 2361 1778 2364 1778 2377 1782 2377 1782 2379 1778 2379 1778 2385 1777 2385 1776 2384 1776 2383 1775 2381 1774 2380 1773 2379 28 _pl _cp 
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1796 2361 1798 2359 1800 2358 1802 2359 1803 2360 1803 2361 1803 2361 1802 2360 1801 2361 1801 2363 1801 2372 1801 2373 1801 2374 1800 2375 1800 2376 
1799 2377 1798 2378 1796 2379 1793 2379 1790 2379 1788 2378 1787 2376 1786 2374 1787 2373 1788 2372 1789 2373 1790 2374 1790 2374 1790 2374 1790 2376 
1790 2376 1790 2376 1791 2377 1793 2378 1795 2378 1796 2377 1796 2375 1796 2373 53 _pl _cp 1796 2371 _m
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1823 2364 1825 2360 1828 2358 1832 2358 1834 2358 1836 2359 1838 2361 1840 2363 1841 2365 1841 2368 1842 2371 1842 2374 1842 2375 28 _pl _cp 1827 2377 _m
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1827 2375 16 _pl _cp 
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1725 2301 1722 2302 1722 2305 1722 2311 1724 2310 1726 2309 1730 2310 1733 2312 1735 2316 1736 2321 1735 2325 1734 2328 1731 2330 1728 2331 1727 2331 
1725 2330 1724 2329 32 _pl _cp 1722 2325 _m
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15 _pl _cp 
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1746 2311 1746 2314 17 _pl _cp 1741 2339 _m
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1758 2312 1758 2315 1758 2328 1762 2328 1762 2330 1758 2330 1758 2336 1757 2336 1756 2335 1755 2333 1754 2332 1753 2331 1752 2331 28 _pl _cp 
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1778 2325 1780 2324 1781 2325 1782 2326 1781 2328 1780 2329 1778 2331 1775 2331 1771 2330 1768 2329 1766 2326 1764 2323 1764 2319 1765 2315 1767 2312 
1770 2310 1774 2309 1776 2309 1777 2310 1779 2310 1780 2311 1781 2314 1782 2316 38 _pl _cp 
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1792 2311 1791 2314 1791 2325 1793 2327 1794 2328 1795 2328 1796 2328 1798 2328 1799 2327 1800 2325 1800 2322 1800 2314 1799 2311 1797 2310 1796 2310 
1796 2310 1807 2310 1807 2310 1806 2310 1804 2311 1803 2314 1803 2323 1803 2326 1802 2329 1800 2330 1798 2331 1796 2331 1795 2330 1793 2329 1791 2327 
45 _pl _cp 
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1827 2334 1827 2315 1827 2312 1824 2311 1823 2311 1823 2310 1848 2310 1850 2317 1849 2317 1848 2315 1846 2314 1845 2313 1844 2312 1842 2312 1839 2312 
1835 2312 1833 2312 1832 2314 1832 2324 1839 2324 1841 2324 1843 2324 1843 2322 1844 2320 1845 2320 1845 2331 1844 2331 1843 2329 1843 2327 1841 2326 
1839 2326 46 _pl _cp 
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1866 2309 1867 2309 1873 2311 1873 2312 1870 2312 1870 2315 1870 2330 1863 2330 1863 2329 1864 2329 1866 2329 1866 2325 1866 2314 1865 2313 1864 2312 
1862 2311 1861 2311 1860 2311 1859 2313 1858 2314 1858 2317 36 _pl _cp 
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1883 2311 1882 2314 17 _pl _cp 
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1903 2311 1905 2314 1907 2317 1906 2317 1905 2315 1903 2314 1901 2312 1899 2312 1896 2313 1894 2315 1892 2318 1891 2322 1891 2322 28 _pl _cp 1901 2324 _m
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1915 2311 1915 2314 1915 2324 1916 2326 1917 2327 1918 2327 1919 2327 1920 2326 1921 2326 1922 2327 1923 2328 1922 2330 1920 2331 1919 2331 1917 2330 
1916 2329 1915 2327 32 _pl _cp 
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1951 2312 1952 2310 1954 2309 1956 2310 1958 2311 1958 2312 1957 2312 1956 2311 1955 2312 1955 2314 1955 2323 1955 2324 1955 2325 1955 2326 1954 2327 
1953 2328 1952 2330 1950 2331 1948 2331 1945 2330 1942 2329 1941 2327 1940 2325 1941 2324 1942 2323 1943 2324 1944 2325 1944 2325 1944 2325 1944 2327 
1944 2327 1944 2327 1945 2328 1947 2329 1949 2329 1950 2328 1951 2326 1951 2324 53 _pl _cp 1951 2321 _m
_sp 1951 2321 1948 2320 1946 2319 1944 2318 1943 2316 1943 2315 1944 2313 1947 2312 1949 2312 1951 2314 10 _pl _cp 
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1966 2311 1966 2314 1966 2325 1967 2326 1969 2327 1970 2328 1971 2328 1972 2328 1973 2327 1974 2325 1974 2322 1974 2314 1974 2311 1971 2310 1971 2310 
1971 2310 1982 2310 1982 2310 1981 2310 1979 2311 1978 2314 1978 2324 1978 2327 1977 2329 1975 2330 1973 2331 1971 2331 1970 2330 1968 2329 1966 2327 
45 _pl _cp 
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2002 2311 2000 2312 1997 2312 1993 2312 1989 2313 1988 2314 1989 2315 1990 2316 1992 2316 1993 2316 1996 2317 1999 2318 2000 2321 2001 2324 2001 2325 
2000 2327 2003 2327 2003 2329 2000 2329 1999 2330 1998 2330 1998 2330 1997 2330 1995 2331 1993 2331 1990 2330 1987 2329 1986 2326 1985 2323 1985 2321 
1986 2320 1987 2318 1989 2317 1989 2316 1988 2316 1986 2314 1985 2312 1986 2311 53 _pl _cp 1989 2309 _m
_sp 1989 2309 1987 2307 1986 2305 1987 2304 1988 2303 1990 2302 1993 2302 1997 2302 1999 2303 2001 2305 2002 2306 2001 2308 1999 2309 1992 2309 1991 2309 
1990 2309 1990 2309 17 _pl _cp 1989 2325 _m
_sp 1989 2325 1989 2322 1990 2319 1992 2318 1993 2317 1995 2317 1996 2318 1997 2320 1997 2322 1997 2325 1996 2327 1994 2328 1992 2329 1990 2328 1989 2325 
1989 2325 16 _pl _cp 
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2014 2311 2013 2314 17 _pl _cp 
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2034 2311 2036 2314 2038 2317 2037 2317 2036 2315 2034 2314 2032 2312 2030 2312 2027 2313 2025 2315 2024 2318 2023 2322 2023 2322 28 _pl _cp 2032 2324 _m
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1540 2235 1538 2235 1537 2238 1537 2245 1539 2243 1541 2243 1545 2244 1548 2246 1550 2250 1551 2254 1550 2258 1549 2261 1546 2263 1543 2264 1542 2264 
1540 2263 1539 2262 32 _pl _cp 1537 2259 _m
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15 _pl _cp 
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1566 2254 1564 2255 1562 2256 1560 2257 1558 2258 1557 2259 1557 2260 1558 2262 1561 2263 1563 2263 1565 2262 1566 2260 1567 2258 1568 2258 1568 2264 
1567 2264 1567 2264 1566 2264 1566 2264 1565 2264 1564 2264 1562 2264 1561 2264 1558 2264 1556 2263 1555 2261 1554 2259 1554 2257 1555 2255 1557 2254 
1559 2252 1562 2251 1565 2249 1566 2247 1565 2245 1562 2244 1560 2245 1557 2246 1556 2247 1555 2251 1554 2251 56 _pl _cp 
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1580 2245 1579 2248 17 _pl _cp 1574 2273 _m
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1606 2259 1606 2258 1606 2252 1606 2250 1606 2249 1606 2247 1607 2246 1609 2245 1610 2244 1612 2243 1614 2243 1614 2234 1618 2234 1618 2243 1621 2244 
1624 2246 1625 2248 1626 2252 1626 2258 1626 2261 1628 2261 1628 2261 1629 2261 1629 2261 1629 2261 1629 2263 1627 2263 1626 2264 1624 2264 1622 2264 
1622 2252 1622 2249 1621 2247 1620 2245 1618 2245 1618 2271 51 _pl _cp 
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1538 2191 1538 2189 1537 2188 1536 2188 1535 2188 1535 2188 1534 2189 1533 2189 1533 2189 1531 2188 1530 2187 1531 2185 1534 2184 1535 2184 1537 2185 
1538 2186 1539 2187 1548 2210 1550 2212 1551 2213 1551 2214 1545 2214 1545 2213 1545 2213 1546 2213 1547 2212 1547 2212 1547 2212 1547 2212 1547 2211 
1547 2211 1546 2210 47 _pl _cp 
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1565 2196 1567 2194 1569 2193 1571 2194 1572 2195 1572 2197 1572 2196 1571 2195 1570 2196 1569 2198 1569 2208 1569 2209 1569 2209 1569 2210 1569 2211 
1568 2213 1567 2214 1565 2215 1562 2215 1559 2215 1557 2213 1556 2212 1555 2210 1555 2209 1557 2208 1558 2208 1559 2210 1559 2210 1559 2210 1559 2211 
1559 2211 1559 2212 1560 2213 1562 2214 1563 2214 1564 2213 1565 2211 1565 2208 53 _pl _cp 1565 2206 _m
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1585 2193 1590 2205 1595 2193 1596 2193 1603 2210 1604 2212 1606 2213 1606 2214 1599 2214 1599 2213 1600 2213 1601 2213 1602 2212 1602 2212 1602 2212 
1602 2212 1601 2211 1601 2211 1601 2210 1597 2199 1593 2210 1592 2211 1592 2211 1592 2212 1592 2212 1593 2213 1594 2213 1594 2213 1594 2214 1585 2214 
1585 2213 1587 2212 1589 2210 1589 2208 49 _pl _cp 
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1627 2218 1627 2200 1627 2198 1626 2196 1625 2195 1623 2195 1623 2195 1623 2194 1648 2194 1650 2202 1648 2202 1647 2200 1646 2198 1644 2197 1643 2197 
1641 2196 1638 2196 1635 2196 1632 2196 1632 2198 1632 2209 1638 2209 1640 2209 1642 2208 1643 2207 1643 2205 1645 2205 1645 2215 1643 2215 1643 2213 
1642 2212 1640 2211 1638 2211 48 _pl _cp 
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1666 2193 1666 2193 1673 2195 1673 2196 1670 2196 1670 2199 1670 2214 1662 2214 1662 2213 1663 2213 1665 2213 1666 2210 1666 2198 1665 2197 1663 2196 
1662 2195 1661 2195 1660 2196 1658 2197 1657 2199 1657 2201 36 _pl _cp 
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1682 2195 1682 2198 17 _pl _cp 
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1702 2195 1704 2198 1706 2201 1705 2201 1704 2199 1702 2198 1700 2197 1698 2196 1695 2197 1693 2199 1692 2202 1691 2206 1691 2206 28 _pl _cp 1700 2208 _m
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1715 2195 1714 2198 1714 2208 1716 2211 1717 2212 1718 2212 1718 2211 1719 2210 1720 2210 1721 2211 1722 2212 1721 2214 1719 2215 1718 2215 1717 2214 
1715 2213 1714 2211 32 _pl _cp 
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1744 2211 1744 2212 1745 2213 1747 2214 1748 2214 1749 2213 1750 2211 1750 2208 53 _pl _cp 1750 2206 _m
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45 _pl _cp 
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1801 2195 1799 2196 1796 2197 1792 2197 1789 2197 1788 2198 1788 2199 1790 2201 1792 2200 1793 2200 1796 2201 1798 2203 1799 2205 1800 2208 1800 2209 
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1785 2204 1786 2203 1788 2201 1788 2201 1788 2200 1785 2198 1785 2196 1785 2195 53 _pl _cp 1788 2194 _m
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1789 2193 1789 2194 17 _pl _cp 1788 2209 _m
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1788 2209 16 _pl _cp 
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1813 2195 1813 2198 17 _pl _cp 
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1833 2195 1835 2198 1837 2201 1836 2201 1835 2199 1834 2198 1831 2197 1829 2196 1826 2197 1824 2199 1823 2202 1822 2206 1822 2206 28 _pl _cp 1831 2208 _m
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1256 2759 1259 2757 1259 2758 1257 2760 1255 2762 1254 2764 1253 2766 1252 2768 1252 2771 1252 2774 1252 2777 1252 2779 1252 2782 1252 2784 1253 2786 
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1268 2767 1268 2770 1268 2780 1269 2782 1270 2783 1271 2783 1271 2782 1272 2782 1273 2781 1274 2782 1275 2784 1274 2785 1273 2786 1272 2786 1270 2785 
1269 2784 1268 2783 32 _pl _cp 
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1284 2767 1283 2770 17 _pl _cp 1279 2794 _m
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1308 2767 1306 2768 1303 2768 1299 2768 1295 2768 1294 2769 1294 2771 1296 2772 1298 2772 1299 2772 1302 2773 1305 2774 1306 2776 1307 2779 1306 2781 
1305 2783 1309 2783 1309 2785 1305 2785 1304 2785 1303 2785 1303 2786 1303 2786 1301 2786 1299 2786 1296 2785 1293 2784 1292 2782 1291 2779 1291 2777 
1292 2775 1293 2774 1295 2773 1294 2772 1294 2772 1292 2770 1291 2769 1291 2768 1291 2767 1292 2766 55 _pl _cp 1294 2765 _m
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1296 2765 1295 2765 17 _pl _cp 1294 2780 _m
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1571 2780 1571 2777 1571 2777 18 _pl _cp 
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1642 2767 1642 2770 17 _pl _cp 1637 2794 _m
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45 _pl _cp 
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1715 2770 1713 2769 1712 2767 1713 2766 1714 2765 1716 2765 21 _pl _cp 
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1745 2767 1744 2770 17 _pl _cp 1740 2794 _m
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1792 2780 1792 2777 1792 2777 18 _pl _cp 
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1818 2784 1817 2783 32 _pl _cp 
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15 _pl _cp 
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1875 2767 1875 2770 1875 2780 1876 2782 1877 2783 1878 2783 1879 2782 1880 2782 1881 2781 1882 2782 1882 2784 1881 2785 1880 2786 1879 2786 1877 2785 
1876 2784 1875 2783 32 _pl _cp 
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1891 2768 1890 2766 1889 2764 1887 2762 1885 2760 1883 2758 36 _pl _cp 
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1850 1510 1848 1511 1846 1512 1843 1514 1842 1516 1843 1517 1846 1518 1848 1518 1849 1517 1851 1515 1852 1513 1852 1513 1852 1519 1852 1519 1851 1519 
1851 1519 1850 1519 1850 1519 1848 1520 1847 1520 1846 1520 1843 1519 1841 1518 1840 1516 1839 1514 1839 1513 1840 1511 1842 1510 1844 1508 1847 1507 
1849 1505 1850 1503 1849 1501 1847 1500 1844 1501 1842 1501 1841 1503 1840 1506 1839 1506 54 _pl _cp 
0 g _f _s _s 
0 g 1856 1491 _m
_sp 1856 1491 1859 1493 1861 1495 1862 1496 1864 1498 1865 1500 1866 1503 1867 1506 1867 1510 1867 1514 1866 1518 1865 1521 1864 1523 1862 1525 1861 1527 
1859 1528 1856 1530 1856 1528 1858 1527 1860 1525 1861 1523 1862 1520 1863 1518 1863 1515 1863 1513 1863 1510 1863 1508 1863 1505 1863 1503 1862 1501 
1861 1499 1860 1496 1858 1494 1856 1492 34 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 1500 2716 _m
/Times-BoldR 600 _ff
(Figure)_S 67 _t
(6.3)_S /Times-RomanR 600 _ff
(.)_S 3000 2716 _m
_U (Body)_S 67 _t
(coordinate)_S 67 _t
(system)_S _u (:)_S 134 _t
(linear)_S 67 _t
(and)_S 67 _t
(angular)_S 67 _t
(velocity)_S 67 _t
(conventions.)_S 67 _t
3000 2483 _m
(Note)_S 67 _t
(that)_S 67 _t
(roll)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rate)_S 67 _t
/Symbol 600 _ff
(\271)_S /Times-RomanR 600 _ff
67 _t
(roll)_S 67 _t
(rate,)_S 3000 2250 _m
(pitch)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rate)_S 67 _t
/Symbol 600 _ff
(\271)_S /Times-RomanR 600 _ff
67 _t
(pitch)_S 67 _t
(rate,)_S 67 _t
(and)_S 3000 2017 _m
(yaw)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rate)_S 67 _t
/Symbol 600 _ff
(\271)_S /Times-RomanR 600 _ff
67 _t
(yaw)_S 67 _t
(rate.)_S 4950 1288 _m
(104)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1980 7428 _m
(Normally)_S 67 _t
(Euler)_S 67 _t
(angles)_S 67 _t
(must)_S 67 _t
(be)_S 67 _t
(restricted)_S 67 _t
(from)_S 67 _t
(representing)_S 67 _t
(a)_S 67 _t
(vertical)_S 67 _t
(orientation)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 375 2210 _m
_sp 2174 2210 2174 2213 375 2213 3 _pl _pf _np _s _s 2171 2210 _m
_sp 2174 2210 2174 2999 2171 2999 3 _pl _pf _np _s _s 375 2996 _m
_sp 2174 2996 2174 2999 375 2999 3 _pl _pf _np _s _s 375 2210 _m
_sp 378 2210 378 2999 375 2999 3 _pl _pf _np 
_s 0 g 721 1731 409 2244 _cw 
_s 
_s 255 g _s 438 2933 _m
_sp 438 2933 944 2933 944 2383 438 2383 4 _pl _pf 
7 _w 0 g _cp _s _s 
_s 1 _w 255 g _s 987 2933 _m
_sp 987 2933 1536 2933 1536 2384 987 2384 4 _pl _pf 
7 _w 0 g _cp _s _s 
_s 1 _w 255 g _s 1578 2933 _m
_sp 1578 2933 2127 2933 2127 2384 1578 2384 4 _pl _pf 
7 _w 0 g _cp _s _s 
1 _w 0 g 543 2627 _m
_sp 543 2627 543 2588 540 2589 538 2591 536 2594 536 2599 536 2616 533 2616 530 2616 528 2615 525 2615 525 2612 526 2612 526 2612 529 2611 
530 2609 530 2607 530 2599 530 2596 530 2593 531 2592 532 2590 534 2588 537 2586 540 2585 543 2585 543 2571 548 2571 548 2585 553 2585 
556 2587 559 2590 560 2594 561 2599 561 2607 561 2609 561 2611 562 2612 564 2612 565 2612 565 2612 565 2612 566 2612 566 2615 563 2615 
560 2616 557 2616 555 2616 555 2599 555 2594 553 2591 551 2589 548 2588 548 2627 54 _pl _cp 
0 g _f _s _s 
0 g 596 2433 _m
_sp 596 2433 614 2433 614 2440 613 2440 613 2438 612 2436 610 2435 608 2435 601 2435 614 2454 597 2454 597 2448 598 2448 600 2451 602 2452 
608 2452 16 _pl _cp 
0 g _f _s _s 
0 g 623 2434 _m
_sp 623 2434 623 2433 623 2433 623 2431 621 2429 620 2428 618 2427 618 2426 621 2427 623 2428 624 2430 625 2433 625 2435 624 2437 622 2438 
621 2438 619 2437 618 2435 619 2434 620 2433 622 2433 21 _pl _cp 
0 g _f _s _s 
0 g 644 2433 _m
_sp 644 2433 662 2433 662 2440 661 2440 660 2438 660 2436 658 2435 656 2435 649 2435 662 2454 645 2454 645 2448 646 2448 647 2451 650 2452 
656 2452 16 _pl _cp 
0 g _f _s _s 
0 g 667 2454 _m
_sp 667 2454 670 2461 671 2462 671 2463 670 2464 669 2465 668 2464 667 2462 665 2456 665 2455 665 2454 664 2454 665 2453 666 2453 667 2453 
667 2454 16 _pl _cp 
0 g _f _s _s _s 607 2469 _m
_sp 623 2517 607 2507 591 2517 3 _pl _pf _np 
_s 7 _w 0 g 607 2722 _m
607 2507 _l _s 
_s 1 _w 0 g _s 861 2722 _m
_sp 812 2738 823 2722 812 2706 3 _pl _pf _np 
_s 7 _w 0 g 607 2722 _m
823 2722 _l _s 
_s 1 _w 0 g _s 481 2849 _m
_sp 503 2804 507 2823 526 2826 3 _pl _pf _np 
_s 7 _w 0 g 607 2722 _m
507 2823 _l _s 
1 _w 0 g 461 2870 _m
_sp 461 2870 457 2864 456 2862 455 2861 453 2860 452 2860 452 2859 460 2859 460 2860 458 2860 458 2861 458 2862 459 2864 462 2868 465 2864 
466 2862 466 2861 466 2860 465 2860 465 2859 474 2859 474 2860 472 2861 470 2864 465 2871 467 2875 468 2877 470 2878 471 2878 472 2879 
472 2880 465 2880 465 2879 465 2879 466 2879 466 2878 466 2877 465 2875 464 2873 462 2875 461 2877 461 2878 461 2879 462 2879 463 2879 
463 2880 453 2880 453 2879 454 2878 456 2878 457 2877 458 2875 52 _pl _cp 
0 g _f _s _s 
0 g 893 2719 _m
_sp 893 2719 888 2728 888 2729 888 2730 887 2731 887 2731 888 2732 889 2732 890 2732 890 2733 880 2733 880 2732 882 2731 884 2728 891 2714 
889 2709 888 2707 887 2707 886 2706 886 2706 885 2707 884 2707 883 2707 883 2707 881 2706 880 2705 881 2703 884 2702 885 2702 887 2703 
888 2704 889 2705 898 2728 900 2731 902 2732 902 2733 895 2733 895 2732 896 2732 897 2732 897 2731 897 2731 897 2731 897 2730 897 2730 
897 2729 897 2728 47 _pl _cp 
0 g _f _s _s 
0 g 843 2650 _m
_sp 843 2650 838 2659 838 2660 838 2661 837 2662 837 2662 838 2663 839 2663 840 2663 840 2664 830 2664 830 2663 832 2662 834 2659 841 2645 
839 2640 838 2638 837 2638 836 2637 836 2637 835 2638 834 2638 834 2638 833 2638 832 2637 831 2636 832 2634 834 2633 835 2633 837 2634 
838 2635 839 2637 849 2659 850 2662 852 2663 852 2664 845 2664 845 2663 846 2663 847 2663 848 2662 848 2662 848 2662 848 2661 847 2661 
847 2660 847 2659 47 _pl _cp 
0 g _f _s _s 
0 g 857 2665 _m
_sp 857 2665 860 2671 861 2672 861 2673 860 2674 859 2675 858 2674 857 2672 855 2666 855 2666 855 2665 854 2664 855 2663 856 2663 857 2664 
857 2664 16 _pl _cp 
0 g _f _s _s 
0 g 523 2883 _m
_sp 523 2883 519 2877 518 2875 517 2874 515 2873 514 2873 514 2872 522 2872 522 2873 521 2873 520 2874 520 2875 521 2877 525 2881 527 2877 
529 2875 529 2874 528 2873 527 2873 527 2872 536 2872 536 2873 534 2874 532 2877 527 2885 530 2888 532 2891 534 2892 534 2893 527 2893 
527 2892 527 2892 528 2892 529 2891 528 2890 527 2888 526 2886 525 2888 523 2890 523 2891 523 2892 525 2892 525 2892 525 2893 515 2893 
515 2892 516 2891 518 2891 519 2890 520 2888 50 _pl _cp 
0 g _f _s _s 
0 g 541 2894 _m
_sp 541 2894 544 2900 544 2901 544 2902 544 2903 543 2904 542 2903 541 2901 539 2895 539 2894 539 2894 538 2893 539 2892 539 2891 540 2892 
541 2893 16 _pl _cp 
0 g _f _s _s _s 536 2856 _m
_sp 542 2818 549 2831 564 2829 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 606 2721 _m
549 2831 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 832 2678 _m
_sp 798 2696 804 2683 794 2672 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 606 2721 _m
804 2683 _l _s 
[] 0 _d 2 _lc 1 _w 0 g 1356 2637 _m
_sp 1356 2637 1356 2643 1354 2649 1352 2653 1350 2656 1346 2658 1342 2659 1338 2658 1335 2657 1332 2654 1330 2650 1329 2647 1328 2645 1327 2641 1327 2638 
1327 2634 1327 2628 1328 2622 1330 2618 1332 2614 1334 2612 1337 2610 1341 2610 1345 2611 1348 2612 1351 2614 1353 2617 1354 2620 1355 2623 1355 2626 
1356 2630 1356 2635 1356 2636 33 _pl _cp 1333 2639 _m
_sp 1333 2639 1333 2641 1333 2643 1333 2644 1334 2645 1335 2650 1337 2653 1339 2655 1341 2656 1344 2655 1346 2653 1348 2650 1349 2645 1350 2639 14 _pl _cp 1350 2636 _m
_sp 1350 2636 1350 2632 1350 2630 1350 2628 1350 2627 1349 2622 1348 2618 1347 2615 1345 2613 1342 2613 1339 2613 1337 2615 1335 2618 1334 2622 1333 2628 
1333 2634 1333 2635 1333 2636 18 _pl _cp 
0 g _f _s _s 
0 g 1189 2433 _m
_sp 1189 2433 1207 2433 1207 2440 1206 2440 1206 2438 1205 2436 1203 2435 1201 2435 1194 2435 1207 2454 1190 2454 1190 2448 1192 2448 1193 2451 1195 2452 
1201 2452 16 _pl _cp 
0 g _f _s _s 
0 g 1216 2434 _m
_sp 1216 2434 1216 2433 1216 2433 1216 2431 1215 2429 1213 2428 1211 2427 1211 2426 1214 2427 1216 2428 1217 2430 1218 2433 1218 2435 1217 2437 1215 2438 
1214 2438 1212 2437 1211 2435 1212 2434 1214 2433 1215 2433 21 _pl _cp 
0 g _f _s _s 
0 g 1237 2433 _m
_sp 1237 2433 1255 2433 1255 2440 1254 2440 1254 2438 1253 2436 1251 2435 1249 2435 1242 2435 1255 2454 1238 2454 1238 2448 1240 2448 1241 2451 1243 2452 
1249 2452 16 _pl _cp 
0 g _f _s _s 
0 g 1260 2454 _m
_sp 1260 2454 1263 2461 1264 2462 1264 2463 1263 2464 1262 2465 1261 2464 1260 2462 1258 2456 1258 2455 1258 2454 1258 2454 1258 2453 1259 2453 1260 2453 
1260 2454 16 _pl _cp 
0 g _f _s _s _s 1199 2469 _m
_sp 1215 2517 1199 2507 1183 2517 3 _pl _pf _np 
_s 7 _w 0 g 1199 2722 _m
1199 2507 _l _s 
_s 1 _w 0 g _s 1452 2722 _m
_sp 1403 2738 1414 2722 1403 2706 3 _pl _pf _np 
_s 7 _w 0 g 1199 2722 _m
1414 2722 _l _s 
_s 1 _w 0 g _s 1072 2849 _m
_sp 1094 2804 1098 2823 1117 2826 3 _pl _pf _np 
_s 7 _w 0 g 1199 2722 _m
1098 2823 _l _s 
1 _w 0 g 1052 2870 _m
_sp 1052 2870 1048 2864 1047 2862 1046 2861 1044 2860 1043 2860 1043 2859 1051 2859 1051 2860 1049 2860 1049 2861 1049 2862 1050 2864 1053 2868 1056 2864 
1057 2862 1057 2861 1057 2860 1056 2860 1056 2859 1065 2859 1065 2860 1063 2861 1061 2864 1056 2871 1059 2875 1061 2878 1063 2879 1063 2880 1056 2880 
1056 2879 1056 2879 1057 2879 1057 2878 1057 2877 1056 2875 1055 2873 1053 2875 1052 2877 1052 2878 1052 2879 1053 2879 1054 2879 1054 2880 1044 2880 
1044 2879 1045 2878 1047 2878 1048 2877 1049 2875 50 _pl _cp 
0 g _f _s _s 
0 g 1484 2719 _m
_sp 1484 2719 1479 2728 1479 2729 1478 2730 1478 2731 1478 2731 1479 2732 1480 2732 1481 2732 1481 2733 1471 2733 1471 2732 1473 2731 1475 2728 1482 2714 
1479 2709 1479 2707 1478 2707 1477 2706 1477 2706 1476 2707 1475 2707 1474 2707 1474 2707 1472 2706 1471 2705 1472 2703 1475 2702 1476 2702 1478 2703 
1479 2704 1480 2705 1489 2728 1491 2731 1493 2732 1493 2733 1486 2733 1486 2732 1486 2732 1488 2732 1488 2731 1488 2731 1488 2731 1488 2730 1488 2730 
1488 2729 1487 2728 47 _pl _cp 
0 g _f _s _s 
0 g 1434 2646 _m
_sp 1434 2646 1430 2655 1429 2656 1429 2656 1429 2657 1429 2658 1429 2659 1430 2659 1431 2659 1431 2660 1421 2660 1421 2659 1423 2658 1425 2655 1432 2641 
1430 2636 1429 2634 1428 2633 1427 2633 1427 2633 1426 2633 1425 2634 1425 2634 1424 2634 1423 2633 1422 2632 1423 2630 1425 2629 1427 2629 1429 2630 
1430 2631 1430 2632 1440 2655 1441 2658 1443 2659 1443 2660 1436 2660 1436 2659 1437 2659 1438 2659 1439 2658 1439 2658 1439 2658 1439 2657 1438 2656 
1438 2656 1438 2655 47 _pl _cp 
0 g _f _s _s 
0 g 1448 2660 _m
_sp 1448 2660 1451 2667 1452 2668 1452 2669 1451 2670 1450 2670 1449 2670 1448 2668 1446 2661 1446 2661 1446 2660 1445 2660 1446 2659 1446 2659 1447 2659 
1448 2660 16 _pl _cp 
0 g _f _s _s 
0 g 1460 2639 _m
_sp 1460 2639 1460 2639 1460 2638 1460 2636 1459 2635 1457 2634 1455 2633 1455 2632 1458 2633 1461 2634 1462 2636 1463 2639 1463 2641 1462 2643 1460 2644 
1458 2644 1456 2643 1455 2641 1456 2639 1458 2638 1459 2639 21 _pl _cp 
0 g _f _s _s 
0 g 1493 2646 _m
_sp 1493 2646 1489 2655 1488 2656 1488 2656 1488 2657 1488 2658 1488 2659 1490 2659 1490 2659 1490 2660 1480 2660 1480 2659 1483 2658 1484 2655 1491 2641 
1489 2636 1488 2634 1488 2633 1487 2633 1486 2633 1485 2633 1484 2634 1484 2634 1484 2634 1482 2633 1481 2632 1482 2630 1484 2629 1486 2629 1488 2630 
1489 2631 1490 2632 1499 2655 1501 2658 1502 2659 1502 2660 1496 2660 1496 2659 1496 2659 1497 2659 1498 2658 1498 2658 1498 2658 1498 2657 1497 2656 
1497 2656 1497 2655 47 _pl _cp 
0 g _f _s _s 
0 g 1507 2660 _m
_sp 1507 2660 1510 2667 1511 2668 1511 2669 1511 2670 1510 2670 1508 2670 1507 2668 1505 2661 1505 2661 1505 2660 1505 2660 1505 2659 1506 2659 1507 2659 
1507 2660 16 _pl _cp 
0 g _f _s _s 
0 g 1516 2660 _m
_sp 1516 2660 1519 2667 1519 2668 1519 2669 1519 2670 1518 2670 1517 2670 1516 2668 1514 2661 1513 2661 1513 2660 1513 2660 1514 2659 1514 2659 1515 2659 
1516 2660 16 _pl _cp 
0 g _f _s _s 
0 g 1115 2883 _m
_sp 1115 2883 1111 2877 1110 2875 1109 2874 1107 2873 1106 2873 1106 2872 1113 2872 1113 2873 1112 2873 1112 2874 1112 2875 1113 2877 1116 2881 1119 2877 
1120 2875 1120 2874 1119 2873 1118 2873 1118 2872 1128 2872 1128 2873 1127 2873 1126 2874 1124 2875 1123 2877 1118 2885 1121 2888 1122 2890 1124 2891 
1125 2891 1126 2892 1126 2893 1118 2893 1118 2892 1119 2892 1120 2892 1120 2891 1120 2890 1119 2888 1117 2886 1116 2888 1114 2890 1114 2891 1115 2892 
1116 2892 1117 2892 1117 2893 1106 2893 1106 2892 1108 2891 1109 2891 1110 2890 1112 2888 54 _pl _cp 
0 g _f _s _s 
0 g 1133 2894 _m
_sp 1133 2894 1135 2900 1136 2901 1136 2902 1136 2903 1135 2904 1134 2903 1132 2901 1130 2895 1130 2894 1130 2894 1130 2893 1130 2892 1131 2891 1132 2892 
1133 2893 16 _pl _cp 
0 g _f _s _s _s 1127 2856 _m
_sp 1133 2818 1140 2831 1155 2829 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1198 2721 _m
1140 2831 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 1423 2678 _m
_sp 1389 2696 1395 2683 1385 2672 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1198 2721 _m
1395 2683 _l 
_s [] 0 _d 2 _lc 1 _w 0 g 1197 2539 _m
1196 2538 _l 1196 2538 _m
1196 2537 _l 1196 2537 _m
1196 2536 _l 1196 2536 _m
1195 2536 _l 1195 2536 _m
1195 2535 _l 1195 2535 _m
1194 2534 _l 1194 2534 _m
1194 2533 _l 1194 2533 _m
1193 2533 _l 1193 2533 _m
1193 2532 _l 1193 2532 _m
1192 2532 _l 1192 2532 _m
1192 2531 _l 1192 2531 _m
1191 2530 _l 1191 2530 _m
1190 2530 _l 1190 2530 _m
1189 2529 _l 1189 2529 _m
1188 2529 _l 1188 2529 _m
1188 2529 _l 1188 2529 _m
1187 2528 _l 1187 2528 _m
1187 2528 _l 1187 2528 _m
1185 2528 _l 1185 2528 _m
1185 2527 _l 1185 2527 _m
1184 2527 _l 1184 2527 _m
1183 2527 _l 1183 2527 _m
1183 2527 _l 1183 2527 _m
1181 2527 _l 1181 2527 _m
1181 2526 _l 1181 2526 _m
1180 2526 _l 1180 2526 _m
1179 2526 _l 1179 2526 _m
1178 2527 _l 1178 2527 _m
1177 2527 _l 1177 2527 _m
1176 2527 _l 1176 2527 _m
1175 2527 _l 1175 2527 _m
1175 2527 _l _s _s 1174 2526 _m
_sp 1174 2526 1171 2528 1175 2529 3 _pl _pf _np 1364 2713 _m
1364 2712 _l 1364 2712 _m
1365 2710 _l 1365 2710 _m
1365 2709 _l 1365 2709 _m
1366 2707 _l 1366 2707 _m
1366 2706 _l 1366 2706 _m
1367 2705 _l 1367 2705 _m
1367 2703 _l 1367 2703 _m
1367 2702 _l 1367 2702 _m
1367 2700 _l 1367 2700 _m
1367 2699 _l 1367 2699 _m
1367 2697 _l 1367 2697 _m
1367 2696 _l 1367 2696 _m
1367 2694 _l 1367 2694 _m
1367 2693 _l 1367 2693 _m
1366 2691 _l 1366 2691 _m
1366 2690 _l 1366 2690 _m
1366 2688 _l 1366 2688 _m
1365 2687 _l 1365 2687 _m
1364 2686 _l 1364 2686 _m
1364 2685 _l 1364 2685 _m
1363 2683 _l 1363 2683 _m
1362 2682 _l 1362 2682 _m
1362 2681 _l 1362 2681 _m
1361 2679 _l 1361 2679 _m
1360 2678 _l 1360 2678 _m
1359 2677 _l 1359 2677 _m
1358 2676 _l 1358 2676 _m
1357 2675 _l 1357 2675 _m
1355 2674 _l 1355 2674 _m
1355 2673 _l 1355 2673 _m
1353 2672 _l 1353 2672 _m
1352 2672 _l _s _s 1353 2669 _m
_sp 1353 2669 1346 2667 1350 2674 3 _pl _pf 
3 _w 0 g _cp _s _s 
_s 1 _w 0 g _s 1181 2855 _m
_sp 1174 2817 1185 2827 1198 2820 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1198 2722 _m
1185 2827 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 1164 2485 _m
_sp 1182 2520 1168 2514 1158 2523 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1198 2722 _m
1168 2514 _l _s 
[] 0 _d 2 _lc 1 _w 0 g 1182 2884 _m
_sp 1182 2884 1178 2878 1177 2876 1176 2875 1174 2875 1173 2874 1173 2873 1181 2873 1181 2874 1180 2875 1179 2875 1179 2876 1180 2878 1183 2882 1186 2878 
1187 2876 1187 2875 1187 2875 1186 2874 1186 2873 1195 2873 1195 2874 1193 2875 1191 2878 1186 2886 1188 2890 1189 2891 1191 2892 1192 2893 1193 2893 
1193 2894 1186 2894 1186 2893 1186 2893 1187 2893 1187 2892 1187 2891 1186 2890 1185 2888 1183 2890 1182 2891 1182 2892 1182 2893 1183 2893 1184 2893 
1184 2894 1174 2894 1174 2893 1175 2893 1177 2892 1178 2891 1179 2890 52 _pl _cp 
0 g _f _s _s 
0 g 1200 2895 _m
_sp 1200 2895 1203 2901 1203 2902 1203 2903 1203 2904 1202 2905 1201 2904 1200 2902 1198 2896 1197 2896 1197 2895 1197 2894 1198 2893 1198 2893 1199 2894 
1200 2894 16 _pl _cp 
0 g _f _s _s 
0 g 1208 2895 _m
_sp 1208 2895 1211 2901 1212 2902 1212 2903 1211 2904 1210 2905 1209 2904 1208 2902 1206 2896 1206 2896 1206 2895 1206 2894 1206 2893 1207 2893 1208 2894 
1208 2894 16 _pl _cp 
0 g _f _s _s 
0 g 1133 2443 _m
_sp 1133 2443 1151 2443 1151 2450 1150 2450 1149 2448 1149 2446 1147 2445 1145 2445 1139 2445 1151 2464 1134 2464 1134 2458 1135 2458 1136 2461 1139 2462 
1145 2462 16 _pl _cp 
0 g _f _s _s 
0 g 1156 2465 _m
_sp 1156 2465 1159 2471 1160 2472 1160 2473 1159 2474 1158 2475 1157 2474 1156 2472 1154 2466 1154 2466 1154 2465 1153 2464 1154 2463 1154 2463 1155 2464 
1156 2464 16 _pl _cp 
0 g _f _s _s 
0 g 1165 2465 _m
_sp 1165 2465 1167 2471 1168 2472 1168 2473 1168 2474 1167 2475 1166 2474 1165 2472 1162 2466 1162 2466 1162 2465 1162 2464 1162 2463 1163 2463 1164 2464 
1165 2464 16 _pl _cp 
0 g _f _s 1162 2790 _m
1162 2791 _l 1162 2791 _m
1162 2792 _l 1162 2792 _m
1162 2793 _l 1162 2793 _m
1162 2794 _l 1162 2794 _m
1162 2796 _l 1162 2796 _m
1163 2796 _l 1163 2796 _m
1163 2797 _l 1163 2797 _m
1163 2799 _l 1163 2799 _m
1163 2800 _l 1163 2800 _m
1163 2801 _l 1163 2801 _m
1164 2802 _l 1164 2802 _m
1165 2803 _l 1165 2803 _m
1165 2804 _l 1165 2804 _m
1165 2805 _l 1165 2805 _m
1166 2806 _l 1166 2806 _m
1166 2807 _l 1166 2807 _m
1167 2807 _l 1167 2807 _m
1168 2808 _l 1168 2808 _m
1168 2809 _l 1168 2809 _m
1169 2809 _l 1169 2809 _m
1170 2810 _l 1170 2810 _m
1171 2811 _l 1171 2811 _m
1172 2812 _l 1172 2812 _m
1173 2812 _l 1173 2812 _m
1174 2813 _l 1174 2813 _m
1175 2813 _l 1175 2813 _m
1175 2814 _l 1175 2814 _m
1177 2814 _l 1177 2814 _m
1178 2815 _l 1178 2815 _m
1179 2815 _l 1179 2815 _m
1180 2815 _l 1180 2815 _m
1181 2815 _l _s _s 1180 2817 _m
_sp 1180 2817 1185 2817 1181 2813 3 _pl _pf 
2 _w 0 g _cp _s _s 
1 _w 0 g 1839 2817 _m
_sp 1839 2817 1839 2820 1839 2822 1839 2824 1839 2825 1840 2827 1840 2828 1840 2828 1839 2831 1836 2832 1833 2831 1832 2828 1832 2827 1833 2826 1833 2825 
1833 2824 1833 2822 1833 2821 1834 2819 1834 2817 1830 2816 1827 2815 1824 2814 1822 2812 1820 2809 1818 2806 1817 2803 1817 2800 1817 2795 1819 2791 
1822 2788 1825 2785 1829 2784 1833 2783 1833 2772 1839 2772 1839 2783 1843 2784 1847 2786 1850 2789 1853 2792 1854 2797 1855 2801 1854 2805 1853 2809 
1850 2812 1847 2815 1843 2816 48 _pl _cp 1834 2815 _m
_sp 1834 2815 1833 2786 1830 2787 1827 2789 1825 2792 1823 2795 1823 2800 1823 2805 1825 2808 1827 2811 1830 2813 11 _pl _cp 1839 2815 _m
_sp 1839 2815 1842 2814 1845 2811 1847 2808 1848 2804 1849 2800 1848 2796 1847 2792 1845 2789 1842 2787 1839 2786 11 _pl _cp 
0 g _f _s 632 2603 _m
631 2601 _l 631 2601 _m
629 2600 _l 629 2600 _m
628 2599 _l 628 2599 _m
627 2599 _l 627 2599 _m
626 2598 _l 626 2598 _m
624 2597 _l 624 2597 _m
623 2597 _l 623 2597 _m
622 2596 _l 622 2596 _m
620 2595 _l 620 2595 _m
619 2595 _l 619 2595 _m
617 2595 _l 617 2595 _m
616 2594 _l 616 2594 _m
614 2594 _l 614 2594 _m
613 2594 _l 613 2594 _m
612 2594 _l 612 2594 _m
610 2594 _l 610 2594 _m
609 2594 _l 609 2594 _m
607 2594 _l 607 2594 _m
606 2594 _l 606 2594 _m
604 2594 _l 604 2594 _m
603 2595 _l 603 2595 _m
601 2595 _l 601 2595 _m
600 2595 _l 600 2595 _m
598 2596 _l 598 2596 _m
597 2597 _l 597 2597 _m
596 2597 _l 596 2597 _m
594 2598 _l 594 2598 _m
593 2599 _l 593 2599 _m
592 2599 _l 592 2599 _m
591 2600 _l 591 2600 _m
590 2601 _l 590 2601 _m
589 2603 _l _s _s 587 2600 _m
_sp 587 2600 583 2606 591 2605 3 _pl _pf _np 794 2719 _m
794 2718 _l 794 2718 _m
794 2716 _l 794 2716 _m
795 2715 _l 795 2715 _m
795 2714 _l 795 2714 _m
795 2713 _l 795 2713 _m
795 2712 _l 795 2712 _m
795 2711 _l 795 2711 _m
795 2710 _l 795 2710 _m
795 2709 _l 795 2709 _m
795 2708 _l 795 2708 _m
795 2707 _l 795 2707 _m
795 2706 _l 795 2706 _m
794 2705 _l 794 2705 _m
794 2704 _l 794 2704 _m
794 2703 _l 794 2703 _m
793 2702 _l 793 2702 _m
793 2700 _l 793 2700 _m
792 2700 _l 792 2700 _m
792 2699 _l 792 2699 _m
791 2698 _l 791 2698 _m
791 2697 _l 791 2697 _m
790 2696 _l 790 2696 _m
790 2695 _l 790 2695 _m
789 2694 _l 789 2694 _m
788 2694 _l 788 2694 _m
787 2693 _l 787 2693 _m
786 2692 _l 786 2692 _m
785 2692 _l 785 2692 _m
784 2691 _l 784 2691 _m
783 2691 _l 783 2691 _m
782 2690 _l 782 2690 _m
782 2690 _l _s _s 782 2688 _m
_sp 782 2688 777 2687 781 2692 3 _pl _pf 
3 _w 0 g _cp _s 
_s 1 _w 0 g 541 2785 _m
541 2786 _l 541 2786 _m
540 2787 _l 540 2787 _m
540 2788 _l 540 2788 _m
540 2789 _l 540 2789 _m
539 2790 _l 539 2790 _m
539 2791 _l 539 2791 _m
539 2792 _l 539 2792 _m
539 2793 _l 539 2793 _m
539 2795 _l 539 2795 _m
539 2796 _l 539 2796 _m
540 2796 _l 540 2796 _m
540 2798 _l 540 2798 _m
540 2799 _l 540 2799 _m
541 2800 _l 541 2800 _m
541 2801 _l 541 2801 _m
541 2802 _l 541 2802 _m
542 2803 _l 542 2803 _m
542 2804 _l 542 2804 _m
543 2805 _l 543 2805 _m
543 2806 _l 543 2806 _m
544 2807 _l 544 2807 _m
544 2807 _l 544 2807 _m
545 2808 _l 545 2808 _m
546 2809 _l 546 2809 _m
547 2809 _l 547 2809 _m
547 2810 _l 547 2810 _m
548 2811 _l 548 2811 _m
549 2812 _l 549 2812 _m
550 2812 _l 550 2812 _m
551 2813 _l 551 2813 _m
552 2813 _l 552 2813 _m
553 2814 _l _s _s 552 2816 _m
_sp 552 2816 558 2816 554 2812 3 _pl _pf 
3 _w 0 g _cp _s _s 
1 _w 0 g 1780 2433 _m
_sp 1780 2433 1798 2433 1798 2440 1797 2440 1796 2438 1795 2436 1794 2435 1792 2435 1785 2435 1798 2454 1781 2454 1781 2448 1782 2448 1783 2451 1786 2452 
1792 2452 16 _pl _cp 
0 g _f _s _s 
0 g 1807 2434 _m
_sp 1807 2434 1807 2433 1807 2433 1807 2431 1806 2429 1804 2428 1802 2427 1802 2426 1805 2427 1807 2428 1808 2430 1809 2433 1809 2435 1808 2437 1806 2438 
1805 2438 1803 2437 1802 2435 1803 2434 1804 2433 1806 2433 21 _pl _cp 
0 g _f _s _s 
0 g 1828 2433 _m
_sp 1828 2433 1846 2433 1846 2440 1845 2440 1844 2438 1843 2436 1842 2435 1840 2435 1833 2435 1846 2454 1829 2454 1829 2448 1830 2448 1831 2451 1834 2452 
1840 2452 16 _pl _cp 
0 g _f _s _s 
0 g 1851 2454 _m
_sp 1851 2454 1854 2461 1855 2462 1855 2463 1854 2464 1853 2465 1852 2464 1851 2462 1849 2456 1848 2455 1848 2454 1848 2454 1849 2453 1849 2453 1850 2453 
1851 2454 16 _pl _cp 
0 g _f _s _s _s 1789 2469 _m
_sp 1806 2517 1789 2507 1773 2517 3 _pl _pf _np 
_s 7 _w 0 g 1789 2722 _m
1789 2507 _l _s 
_s 1 _w 0 g _s 2043 2722 _m
_sp 1995 2738 2005 2722 1995 2706 3 _pl _pf _np 
_s 7 _w 0 g 1789 2722 _m
2005 2722 _l _s 
_s 1 _w 0 g _s 1663 2849 _m
_sp 1685 2804 1689 2823 1708 2826 3 _pl _pf _np 
_s 7 _w 0 g 1789 2722 _m
1689 2823 _l _s 
1 _w 0 g 1643 2870 _m
_sp 1643 2870 1639 2864 1638 2862 1637 2861 1635 2860 1634 2860 1634 2859 1642 2859 1642 2860 1640 2860 1640 2861 1640 2862 1641 2864 1644 2868 1647 2864 
1648 2862 1648 2861 1648 2860 1647 2860 1647 2859 1656 2859 1656 2860 1654 2861 1652 2864 1647 2871 1649 2875 1651 2877 1652 2878 1653 2878 1654 2879 
1654 2880 1647 2880 1647 2879 1647 2879 1648 2879 1648 2878 1648 2877 1647 2875 1646 2873 1644 2875 1643 2877 1643 2878 1643 2879 1644 2879 1645 2879 
1645 2880 1635 2880 1635 2879 1636 2878 1638 2878 1639 2877 1640 2875 52 _pl _cp 
0 g _f _s _s 
0 g 2075 2719 _m
_sp 2075 2719 2070 2728 2070 2729 2070 2730 2069 2731 2069 2731 2070 2732 2071 2732 2072 2732 2072 2733 2062 2733 2062 2732 2064 2731 2066 2728 2073 2714 
2071 2709 2070 2707 2069 2707 2068 2706 2068 2706 2067 2707 2066 2707 2065 2707 2065 2707 2063 2706 2062 2705 2063 2703 2066 2702 2067 2702 2069 2703 
2070 2704 2071 2705 2080 2728 2082 2731 2084 2732 2084 2733 2077 2733 2077 2732 2077 2732 2079 2732 2079 2731 2079 2731 2079 2731 2079 2730 2079 2730 
2079 2729 2078 2728 47 _pl _cp 
0 g _f _s _s 
0 g 2025 2646 _m
_sp 2025 2646 2021 2655 2020 2656 2020 2656 2020 2657 2020 2658 2020 2659 2022 2659 2023 2659 2023 2660 2013 2660 2013 2659 2015 2658 2017 2655 2024 2641 
2021 2636 2020 2634 2020 2633 2019 2633 2018 2633 2018 2633 2017 2634 2016 2634 2016 2634 2014 2633 2013 2632 2014 2630 2017 2629 2018 2629 2020 2630 
2021 2631 2022 2632 2031 2655 2033 2658 2035 2659 2035 2660 2028 2660 2028 2659 2028 2659 2029 2659 2030 2658 2030 2658 2030 2658 2030 2657 2030 2656 
2030 2656 2029 2655 47 _pl _cp 
0 g _f _s _s 
0 g 2040 2660 _m
_sp 2040 2660 2042 2667 2043 2668 2043 2669 2043 2670 2042 2670 2041 2670 2039 2668 2037 2661 2037 2661 2037 2660 2037 2660 2037 2659 2038 2659 2039 2659 
2040 2660 16 _pl _cp 
0 g _f _s _s 
0 g 2051 2639 _m
_sp 2051 2639 2051 2639 2051 2638 2051 2636 2050 2635 2048 2634 2046 2633 2046 2632 2049 2633 2052 2634 2053 2636 2054 2639 2054 2641 2053 2643 2051 2644 
2050 2644 2047 2643 2046 2641 2047 2639 2049 2638 2050 2639 21 _pl _cp 
0 g _f _s _s 
0 g 2084 2646 _m
_sp 2084 2646 2080 2655 2080 2656 2079 2656 2079 2657 2079 2658 2080 2659 2081 2659 2082 2659 2082 2660 2072 2660 2072 2659 2074 2658 2076 2655 2083 2641 
2080 2636 2080 2634 2079 2633 2078 2633 2078 2633 2077 2633 2076 2634 2075 2634 2075 2634 2073 2633 2072 2632 2073 2630 2076 2629 2077 2629 2079 2630 
2080 2631 2081 2632 2090 2655 2092 2658 2094 2659 2094 2660 2087 2660 2087 2659 2087 2659 2089 2659 2089 2658 2089 2658 2089 2658 2089 2657 2089 2656 
2089 2656 2088 2655 47 _pl _cp 
0 g _f _s _s 
0 g 2099 2660 _m
_sp 2099 2660 2102 2667 2102 2668 2102 2669 2102 2670 2101 2670 2100 2670 2098 2668 2097 2661 2096 2661 2096 2660 2096 2660 2097 2659 2097 2659 2098 2659 
2099 2660 16 _pl _cp 
0 g _f _s _s 
0 g 2107 2660 _m
_sp 2107 2660 2110 2667 2111 2668 2111 2669 2110 2670 2109 2670 2108 2670 2107 2668 2105 2661 2104 2661 2104 2660 2104 2660 2105 2659 2105 2659 2106 2659 
2107 2660 16 _pl _cp 
0 g _f _s _s 
0 g 1706 2883 _m
_sp 1706 2883 1701 2877 1699 2874 1697 2873 1697 2872 1704 2872 1704 2873 1703 2873 1702 2874 1702 2875 1704 2877 1707 2881 1710 2877 1711 2875 1711 2874 
1710 2873 1709 2873 1709 2872 1719 2872 1719 2873 1718 2873 1717 2874 1715 2875 1714 2877 1709 2885 1712 2888 1713 2890 1714 2891 1715 2891 1717 2892 
1717 2893 1709 2893 1709 2892 1709 2892 1710 2892 1711 2891 1711 2890 1709 2888 1708 2886 1707 2888 1705 2890 1705 2891 1706 2892 1707 2892 1707 2892 
1707 2893 1697 2893 1697 2892 1699 2891 1700 2891 1701 2890 1702 2888 52 _pl _cp 
0 g _f _s _s 
0 g 1723 2894 _m
_sp 1723 2894 1726 2900 1727 2901 1727 2902 1727 2903 1726 2904 1724 2903 1723 2901 1721 2895 1721 2894 1721 2894 1720 2893 1721 2892 1722 2891 1723 2892 
1723 2893 16 _pl _cp 
0 g _f _s _s _s 1718 2856 _m
_sp 1724 2818 1732 2831 1746 2829 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1788 2721 _m
1732 2831 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 2015 2678 _m
_sp 1981 2696 1986 2683 1976 2672 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1788 2721 _m
1986 2683 _l 
_s [] 0 _d 2 _lc 1 _w 0 g 1921 2695 _m
1921 2694 _l 1921 2694 _m
1921 2693 _l 1921 2693 _m
1921 2691 _l 1921 2691 _m
1921 2690 _l 1921 2690 _m
1921 2689 _l 1921 2689 _m
1921 2687 _l 1921 2687 _m
1921 2686 _l 1921 2686 _m
1920 2685 _l 1920 2685 _m
1920 2684 _l 1920 2684 _m
1920 2682 _l 1920 2682 _m
1919 2681 _l 1919 2681 _m
1918 2680 _l 1918 2680 _m
1918 2679 _l 1918 2679 _m
1917 2678 _l 1917 2678 _m
1916 2676 _l 1916 2676 _m
1916 2675 _l 1916 2675 _m
1915 2674 _l 1915 2674 _m
1914 2673 _l 1914 2673 _m
1913 2672 _l 1913 2672 _m
1912 2671 _l 1912 2671 _m
1911 2670 _l 1911 2670 _m
1910 2669 _l 1910 2669 _m
1909 2668 _l 1909 2668 _m
1908 2668 _l 1908 2668 _m
1907 2667 _l 1907 2667 _m
1906 2667 _l 1906 2667 _m
1905 2666 _l 1905 2666 _m
1903 2666 _l 1903 2666 _m
1902 2665 _l 1902 2665 _m
1901 2665 _l 1901 2665 _m
1899 2664 _l 1899 2664 _m
1898 2664 _l _s _s 1899 2661 _m
_sp 1899 2661 1893 2662 1897 2667 3 _pl _pf 
3 _w 0 g _cp _s 
_s 1 _w 0 g 1758 2796 _m
1759 2797 _l 1759 2797 _m
1760 2799 _l 1760 2799 _m
1761 2800 _l 1761 2800 _m
1762 2801 _l 1762 2801 _m
1763 2802 _l 1763 2802 _m
1764 2802 _l 1764 2802 _m
1766 2803 _l 1766 2803 _m
1767 2804 _l 1767 2804 _m
1768 2805 _l 1768 2805 _m
1770 2805 _l 1770 2805 _m
1771 2806 _l 1771 2806 _m
1772 2806 _l 1772 2806 _m
1774 2807 _l 1774 2807 _m
1775 2807 _l 1775 2807 _m
1777 2807 _l 1777 2807 _m
1778 2807 _l 1778 2807 _m
1780 2808 _l 1780 2808 _m
1781 2808 _l 1781 2808 _m
1783 2808 _l 1783 2808 _m
1784 2807 _l 1784 2807 _m
1786 2807 _l 1786 2807 _m
1787 2807 _l 1787 2807 _m
1788 2807 _l 1788 2807 _m
1790 2807 _l 1790 2807 _m
1791 2806 _l 1791 2806 _m
1793 2806 _l 1793 2806 _m
1794 2805 _l 1794 2805 _m
1795 2804 _l 1795 2804 _m
1797 2804 _l 1797 2804 _m
1798 2803 _l 1798 2803 _m
1800 2802 _l 1800 2802 _m
1801 2801 _l _s _s 1802 2804 _m
_sp 1802 2804 1806 2797 1799 2799 3 _pl _pf _np _s _s 1772 2855 _m
_sp 1765 2817 1776 2827 1789 2820 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1789 2722 _m
1776 2827 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 1755 2485 _m
_sp 1773 2520 1759 2514 1749 2523 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1789 2722 _m
1759 2514 _l _s 
[] 0 _d 2 _lc 1 _w 0 g 1773 2884 _m
_sp 1773 2884 1769 2878 1768 2876 1767 2875 1765 2875 1764 2874 1764 2873 1772 2873 1772 2874 1771 2875 1770 2875 1770 2876 1771 2878 1774 2882 1777 2878 
1779 2876 1779 2875 1778 2875 1777 2874 1777 2873 1786 2873 1786 2874 1784 2875 1782 2878 1777 2886 1780 2890 1782 2892 1784 2893 1784 2894 1777 2894 
1777 2893 1777 2893 1778 2893 1779 2892 1778 2891 1777 2890 1776 2888 1774 2890 1773 2891 1773 2892 1773 2893 1774 2893 1775 2893 1775 2894 1765 2894 
1765 2893 1766 2893 1768 2892 1769 2891 1770 2890 50 _pl _cp 
0 g _f _s _s 
0 g 1791 2895 _m
_sp 1791 2895 1794 2901 1794 2902 1794 2903 1794 2904 1793 2905 1792 2904 1791 2902 1789 2896 1788 2896 1788 2895 1788 2894 1789 2893 1789 2893 1790 2894 
1791 2894 16 _pl _cp 
0 g _f _s _s 
0 g 1799 2895 _m
_sp 1799 2895 1802 2901 1803 2902 1803 2903 1802 2904 1801 2905 1800 2904 1799 2902 1797 2896 1797 2896 1797 2895 1797 2894 1797 2893 1798 2893 1799 2894 
1799 2894 16 _pl _cp 
0 g _f _s _s 
0 g 1811 2874 _m
_sp 1811 2874 1811 2873 1811 2873 1811 2871 1810 2870 1808 2868 1806 2867 1806 2866 1809 2867 1812 2868 1813 2871 1814 2873 1814 2875 1813 2877 1811 2878 
1809 2878 1807 2877 1806 2876 1807 2874 1809 2873 1810 2873 21 _pl _cp 
0 g _f _s _s 
0 g 1839 2895 _m
_sp 1839 2895 1838 2895 1831 2893 1831 2891 1832 2891 1834 2891 1835 2888 1835 2878 1834 2875 1832 2874 1831 2874 1831 2873 1842 2873 1842 2874 1841 2874 
1839 2875 1839 2878 1839 2889 1840 2890 1842 2891 1843 2892 1844 2892 1845 2892 1846 2891 1847 2889 1847 2886 1847 2878 1847 2875 1844 2874 1844 2874 
1844 2873 1855 2873 1855 2874 1854 2874 1852 2875 1851 2878 1851 2888 1851 2891 1850 2893 1848 2894 1846 2895 1844 2895 1842 2894 1841 2893 1839 2891 
45 _pl _cp 
0 g _f _s _s 
0 g 1859 2886 _m
_sp 1859 2886 1874 2886 1873 2890 1871 2892 1869 2894 1865 2895 1861 2894 1859 2892 1857 2888 1856 2884 1857 2879 1858 2876 1861 2874 1865 2873 1868 2874 
1871 2875 1873 2878 1875 2881 1874 2881 1873 2879 1871 2878 1869 2876 1867 2876 1864 2877 1861 2879 1860 2882 1859 2886 1859 2886 28 _pl _cp 1869 2888 _m
_sp 1869 2888 1868 2890 1867 2892 1866 2893 1864 2893 1862 2893 1861 2892 1860 2890 1859 2888 9 _pl _cp 
0 g _f _s _s 
0 g 1888 2879 _m
_sp 1888 2879 1883 2890 1883 2891 1883 2891 1883 2892 1883 2892 1883 2893 1885 2893 1885 2893 1885 2894 1876 2894 1876 2893 1878 2892 1879 2890 1886 2873 
1887 2873 1892 2885 1898 2873 1899 2873 1905 2890 1907 2892 1908 2893 1908 2894 1902 2894 1902 2893 1902 2893 1903 2893 1904 2892 1904 2892 1904 2892 
1904 2891 1904 2891 1904 2891 1903 2890 1899 2879 1895 2890 1895 2891 1895 2891 1895 2891 1895 2892 1895 2893 1896 2893 1896 2893 1896 2894 1888 2894 
1888 2893 1890 2892 1891 2890 1892 2888 49 _pl _cp 
0 g _f _s _s 
0 g 1934 2884 _m
_sp 1934 2884 1930 2878 1929 2876 1928 2875 1926 2875 1925 2874 1925 2873 1933 2873 1933 2874 1931 2875 1931 2875 1931 2876 1932 2878 1935 2882 1938 2878 
1939 2876 1939 2875 1939 2875 1938 2874 1938 2873 1947 2873 1947 2874 1945 2875 1943 2878 1938 2886 1940 2890 1942 2891 1943 2892 1944 2893 1945 2893 
1945 2894 1938 2894 1938 2893 1938 2893 1939 2893 1939 2892 1939 2891 1938 2890 1936 2888 1935 2890 1934 2891 1934 2892 1934 2893 1935 2893 1936 2893 
1936 2894 1926 2894 1926 2893 1927 2893 1929 2892 1930 2891 1931 2890 52 _pl _cp 
0 g _f _s _s 
0 g 1724 2443 _m
_sp 1724 2443 1742 2443 1742 2450 1741 2450 1740 2448 1740 2446 1738 2445 1736 2445 1730 2445 1742 2464 1726 2464 1726 2458 1727 2458 1727 2461 1730 2462 
1736 2462 16 _pl _cp 
0 g _f _s _s 
0 g 1747 2465 _m
_sp 1747 2465 1750 2471 1751 2472 1751 2473 1750 2474 1749 2475 1748 2474 1747 2472 1745 2466 1745 2466 1745 2465 1745 2464 1745 2463 1746 2463 1747 2464 
1747 2464 16 _pl _cp 
0 g _f _s _s 
0 g 1756 2465 _m
_sp 1756 2465 1759 2471 1759 2472 1759 2473 1759 2474 1758 2475 1757 2474 1755 2472 1754 2466 1753 2466 1753 2465 1753 2464 1754 2463 1754 2463 1755 2464 
1756 2464 16 _pl _cp 
0 g _f _s 1767 2572 _m
1767 2572 _l 1767 2572 _m
1766 2572 _l 1766 2572 _m
1765 2572 _l 1765 2572 _m
1764 2572 _l 1764 2572 _m
1763 2572 _l 1763 2572 _m
1762 2572 _l 1762 2572 _m
1762 2573 _l 1762 2573 _m
1761 2573 _l 1761 2573 _m
1760 2573 _l 1760 2573 _m
1759 2573 _l 1759 2573 _m
1759 2574 _l 1759 2574 _m
1758 2574 _l 1758 2574 _m
1757 2575 _l 1757 2575 _m
1756 2575 _l 1756 2575 _m
1756 2575 _l 1756 2575 _m
1755 2576 _l 1755 2576 _m
1754 2576 _l 1754 2576 _m
1754 2577 _l 1754 2577 _m
1753 2577 _l 1753 2577 _m
1753 2578 _l 1753 2578 _m
1752 2578 _l 1752 2578 _m
1752 2579 _l 1752 2579 _m
1752 2579 _l 1752 2579 _m
1751 2580 _l 1751 2580 _m
1750 2581 _l 1750 2581 _m
1750 2582 _l 1750 2582 _m
1750 2582 _l 1750 2582 _m
1749 2583 _l 1749 2583 _m
1749 2584 _l 1749 2584 _m
1749 2584 _l 1749 2584 _m
1749 2585 _l 1749 2585 _m
1749 2586 _l _s _s 1747 2585 _m
_sp 1747 2585 1748 2589 1750 2586 3 _pl _pf _np _s _s 1964 2621 _m
_sp 1937 2649 1939 2634 1926 2628 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1786 2718 _m
1939 2634 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 1726 2527 _m
_sp 1750 2557 1735 2554 1727 2565 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1788 2718 _m
1735 2554 _l _s 
[] 0 _d 2 _lc 1 _w 0 g 1932 2588 _m
_sp 1932 2588 1932 2588 1925 2585 1925 2584 1926 2584 1928 2583 1929 2580 1929 2570 1928 2567 1926 2566 1925 2566 1925 2566 1936 2566 1936 2566 1935 2566 
1933 2567 1932 2570 1932 2581 1934 2583 1935 2584 1937 2584 1938 2584 1939 2584 1940 2583 1941 2581 1941 2578 1941 2570 1940 2567 1938 2566 1938 2566 
1938 2566 1949 2566 1949 2566 1948 2566 1945 2567 1945 2570 1945 2580 1945 2583 1944 2585 1942 2586 1939 2587 1937 2587 1936 2586 1934 2585 1932 2583 
45 _pl _cp 
0 g _f _s _s 
0 g 1953 2578 _m
_sp 1953 2578 1968 2578 1967 2582 1965 2585 1962 2586 1959 2587 1955 2586 1952 2584 1950 2580 1949 2576 1950 2571 1952 2568 1954 2566 1958 2565 1961 2566 
1964 2567 1967 2570 1969 2573 1968 2573 1966 2571 1965 2570 1963 2568 1961 2568 1958 2569 1955 2571 1954 2574 1953 2578 1953 2578 28 _pl _cp 1963 2580 _m
_sp 1963 2580 1962 2582 1961 2584 1960 2585 1958 2585 1957 2585 1955 2584 1954 2582 1953 2580 9 _pl _cp 
0 g _f _s _s 
0 g 1982 2571 _m
_sp 1982 2571 1977 2582 1977 2583 1977 2583 1976 2584 1976 2584 1977 2585 1978 2585 1979 2585 1979 2586 1970 2586 1970 2585 1972 2584 1973 2582 1980 2565 
1981 2565 1986 2577 1992 2565 1992 2565 1999 2582 2001 2584 2002 2585 2002 2586 1996 2586 1996 2585 1996 2585 1997 2585 1998 2584 1998 2584 1998 2584 
1998 2584 1997 2583 1997 2583 1997 2582 1993 2571 1989 2582 1989 2583 1988 2583 1988 2584 1988 2584 1989 2585 1990 2585 1990 2585 1990 2586 1982 2586 
1982 2585 1983 2584 1985 2582 1985 2580 49 _pl _cp 
0 g _f _s _s 
0 g 2031 2572 _m
_sp 2031 2572 2027 2582 2027 2583 2026 2583 2026 2584 2026 2584 2027 2585 2028 2585 2029 2585 2029 2586 2019 2586 2019 2585 2021 2584 2023 2582 2030 2568 
2027 2563 2027 2561 2026 2560 2025 2559 2024 2559 2024 2560 2023 2560 2022 2560 2022 2560 2020 2559 2019 2558 2020 2556 2023 2555 2024 2555 2026 2556 
2027 2558 2028 2559 2037 2582 2039 2584 2041 2585 2041 2586 2034 2586 2034 2585 2034 2585 2036 2585 2036 2584 2036 2584 2036 2584 2036 2584 2036 2583 
2036 2583 2035 2582 47 _pl _cp 
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1619 2502 1618 2505 1618 2516 1620 2518 1621 2519 1623 2520 1624 2520 1625 2520 1626 2518 1627 2516 1627 2513 1627 2505 1626 2502 1624 2502 1624 2502 
1624 2501 1634 2501 1634 2502 1633 2502 1631 2502 1631 2505 1631 2516 1631 2518 1630 2520 1628 2521 1625 2522 1623 2522 1622 2521 1620 2520 1618 2518 
45 _pl _cp 
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1650 2502 1652 2505 1654 2508 1653 2509 1652 2506 1651 2505 1649 2504 1646 2503 1643 2504 1641 2506 1640 2509 1639 2513 1639 2513 28 _pl _cp 1648 2515 _m
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1666 2500 1672 2513 1678 2500 1678 2500 1685 2517 1687 2520 1688 2520 1688 2522 1682 2522 1682 2520 1682 2520 1683 2520 1684 2519 1684 2519 1684 2519 
1684 2519 1683 2518 1683 2518 1683 2517 1679 2506 1675 2517 1674 2518 1674 2518 1674 2519 1674 2519 1675 2520 1676 2520 1676 2520 1676 2522 1667 2522 
1667 2520 1669 2520 1671 2517 1671 2515 49 _pl _cp 
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1718 2520 16 _pl _cp 
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530 2609 530 2607 530 2599 530 2596 530 2593 531 2592 532 2590 534 2588 537 2586 540 2585 543 2585 543 2571 548 2571 548 2585 553 2585 
556 2587 559 2590 560 2594 561 2599 561 2607 561 2609 561 2611 562 2612 564 2612 565 2612 565 2612 565 2612 566 2612 566 2615 563 2615 
560 2616 557 2616 555 2616 555 2599 555 2594 553 2591 551 2589 548 2588 548 2627 54 _pl _cp 
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608 2452 16 _pl _cp 
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621 2438 619 2437 618 2435 619 2434 620 2433 622 2433 21 _pl _cp 
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656 2452 16 _pl _cp 
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667 2454 16 _pl _cp 
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466 2862 466 2861 466 2860 465 2860 465 2859 474 2859 474 2860 472 2861 470 2864 465 2871 467 2875 468 2877 470 2878 471 2878 472 2879 
472 2880 465 2880 465 2879 465 2879 466 2879 466 2878 466 2877 465 2875 464 2873 462 2875 461 2877 461 2878 461 2879 462 2879 463 2879 
463 2880 453 2880 453 2879 454 2878 456 2878 457 2877 458 2875 52 _pl _cp 
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889 2709 888 2707 887 2707 886 2706 886 2706 885 2707 884 2707 883 2707 883 2707 881 2706 880 2705 881 2703 884 2702 885 2702 887 2703 
888 2704 889 2705 898 2728 900 2731 902 2732 902 2733 895 2733 895 2732 896 2732 897 2732 897 2731 897 2731 897 2731 897 2730 897 2730 
897 2729 897 2728 47 _pl _cp 
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839 2640 838 2638 837 2638 836 2637 836 2637 835 2638 834 2638 834 2638 833 2638 832 2637 831 2636 832 2634 834 2633 835 2633 837 2634 
838 2635 839 2637 849 2659 850 2662 852 2663 852 2664 845 2664 845 2663 846 2663 847 2663 848 2662 848 2662 848 2662 848 2661 847 2661 
847 2660 847 2659 47 _pl _cp 
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857 2664 16 _pl _cp 
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529 2875 529 2874 528 2873 527 2873 527 2872 536 2872 536 2873 534 2874 532 2877 527 2885 530 2888 532 2891 534 2892 534 2893 527 2893 
527 2892 527 2892 528 2892 529 2891 528 2890 527 2888 526 2886 525 2888 523 2890 523 2891 523 2892 525 2892 525 2892 525 2893 515 2893 
515 2892 516 2891 518 2891 519 2890 520 2888 50 _pl _cp 
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541 2893 16 _pl _cp 
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[] 0 _d 2 _lc 1 _w 0 g 1356 2637 _m
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1327 2634 1327 2628 1328 2622 1330 2618 1332 2614 1334 2612 1337 2610 1341 2610 1345 2611 1348 2612 1351 2614 1353 2617 1354 2620 1355 2623 1355 2626 
1356 2630 1356 2635 1356 2636 33 _pl _cp 1333 2639 _m
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1333 2634 1333 2635 1333 2636 18 _pl _cp 
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1201 2452 16 _pl _cp 
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1214 2438 1212 2437 1211 2435 1212 2434 1214 2433 1215 2433 21 _pl _cp 
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1249 2452 16 _pl _cp 
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1260 2454 16 _pl _cp 
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1199 2507 _l _s 
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1414 2722 _l _s 
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1057 2862 1057 2861 1057 2860 1056 2860 1056 2859 1065 2859 1065 2860 1063 2861 1061 2864 1056 2871 1059 2875 1061 2878 1063 2879 1063 2880 1056 2880 
1056 2879 1056 2879 1057 2879 1057 2878 1057 2877 1056 2875 1055 2873 1053 2875 1052 2877 1052 2878 1052 2879 1053 2879 1054 2879 1054 2880 1044 2880 
1044 2879 1045 2878 1047 2878 1048 2877 1049 2875 50 _pl _cp 
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1479 2709 1479 2707 1478 2707 1477 2706 1477 2706 1476 2707 1475 2707 1474 2707 1474 2707 1472 2706 1471 2705 1472 2703 1475 2702 1476 2702 1478 2703 
1479 2704 1480 2705 1489 2728 1491 2731 1493 2732 1493 2733 1486 2733 1486 2732 1486 2732 1488 2732 1488 2731 1488 2731 1488 2731 1488 2730 1488 2730 
1488 2729 1487 2728 47 _pl _cp 
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1430 2636 1429 2634 1428 2633 1427 2633 1427 2633 1426 2633 1425 2634 1425 2634 1424 2634 1423 2633 1422 2632 1423 2630 1425 2629 1427 2629 1429 2630 
1430 2631 1430 2632 1440 2655 1441 2658 1443 2659 1443 2660 1436 2660 1436 2659 1437 2659 1438 2659 1439 2658 1439 2658 1439 2658 1439 2657 1438 2656 
1438 2656 1438 2655 47 _pl _cp 
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1448 2660 16 _pl _cp 
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1458 2644 1456 2643 1455 2641 1456 2639 1458 2638 1459 2639 21 _pl _cp 
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1489 2636 1488 2634 1488 2633 1487 2633 1486 2633 1485 2633 1484 2634 1484 2634 1484 2634 1482 2633 1481 2632 1482 2630 1484 2629 1486 2629 1488 2630 
1489 2631 1490 2632 1499 2655 1501 2658 1502 2659 1502 2660 1496 2660 1496 2659 1496 2659 1497 2659 1498 2658 1498 2658 1498 2658 1498 2657 1497 2656 
1497 2656 1497 2655 47 _pl _cp 
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1507 2660 16 _pl _cp 
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1516 2660 16 _pl _cp 
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_sp 1115 2883 1111 2877 1110 2875 1109 2874 1107 2873 1106 2873 1106 2872 1113 2872 1113 2873 1112 2873 1112 2874 1112 2875 1113 2877 1116 2881 1119 2877 
1120 2875 1120 2874 1119 2873 1118 2873 1118 2872 1128 2872 1128 2873 1127 2873 1126 2874 1124 2875 1123 2877 1118 2885 1121 2888 1122 2890 1124 2891 
1125 2891 1126 2892 1126 2893 1118 2893 1118 2892 1119 2892 1120 2892 1120 2891 1120 2890 1119 2888 1117 2886 1116 2888 1114 2890 1114 2891 1115 2892 
1116 2892 1117 2892 1117 2893 1106 2893 1106 2892 1108 2891 1109 2891 1110 2890 1112 2888 54 _pl _cp 
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1133 2893 16 _pl _cp 
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1140 2831 _l _s 
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1187 2876 1187 2875 1187 2875 1186 2874 1186 2873 1195 2873 1195 2874 1193 2875 1191 2878 1186 2886 1188 2890 1189 2891 1191 2892 1192 2893 1193 2893 
1193 2894 1186 2894 1186 2893 1186 2893 1187 2893 1187 2892 1187 2891 1186 2890 1185 2888 1183 2890 1182 2891 1182 2892 1182 2893 1183 2893 1184 2893 
1184 2894 1174 2894 1174 2893 1175 2893 1177 2892 1178 2891 1179 2890 52 _pl _cp 
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1200 2894 16 _pl _cp 
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1208 2894 16 _pl _cp 
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1145 2462 16 _pl _cp 
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1156 2464 16 _pl _cp 
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1165 2464 16 _pl _cp 
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_sp 1839 2817 1839 2820 1839 2822 1839 2824 1839 2825 1840 2827 1840 2828 1840 2828 1839 2831 1836 2832 1833 2831 1832 2828 1832 2827 1833 2826 1833 2825 
1833 2824 1833 2822 1833 2821 1834 2819 1834 2817 1830 2816 1827 2815 1824 2814 1822 2812 1820 2809 1818 2806 1817 2803 1817 2800 1817 2795 1819 2791 
1822 2788 1825 2785 1829 2784 1833 2783 1833 2772 1839 2772 1839 2783 1843 2784 1847 2786 1850 2789 1853 2792 1854 2797 1855 2801 1854 2805 1853 2809 
1850 2812 1847 2815 1843 2816 48 _pl _cp 1834 2815 _m
_sp 1834 2815 1833 2786 1830 2787 1827 2789 1825 2792 1823 2795 1823 2800 1823 2805 1825 2808 1827 2811 1830 2813 11 _pl _cp 1839 2815 _m
_sp 1839 2815 1842 2814 1845 2811 1847 2808 1848 2804 1849 2800 1848 2796 1847 2792 1845 2789 1842 2787 1839 2786 11 _pl _cp 
0 g _f _s 632 2603 _m
631 2601 _l 631 2601 _m
629 2600 _l 629 2600 _m
628 2599 _l 628 2599 _m
627 2599 _l 627 2599 _m
626 2598 _l 626 2598 _m
624 2597 _l 624 2597 _m
623 2597 _l 623 2597 _m
622 2596 _l 622 2596 _m
620 2595 _l 620 2595 _m
619 2595 _l 619 2595 _m
617 2595 _l 617 2595 _m
616 2594 _l 616 2594 _m
614 2594 _l 614 2594 _m
613 2594 _l 613 2594 _m
612 2594 _l 612 2594 _m
610 2594 _l 610 2594 _m
609 2594 _l 609 2594 _m
607 2594 _l 607 2594 _m
606 2594 _l 606 2594 _m
604 2594 _l 604 2594 _m
603 2595 _l 603 2595 _m
601 2595 _l 601 2595 _m
600 2595 _l 600 2595 _m
598 2596 _l 598 2596 _m
597 2597 _l 597 2597 _m
596 2597 _l 596 2597 _m
594 2598 _l 594 2598 _m
593 2599 _l 593 2599 _m
592 2599 _l 592 2599 _m
591 2600 _l 591 2600 _m
590 2601 _l 590 2601 _m
589 2603 _l _s _s 587 2600 _m
_sp 587 2600 583 2606 591 2605 3 _pl _pf _np 794 2719 _m
794 2718 _l 794 2718 _m
794 2716 _l 794 2716 _m
795 2715 _l 795 2715 _m
795 2714 _l 795 2714 _m
795 2713 _l 795 2713 _m
795 2712 _l 795 2712 _m
795 2711 _l 795 2711 _m
795 2710 _l 795 2710 _m
795 2709 _l 795 2709 _m
795 2708 _l 795 2708 _m
795 2707 _l 795 2707 _m
795 2706 _l 795 2706 _m
794 2705 _l 794 2705 _m
794 2704 _l 794 2704 _m
794 2703 _l 794 2703 _m
793 2702 _l 793 2702 _m
793 2700 _l 793 2700 _m
792 2700 _l 792 2700 _m
792 2699 _l 792 2699 _m
791 2698 _l 791 2698 _m
791 2697 _l 791 2697 _m
790 2696 _l 790 2696 _m
790 2695 _l 790 2695 _m
789 2694 _l 789 2694 _m
788 2694 _l 788 2694 _m
787 2693 _l 787 2693 _m
786 2692 _l 786 2692 _m
785 2692 _l 785 2692 _m
784 2691 _l 784 2691 _m
783 2691 _l 783 2691 _m
782 2690 _l 782 2690 _m
782 2690 _l _s _s 782 2688 _m
_sp 782 2688 777 2687 781 2692 3 _pl _pf 
3 _w 0 g _cp _s 
_s 1 _w 0 g 541 2785 _m
541 2786 _l 541 2786 _m
540 2787 _l 540 2787 _m
540 2788 _l 540 2788 _m
540 2789 _l 540 2789 _m
539 2790 _l 539 2790 _m
539 2791 _l 539 2791 _m
539 2792 _l 539 2792 _m
539 2793 _l 539 2793 _m
539 2795 _l 539 2795 _m
539 2796 _l 539 2796 _m
540 2796 _l 540 2796 _m
540 2798 _l 540 2798 _m
540 2799 _l 540 2799 _m
541 2800 _l 541 2800 _m
541 2801 _l 541 2801 _m
541 2802 _l 541 2802 _m
542 2803 _l 542 2803 _m
542 2804 _l 542 2804 _m
543 2805 _l 543 2805 _m
543 2806 _l 543 2806 _m
544 2807 _l 544 2807 _m
544 2807 _l 544 2807 _m
545 2808 _l 545 2808 _m
546 2809 _l 546 2809 _m
547 2809 _l 547 2809 _m
547 2810 _l 547 2810 _m
548 2811 _l 548 2811 _m
549 2812 _l 549 2812 _m
550 2812 _l 550 2812 _m
551 2813 _l 551 2813 _m
552 2813 _l 552 2813 _m
553 2814 _l _s _s 552 2816 _m
_sp 552 2816 558 2816 554 2812 3 _pl _pf 
3 _w 0 g _cp _s _s 
1 _w 0 g 1780 2433 _m
_sp 1780 2433 1798 2433 1798 2440 1797 2440 1796 2438 1795 2436 1794 2435 1792 2435 1785 2435 1798 2454 1781 2454 1781 2448 1782 2448 1783 2451 1786 2452 
1792 2452 16 _pl _cp 
0 g _f _s _s 
0 g 1807 2434 _m
_sp 1807 2434 1807 2433 1807 2433 1807 2431 1806 2429 1804 2428 1802 2427 1802 2426 1805 2427 1807 2428 1808 2430 1809 2433 1809 2435 1808 2437 1806 2438 
1805 2438 1803 2437 1802 2435 1803 2434 1804 2433 1806 2433 21 _pl _cp 
0 g _f _s _s 
0 g 1828 2433 _m
_sp 1828 2433 1846 2433 1846 2440 1845 2440 1844 2438 1843 2436 1842 2435 1840 2435 1833 2435 1846 2454 1829 2454 1829 2448 1830 2448 1831 2451 1834 2452 
1840 2452 16 _pl _cp 
0 g _f _s _s 
0 g 1851 2454 _m
_sp 1851 2454 1854 2461 1855 2462 1855 2463 1854 2464 1853 2465 1852 2464 1851 2462 1849 2456 1848 2455 1848 2454 1848 2454 1849 2453 1849 2453 1850 2453 
1851 2454 16 _pl _cp 
0 g _f _s _s _s 1789 2469 _m
_sp 1806 2517 1789 2507 1773 2517 3 _pl _pf _np 
_s 7 _w 0 g 1789 2722 _m
1789 2507 _l _s 
_s 1 _w 0 g _s 2043 2722 _m
_sp 1995 2738 2005 2722 1995 2706 3 _pl _pf _np 
_s 7 _w 0 g 1789 2722 _m
2005 2722 _l _s 
_s 1 _w 0 g _s 1663 2849 _m
_sp 1685 2804 1689 2823 1708 2826 3 _pl _pf _np 
_s 7 _w 0 g 1789 2722 _m
1689 2823 _l _s 
1 _w 0 g 1643 2870 _m
_sp 1643 2870 1639 2864 1638 2862 1637 2861 1635 2860 1634 2860 1634 2859 1642 2859 1642 2860 1640 2860 1640 2861 1640 2862 1641 2864 1644 2868 1647 2864 
1648 2862 1648 2861 1648 2860 1647 2860 1647 2859 1656 2859 1656 2860 1654 2861 1652 2864 1647 2871 1649 2875 1651 2877 1652 2878 1653 2878 1654 2879 
1654 2880 1647 2880 1647 2879 1647 2879 1648 2879 1648 2878 1648 2877 1647 2875 1646 2873 1644 2875 1643 2877 1643 2878 1643 2879 1644 2879 1645 2879 
1645 2880 1635 2880 1635 2879 1636 2878 1638 2878 1639 2877 1640 2875 52 _pl _cp 
0 g _f _s _s 
0 g 2075 2719 _m
_sp 2075 2719 2070 2728 2070 2729 2070 2730 2069 2731 2069 2731 2070 2732 2071 2732 2072 2732 2072 2733 2062 2733 2062 2732 2064 2731 2066 2728 2073 2714 
2071 2709 2070 2707 2069 2707 2068 2706 2068 2706 2067 2707 2066 2707 2065 2707 2065 2707 2063 2706 2062 2705 2063 2703 2066 2702 2067 2702 2069 2703 
2070 2704 2071 2705 2080 2728 2082 2731 2084 2732 2084 2733 2077 2733 2077 2732 2077 2732 2079 2732 2079 2731 2079 2731 2079 2731 2079 2730 2079 2730 
2079 2729 2078 2728 47 _pl _cp 
0 g _f _s _s 
0 g 2025 2646 _m
_sp 2025 2646 2021 2655 2020 2656 2020 2656 2020 2657 2020 2658 2020 2659 2022 2659 2023 2659 2023 2660 2013 2660 2013 2659 2015 2658 2017 2655 2024 2641 
2021 2636 2020 2634 2020 2633 2019 2633 2018 2633 2018 2633 2017 2634 2016 2634 2016 2634 2014 2633 2013 2632 2014 2630 2017 2629 2018 2629 2020 2630 
2021 2631 2022 2632 2031 2655 2033 2658 2035 2659 2035 2660 2028 2660 2028 2659 2028 2659 2029 2659 2030 2658 2030 2658 2030 2658 2030 2657 2030 2656 
2030 2656 2029 2655 47 _pl _cp 
0 g _f _s _s 
0 g 2040 2660 _m
_sp 2040 2660 2042 2667 2043 2668 2043 2669 2043 2670 2042 2670 2041 2670 2039 2668 2037 2661 2037 2661 2037 2660 2037 2660 2037 2659 2038 2659 2039 2659 
2040 2660 16 _pl _cp 
0 g _f _s _s 
0 g 2051 2639 _m
_sp 2051 2639 2051 2639 2051 2638 2051 2636 2050 2635 2048 2634 2046 2633 2046 2632 2049 2633 2052 2634 2053 2636 2054 2639 2054 2641 2053 2643 2051 2644 
2050 2644 2047 2643 2046 2641 2047 2639 2049 2638 2050 2639 21 _pl _cp 
0 g _f _s _s 
0 g 2084 2646 _m
_sp 2084 2646 2080 2655 2080 2656 2079 2656 2079 2657 2079 2658 2080 2659 2081 2659 2082 2659 2082 2660 2072 2660 2072 2659 2074 2658 2076 2655 2083 2641 
2080 2636 2080 2634 2079 2633 2078 2633 2078 2633 2077 2633 2076 2634 2075 2634 2075 2634 2073 2633 2072 2632 2073 2630 2076 2629 2077 2629 2079 2630 
2080 2631 2081 2632 2090 2655 2092 2658 2094 2659 2094 2660 2087 2660 2087 2659 2087 2659 2089 2659 2089 2658 2089 2658 2089 2658 2089 2657 2089 2656 
2089 2656 2088 2655 47 _pl _cp 
0 g _f _s _s 
0 g 2099 2660 _m
_sp 2099 2660 2102 2667 2102 2668 2102 2669 2102 2670 2101 2670 2100 2670 2098 2668 2097 2661 2096 2661 2096 2660 2096 2660 2097 2659 2097 2659 2098 2659 
2099 2660 16 _pl _cp 
0 g _f _s _s 
0 g 2107 2660 _m
_sp 2107 2660 2110 2667 2111 2668 2111 2669 2110 2670 2109 2670 2108 2670 2107 2668 2105 2661 2104 2661 2104 2660 2104 2660 2105 2659 2105 2659 2106 2659 
2107 2660 16 _pl _cp 
0 g _f _s _s 
0 g 1706 2883 _m
_sp 1706 2883 1701 2877 1699 2874 1697 2873 1697 2872 1704 2872 1704 2873 1703 2873 1702 2874 1702 2875 1704 2877 1707 2881 1710 2877 1711 2875 1711 2874 
1710 2873 1709 2873 1709 2872 1719 2872 1719 2873 1718 2873 1717 2874 1715 2875 1714 2877 1709 2885 1712 2888 1713 2890 1714 2891 1715 2891 1717 2892 
1717 2893 1709 2893 1709 2892 1709 2892 1710 2892 1711 2891 1711 2890 1709 2888 1708 2886 1707 2888 1705 2890 1705 2891 1706 2892 1707 2892 1707 2892 
1707 2893 1697 2893 1697 2892 1699 2891 1700 2891 1701 2890 1702 2888 52 _pl _cp 
0 g _f _s _s 
0 g 1723 2894 _m
_sp 1723 2894 1726 2900 1727 2901 1727 2902 1727 2903 1726 2904 1724 2903 1723 2901 1721 2895 1721 2894 1721 2894 1720 2893 1721 2892 1722 2891 1723 2892 
1723 2893 16 _pl _cp 
0 g _f _s _s _s 1718 2856 _m
_sp 1724 2818 1732 2831 1746 2829 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1788 2721 _m
1732 2831 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 2015 2678 _m
_sp 1981 2696 1986 2683 1976 2672 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1788 2721 _m
1986 2683 _l 
_s [] 0 _d 2 _lc 1 _w 0 g 1921 2695 _m
1921 2694 _l 1921 2694 _m
1921 2693 _l 1921 2693 _m
1921 2691 _l 1921 2691 _m
1921 2690 _l 1921 2690 _m
1921 2689 _l 1921 2689 _m
1921 2687 _l 1921 2687 _m
1921 2686 _l 1921 2686 _m
1920 2685 _l 1920 2685 _m
1920 2684 _l 1920 2684 _m
1920 2682 _l 1920 2682 _m
1919 2681 _l 1919 2681 _m
1918 2680 _l 1918 2680 _m
1918 2679 _l 1918 2679 _m
1917 2678 _l 1917 2678 _m
1916 2676 _l 1916 2676 _m
1916 2675 _l 1916 2675 _m
1915 2674 _l 1915 2674 _m
1914 2673 _l 1914 2673 _m
1913 2672 _l 1913 2672 _m
1912 2671 _l 1912 2671 _m
1911 2670 _l 1911 2670 _m
1910 2669 _l 1910 2669 _m
1909 2668 _l 1909 2668 _m
1908 2668 _l 1908 2668 _m
1907 2667 _l 1907 2667 _m
1906 2667 _l 1906 2667 _m
1905 2666 _l 1905 2666 _m
1903 2666 _l 1903 2666 _m
1902 2665 _l 1902 2665 _m
1901 2665 _l 1901 2665 _m
1899 2664 _l 1899 2664 _m
1898 2664 _l _s _s 1899 2661 _m
_sp 1899 2661 1893 2662 1897 2667 3 _pl _pf 
3 _w 0 g _cp _s 
_s 1 _w 0 g 1758 2796 _m
1759 2797 _l 1759 2797 _m
1760 2799 _l 1760 2799 _m
1761 2800 _l 1761 2800 _m
1762 2801 _l 1762 2801 _m
1763 2802 _l 1763 2802 _m
1764 2802 _l 1764 2802 _m
1766 2803 _l 1766 2803 _m
1767 2804 _l 1767 2804 _m
1768 2805 _l 1768 2805 _m
1770 2805 _l 1770 2805 _m
1771 2806 _l 1771 2806 _m
1772 2806 _l 1772 2806 _m
1774 2807 _l 1774 2807 _m
1775 2807 _l 1775 2807 _m
1777 2807 _l 1777 2807 _m
1778 2807 _l 1778 2807 _m
1780 2808 _l 1780 2808 _m
1781 2808 _l 1781 2808 _m
1783 2808 _l 1783 2808 _m
1784 2807 _l 1784 2807 _m
1786 2807 _l 1786 2807 _m
1787 2807 _l 1787 2807 _m
1788 2807 _l 1788 2807 _m
1790 2807 _l 1790 2807 _m
1791 2806 _l 1791 2806 _m
1793 2806 _l 1793 2806 _m
1794 2805 _l 1794 2805 _m
1795 2804 _l 1795 2804 _m
1797 2804 _l 1797 2804 _m
1798 2803 _l 1798 2803 _m
1800 2802 _l 1800 2802 _m
1801 2801 _l _s _s 1802 2804 _m
_sp 1802 2804 1806 2797 1799 2799 3 _pl _pf _np _s _s 1772 2855 _m
_sp 1765 2817 1776 2827 1789 2820 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1789 2722 _m
1776 2827 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 1755 2485 _m
_sp 1773 2520 1759 2514 1749 2523 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1789 2722 _m
1759 2514 _l _s 
[] 0 _d 2 _lc 1 _w 0 g 1773 2884 _m
_sp 1773 2884 1769 2878 1768 2876 1767 2875 1765 2875 1764 2874 1764 2873 1772 2873 1772 2874 1771 2875 1770 2875 1770 2876 1771 2878 1774 2882 1777 2878 
1779 2876 1779 2875 1778 2875 1777 2874 1777 2873 1786 2873 1786 2874 1784 2875 1782 2878 1777 2886 1780 2890 1782 2892 1784 2893 1784 2894 1777 2894 
1777 2893 1777 2893 1778 2893 1779 2892 1778 2891 1777 2890 1776 2888 1774 2890 1773 2891 1773 2892 1773 2893 1774 2893 1775 2893 1775 2894 1765 2894 
1765 2893 1766 2893 1768 2892 1769 2891 1770 2890 50 _pl _cp 
0 g _f _s _s 
0 g 1791 2895 _m
_sp 1791 2895 1794 2901 1794 2902 1794 2903 1794 2904 1793 2905 1792 2904 1791 2902 1789 2896 1788 2896 1788 2895 1788 2894 1789 2893 1789 2893 1790 2894 
1791 2894 16 _pl _cp 
0 g _f _s _s 
0 g 1799 2895 _m
_sp 1799 2895 1802 2901 1803 2902 1803 2903 1802 2904 1801 2905 1800 2904 1799 2902 1797 2896 1797 2896 1797 2895 1797 2894 1797 2893 1798 2893 1799 2894 
1799 2894 16 _pl _cp 
0 g _f _s _s 
0 g 1811 2874 _m
_sp 1811 2874 1811 2873 1811 2873 1811 2871 1810 2870 1808 2868 1806 2867 1806 2866 1809 2867 1812 2868 1813 2871 1814 2873 1814 2875 1813 2877 1811 2878 
1809 2878 1807 2877 1806 2876 1807 2874 1809 2873 1810 2873 21 _pl _cp 
0 g _f _s _s 
0 g 1839 2895 _m
_sp 1839 2895 1838 2895 1831 2893 1831 2891 1832 2891 1834 2891 1835 2888 1835 2878 1834 2875 1832 2874 1831 2874 1831 2873 1842 2873 1842 2874 1841 2874 
1839 2875 1839 2878 1839 2889 1840 2890 1842 2891 1843 2892 1844 2892 1845 2892 1846 2891 1847 2889 1847 2886 1847 2878 1847 2875 1844 2874 1844 2874 
1844 2873 1855 2873 1855 2874 1854 2874 1852 2875 1851 2878 1851 2888 1851 2891 1850 2893 1848 2894 1846 2895 1844 2895 1842 2894 1841 2893 1839 2891 
45 _pl _cp 
0 g _f _s _s 
0 g 1859 2886 _m
_sp 1859 2886 1874 2886 1873 2890 1871 2892 1869 2894 1865 2895 1861 2894 1859 2892 1857 2888 1856 2884 1857 2879 1858 2876 1861 2874 1865 2873 1868 2874 
1871 2875 1873 2878 1875 2881 1874 2881 1873 2879 1871 2878 1869 2876 1867 2876 1864 2877 1861 2879 1860 2882 1859 2886 1859 2886 28 _pl _cp 1869 2888 _m
_sp 1869 2888 1868 2890 1867 2892 1866 2893 1864 2893 1862 2893 1861 2892 1860 2890 1859 2888 9 _pl _cp 
0 g _f _s _s 
0 g 1888 2879 _m
_sp 1888 2879 1883 2890 1883 2891 1883 2891 1883 2892 1883 2892 1883 2893 1885 2893 1885 2893 1885 2894 1876 2894 1876 2893 1878 2892 1879 2890 1886 2873 
1887 2873 1892 2885 1898 2873 1899 2873 1905 2890 1907 2892 1908 2893 1908 2894 1902 2894 1902 2893 1902 2893 1903 2893 1904 2892 1904 2892 1904 2892 
1904 2891 1904 2891 1904 2891 1903 2890 1899 2879 1895 2890 1895 2891 1895 2891 1895 2891 1895 2892 1895 2893 1896 2893 1896 2893 1896 2894 1888 2894 
1888 2893 1890 2892 1891 2890 1892 2888 49 _pl _cp 
0 g _f _s _s 
0 g 1934 2884 _m
_sp 1934 2884 1930 2878 1929 2876 1928 2875 1926 2875 1925 2874 1925 2873 1933 2873 1933 2874 1931 2875 1931 2875 1931 2876 1932 2878 1935 2882 1938 2878 
1939 2876 1939 2875 1939 2875 1938 2874 1938 2873 1947 2873 1947 2874 1945 2875 1943 2878 1938 2886 1940 2890 1942 2891 1943 2892 1944 2893 1945 2893 
1945 2894 1938 2894 1938 2893 1938 2893 1939 2893 1939 2892 1939 2891 1938 2890 1936 2888 1935 2890 1934 2891 1934 2892 1934 2893 1935 2893 1936 2893 
1936 2894 1926 2894 1926 2893 1927 2893 1929 2892 1930 2891 1931 2890 52 _pl _cp 
0 g _f _s _s 
0 g 1724 2443 _m
_sp 1724 2443 1742 2443 1742 2450 1741 2450 1740 2448 1740 2446 1738 2445 1736 2445 1730 2445 1742 2464 1726 2464 1726 2458 1727 2458 1727 2461 1730 2462 
1736 2462 16 _pl _cp 
0 g _f _s _s 
0 g 1747 2465 _m
_sp 1747 2465 1750 2471 1751 2472 1751 2473 1750 2474 1749 2475 1748 2474 1747 2472 1745 2466 1745 2466 1745 2465 1745 2464 1745 2463 1746 2463 1747 2464 
1747 2464 16 _pl _cp 
0 g _f _s _s 
0 g 1756 2465 _m
_sp 1756 2465 1759 2471 1759 2472 1759 2473 1759 2474 1758 2475 1757 2474 1755 2472 1754 2466 1753 2466 1753 2465 1753 2464 1754 2463 1754 2463 1755 2464 
1756 2464 16 _pl _cp 
0 g _f _s 1767 2572 _m
1767 2572 _l 1767 2572 _m
1766 2572 _l 1766 2572 _m
1765 2572 _l 1765 2572 _m
1764 2572 _l 1764 2572 _m
1763 2572 _l 1763 2572 _m
1762 2572 _l 1762 2572 _m
1762 2573 _l 1762 2573 _m
1761 2573 _l 1761 2573 _m
1760 2573 _l 1760 2573 _m
1759 2573 _l 1759 2573 _m
1759 2574 _l 1759 2574 _m
1758 2574 _l 1758 2574 _m
1757 2575 _l 1757 2575 _m
1756 2575 _l 1756 2575 _m
1756 2575 _l 1756 2575 _m
1755 2576 _l 1755 2576 _m
1754 2576 _l 1754 2576 _m
1754 2577 _l 1754 2577 _m
1753 2577 _l 1753 2577 _m
1753 2578 _l 1753 2578 _m
1752 2578 _l 1752 2578 _m
1752 2579 _l 1752 2579 _m
1752 2579 _l 1752 2579 _m
1751 2580 _l 1751 2580 _m
1750 2581 _l 1750 2581 _m
1750 2582 _l 1750 2582 _m
1750 2582 _l 1750 2582 _m
1749 2583 _l 1749 2583 _m
1749 2584 _l 1749 2584 _m
1749 2584 _l 1749 2584 _m
1749 2585 _l 1749 2585 _m
1749 2586 _l _s _s 1747 2585 _m
_sp 1747 2585 1748 2589 1750 2586 3 _pl _pf _np _s _s 1964 2621 _m
_sp 1937 2649 1939 2634 1926 2628 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1786 2718 _m
1939 2634 _l _s 
_s [] 0 _d 2 _lc 1 _w 0 g _s 1726 2527 _m
_sp 1750 2557 1735 2554 1727 2565 3 _pl _pf _np 
_s [16 6 4 6 ] 0 _d 0 _lc 2 _w 0 g 1788 2718 _m
1735 2554 _l _s 
[] 0 _d 2 _lc 1 _w 0 g 1932 2588 _m
_sp 1932 2588 1932 2588 1925 2585 1925 2584 1926 2584 1928 2583 1929 2580 1929 2570 1928 2567 1926 2566 1925 2566 1925 2566 1936 2566 1936 2566 1935 2566 
1933 2567 1932 2570 1932 2581 1934 2583 1935 2584 1937 2584 1938 2584 1939 2584 1940 2583 1941 2581 1941 2578 1941 2570 1940 2567 1938 2566 1938 2566 
1938 2566 1949 2566 1949 2566 1948 2566 1945 2567 1945 2570 1945 2580 1945 2583 1944 2585 1942 2586 1939 2587 1937 2587 1936 2586 1934 2585 1932 2583 
45 _pl _cp 
0 g _f _s _s 
0 g 1953 2578 _m
_sp 1953 2578 1968 2578 1967 2582 1965 2585 1962 2586 1959 2587 1955 2586 1952 2584 1950 2580 1949 2576 1950 2571 1952 2568 1954 2566 1958 2565 1961 2566 
1964 2567 1967 2570 1969 2573 1968 2573 1966 2571 1965 2570 1963 2568 1961 2568 1958 2569 1955 2571 1954 2574 1953 2578 1953 2578 28 _pl _cp 1963 2580 _m
_sp 1963 2580 1962 2582 1961 2584 1960 2585 1958 2585 1957 2585 1955 2584 1954 2582 1953 2580 9 _pl _cp 
0 g _f _s _s 
0 g 1982 2571 _m
_sp 1982 2571 1977 2582 1977 2583 1977 2583 1976 2584 1976 2584 1977 2585 1978 2585 1979 2585 1979 2586 1970 2586 1970 2585 1972 2584 1973 2582 1980 2565 
1981 2565 1986 2577 1992 2565 1992 2565 1999 2582 2001 2584 2002 2585 2002 2586 1996 2586 1996 2585 1996 2585 1997 2585 1998 2584 1998 2584 1998 2584 
1998 2584 1997 2583 1997 2583 1997 2582 1993 2571 1989 2582 1989 2583 1988 2583 1988 2584 1988 2584 1989 2585 1990 2585 1990 2585 1990 2586 1982 2586 
1982 2585 1983 2584 1985 2582 1985 2580 49 _pl _cp 
0 g _f _s _s 
0 g 2031 2572 _m
_sp 2031 2572 2027 2582 2027 2583 2026 2583 2026 2584 2026 2584 2027 2585 2028 2585 2029 2585 2029 2586 2019 2586 2019 2585 2021 2584 2023 2582 2030 2568 
2027 2563 2027 2561 2026 2560 2025 2559 2024 2559 2024 2560 2023 2560 2022 2560 2022 2560 2020 2559 2019 2558 2020 2556 2023 2555 2024 2555 2026 2556 
2027 2558 2028 2559 2037 2582 2039 2584 2041 2585 2041 2586 2034 2586 2034 2585 2034 2585 2036 2585 2036 2584 2036 2584 2036 2584 2036 2584 2036 2583 
2036 2583 2035 2582 47 _pl _cp 
0 g _f _s _s 
0 g 1618 2523 _m
_sp 1618 2523 1618 2523 1611 2520 1611 2519 1612 2519 1614 2518 1614 2515 1614 2505 1614 2502 1612 2502 1611 2502 1611 2501 1621 2501 1621 2502 1621 2502 
1619 2502 1618 2505 1618 2516 1620 2518 1621 2519 1623 2520 1624 2520 1625 2520 1626 2518 1627 2516 1627 2513 1627 2505 1626 2502 1624 2502 1624 2502 
1624 2501 1634 2501 1634 2502 1633 2502 1631 2502 1631 2505 1631 2516 1631 2518 1630 2520 1628 2521 1625 2522 1623 2522 1622 2521 1620 2520 1618 2518 
45 _pl _cp 
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1650 2502 1652 2505 1654 2508 1653 2509 1652 2506 1651 2505 1649 2504 1646 2503 1643 2504 1641 2506 1640 2509 1639 2513 1639 2513 28 _pl _cp 1648 2515 _m
_sp 1648 2515 1648 2517 1647 2519 1646 2520 1644 2520 1642 2520 1640 2519 1639 2517 1639 2515 9 _pl _cp 
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1666 2500 1672 2513 1678 2500 1678 2500 1685 2517 1687 2520 1688 2520 1688 2522 1682 2522 1682 2520 1682 2520 1683 2520 1684 2519 1684 2519 1684 2519 
1684 2519 1683 2518 1683 2518 1683 2517 1679 2506 1675 2517 1674 2518 1674 2518 1674 2519 1674 2519 1675 2520 1676 2520 1676 2520 1676 2522 1667 2522 
1667 2520 1669 2520 1671 2517 1671 2515 49 _pl _cp 
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1718 2520 16 _pl _cp 
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442 2314 442 2312 441 2311 439 2311 438 2311 438 2310 451 2310 451 2311 451 2311 449 2311 448 2312 447 2314 447 2316 447 2325 454 2325 
456 2325 458 2324 458 2323 459 2321 460 2321 460 2331 459 2331 458 2329 458 2328 456 2327 454 2327 41 _pl _cp 
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472 2311 472 2314 17 _pl _cp 467 2339 _m
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485 2311 484 2314 484 2324 486 2327 487 2328 487 2328 488 2327 489 2326 490 2326 491 2327 492 2329 491 2330 489 2331 488 2331 487 2330 
485 2329 484 2328 32 _pl _cp 
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505 2321 503 2322 501 2323 499 2324 497 2325 496 2326 496 2327 497 2329 500 2330 503 2330 504 2329 506 2327 507 2324 507 2324 507 2331 
507 2331 506 2330 505 2330 505 2330 505 2330 503 2331 502 2331 500 2331 497 2331 495 2330 494 2328 493 2325 493 2324 495 2322 496 2321 
499 2319 502 2318 505 2316 505 2314 504 2312 501 2311 499 2311 497 2312 496 2313 495 2314 495 2315 494 2317 493 2317 58 _pl _cp 
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518 2313 517 2315 517 2329 522 2329 522 2331 517 2331 517 2337 517 2337 516 2335 515 2334 514 2333 513 2332 512 2331 28 _pl _cp 
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547 2311 546 2314 546 2324 548 2327 549 2328 550 2328 550 2327 551 2326 552 2326 553 2327 554 2329 553 2330 551 2331 550 2331 549 2330 
547 2329 546 2328 32 _pl _cp 
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556 2324 16 _pl _cp 560 2322 _m
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560 2325 560 2322 560 2322 18 _pl _cp 
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586 2313 585 2315 585 2329 589 2329 589 2331 585 2331 585 2337 584 2337 583 2335 582 2334 581 2333 580 2332 579 2331 28 _pl _cp 
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604 2312 605 2310 606 2310 609 2310 611 2311 611 2313 610 2312 609 2311 608 2312 607 2314 607 2324 607 2325 607 2325 607 2327 607 2328 
606 2329 605 2330 603 2331 600 2331 597 2331 595 2330 594 2328 593 2326 593 2325 595 2324 596 2324 597 2326 597 2326 597 2326 597 2328 
597 2328 597 2328 598 2329 600 2330 601 2330 603 2329 604 2327 604 2324 53 _pl _cp 604 2322 _m
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619 2313 619 2315 619 2329 623 2329 623 2331 619 2331 619 2337 618 2337 617 2335 616 2334 615 2333 614 2332 613 2331 28 _pl _cp 
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640 2312 642 2314 644 2317 644 2318 642 2316 641 2314 639 2313 636 2312 633 2313 631 2315 630 2318 629 2322 629 2323 28 _pl _cp 638 2324 _m
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673 2312 675 2310 676 2310 679 2310 681 2311 681 2313 680 2312 679 2311 678 2312 677 2314 677 2324 677 2325 677 2325 677 2327 677 2328 
676 2329 675 2330 673 2331 670 2331 667 2331 665 2330 664 2328 663 2326 663 2325 665 2324 666 2324 667 2326 667 2326 667 2326 667 2328 
667 2328 667 2328 668 2329 670 2330 671 2330 672 2329 673 2327 673 2324 53 _pl _cp 673 2322 _m
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703 2321 702 2325 701 2328 698 2330 695 2331 694 2331 692 2330 691 2329 689 2328 24 _pl _cp 689 2313 _m
_sp 689 2313 691 2311 693 2311 696 2312 698 2313 699 2316 699 2319 699 2323 698 2326 696 2328 693 2329 690 2328 689 2325 13 _pl _cp 
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_sp 706 2320 707 2316 709 2313 712 2311 716 2310 720 2311 724 2313 726 2316 727 2321 726 2325 724 2328 721 2330 717 2331 712 2330 709 2328 
707 2324 16 _pl _cp 710 2322 _m
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710 2325 710 2322 710 2322 18 _pl _cp 
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744 2309 744 2309 751 2311 751 2312 748 2313 748 2316 748 2331 741 2331 741 2330 741 2330 743 2329 744 2326 744 2314 743 2313 742 2312 
740 2311 739 2311 738 2312 736 2313 735 2315 735 2317 36 _pl _cp 
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760 2313 759 2315 759 2329 763 2329 763 2331 759 2331 759 2337 758 2337 757 2335 756 2334 756 2333 755 2332 753 2331 28 _pl _cp 
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794 2329 16 _pl _cp 
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839 2321 838 2325 836 2328 834 2330 830 2331 829 2331 827 2330 826 2329 824 2328 24 _pl _cp 824 2313 _m
_sp 824 2313 826 2311 828 2311 831 2312 833 2313 834 2316 834 2319 834 2323 833 2326 831 2328 828 2329 825 2328 824 2325 13 _pl _cp 
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849 2307 848 2305 847 2304 846 2304 846 2304 845 2304 844 2305 844 2305 843 2305 842 2304 841 2303 842 2301 844 2300 846 2300 847 2301 
848 2302 849 2303 859 2326 860 2329 862 2330 862 2331 856 2331 856 2330 856 2330 857 2329 857 2328 857 2328 857 2328 857 2328 857 2327 
857 2327 857 2326 47 _pl _cp 
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885 2326 885 2324 885 2319 885 2317 886 2316 886 2314 887 2313 888 2312 890 2311 892 2310 894 2310 894 2301 898 2301 898 2310 901 2311 
904 2312 905 2315 906 2319 906 2324 906 2328 908 2328 909 2328 909 2328 909 2328 909 2328 909 2330 907 2330 906 2330 904 2330 902 2331 
902 2319 902 2316 901 2314 900 2312 898 2312 898 2338 51 _pl _cp 
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_sp 920 2311 920 2310 920 2310 920 2308 919 2306 917 2305 915 2304 915 2303 918 2304 921 2305 922 2307 923 2310 923 2312 921 2313 920 2315 
918 2315 916 2314 915 2312 916 2311 918 2310 919 2310 21 _pl _cp 
0 g _f _s _s 
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_sp 1030 2330 1030 2329 1032 2329 1032 2316 1032 2313 1033 2311 1035 2310 1037 2310 1038 2310 1040 2310 1041 2311 1042 2313 1042 2314 1040 2312 1039 2312 
1038 2313 1037 2315 1037 2329 1041 2329 1041 2331 1037 2331 1037 2337 1036 2337 1035 2335 1034 2334 1033 2333 1032 2332 1031 2331 28 _pl _cp 
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_sp 1050 2342 1049 2342 1043 2340 1043 2339 1043 2339 1045 2338 1046 2335 1046 2314 1045 2311 1043 2311 1043 2311 1043 2310 1053 2310 1053 2311 1053 2311 
1051 2311 1050 2314 1050 2326 1051 2327 1053 2328 1054 2329 1055 2329 1057 2329 1058 2328 1059 2326 1059 2322 1059 2314 1058 2311 1056 2311 1055 2311 
1055 2310 1066 2310 1066 2311 1065 2311 1063 2311 1062 2314 1062 2324 1062 2327 1061 2329 1059 2331 1057 2331 1055 2331 1054 2331 1052 2330 1050 2328 
45 _pl _cp 
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_sp 1071 2323 1085 2323 1084 2326 1083 2329 1080 2330 1077 2331 1073 2330 1070 2328 1068 2324 1067 2320 1068 2316 1070 2313 1072 2311 1076 2310 1079 2310 
1082 2312 1084 2314 1086 2317 1085 2318 1084 2316 1082 2314 1080 2313 1078 2312 1075 2313 1073 2315 1072 2318 1071 2322 1071 2323 28 _pl _cp 1080 2324 _m
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1095 2311 1094 2314 1094 2325 1095 2327 1097 2328 1098 2329 1099 2329 1100 2329 1101 2327 1102 2325 1102 2322 1102 2314 1102 2311 1100 2311 1099 2311 
1099 2310 1110 2310 1110 2311 1109 2311 1107 2311 1106 2314 1106 2325 1106 2328 1105 2330 1103 2331 1101 2331 1099 2331 1098 2330 1096 2329 1094 2328 
45 _pl _cp 
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_sp 1133 2332 1133 2332 1126 2329 1126 2328 1126 2328 1129 2327 1129 2324 1129 2314 1129 2311 1126 2311 1126 2311 1126 2310 1137 2310 1137 2311 1136 2311 
1134 2311 1133 2314 1133 2324 1135 2327 1136 2328 1137 2328 1137 2327 1138 2326 1139 2326 1140 2327 1141 2329 1140 2330 1138 2331 1137 2331 1136 2330 
1134 2329 1133 2328 32 _pl _cp 
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_sp 1142 2320 1143 2316 1145 2313 1149 2311 1153 2310 1157 2311 1160 2313 1162 2316 1163 2321 1162 2325 1160 2328 1157 2330 1153 2331 1149 2330 1145 2328 
1143 2324 16 _pl _cp 1146 2322 _m
_sp 1146 2322 1147 2317 1149 2314 1151 2312 1153 2311 1156 2312 1158 2313 1159 2316 1159 2319 1158 2323 1157 2327 1155 2329 1152 2330 1150 2329 1148 2328 
1147 2325 1146 2322 1146 2322 18 _pl _cp 
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_sp 1165 2330 1165 2329 1167 2329 1167 2316 1167 2313 1168 2311 1170 2310 1172 2310 1173 2310 1175 2310 1176 2311 1177 2313 1177 2314 1176 2312 1174 2312 
1173 2313 1172 2315 1172 2329 1176 2329 1176 2331 1172 2331 1172 2337 1171 2337 1170 2335 1169 2334 1168 2333 1167 2332 1166 2331 28 _pl _cp 
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1190 2312 1192 2310 1194 2310 1196 2310 1198 2311 1198 2313 1197 2312 1196 2311 1195 2312 1194 2314 1194 2324 1194 2325 1194 2325 1194 2327 1194 2328 
1193 2329 1192 2330 1190 2331 1187 2331 1184 2331 1182 2330 1181 2328 1180 2326 1180 2325 1182 2324 1183 2324 1184 2326 1184 2326 1184 2326 1184 2328 
1184 2328 1184 2328 1185 2329 1187 2330 1188 2330 1189 2329 1190 2327 1190 2324 53 _pl _cp 1190 2322 _m
_sp 1190 2322 1188 2321 1186 2320 1184 2319 1183 2317 1183 2316 1184 2313 1186 2312 1188 2312 1190 2314 10 _pl _cp 
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_sp 1199 2330 1199 2329 1201 2329 1201 2316 1201 2313 1202 2311 1204 2310 1206 2310 1207 2310 1208 2310 1210 2311 1211 2313 1211 2314 1209 2312 1208 2312 
1206 2313 1206 2315 1206 2329 1210 2329 1210 2331 1206 2331 1206 2337 1205 2337 1204 2335 1203 2334 1202 2333 1201 2332 1200 2331 28 _pl _cp 
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1227 2312 1229 2314 1231 2317 1230 2318 1229 2316 1228 2314 1226 2313 1223 2312 1220 2313 1218 2315 1217 2318 1216 2322 1216 2323 28 _pl _cp 1225 2324 _m
_sp 1225 2324 1225 2327 1224 2329 1223 2330 1221 2330 1219 2330 1217 2329 1216 2327 1216 2324 9 _pl _cp 
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1260 2312 1261 2310 1263 2310 1266 2310 1268 2311 1268 2313 1267 2312 1266 2311 1265 2312 1264 2314 1264 2324 1264 2325 1264 2325 1264 2327 1264 2328 
1263 2329 1262 2330 1260 2331 1257 2331 1254 2331 1252 2330 1251 2328 1250 2326 1250 2325 1252 2324 1253 2324 1254 2326 1254 2326 1254 2326 1254 2328 
1254 2328 1254 2328 1255 2329 1257 2330 1258 2330 1259 2329 1260 2327 1260 2324 53 _pl _cp 1260 2322 _m
_sp 1260 2322 1258 2321 1256 2320 1254 2319 1253 2317 1253 2316 1254 2313 1256 2312 1258 2312 1260 2314 10 _pl _cp 
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1290 2321 1289 2325 1288 2328 1285 2330 1282 2331 1280 2331 1279 2330 1277 2329 1275 2328 24 _pl _cp 1275 2313 _m
_sp 1275 2313 1278 2311 1280 2311 1283 2312 1285 2313 1286 2316 1286 2319 1285 2323 1284 2326 1282 2328 1280 2329 1278 2329 1277 2328 1276 2326 1275 2325 
15 _pl _cp 
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1294 2324 16 _pl _cp 1297 2322 _m
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1297 2325 1297 2322 1297 2322 18 _pl _cp 
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1331 2309 1331 2309 1338 2311 1338 2312 1335 2313 1335 2316 1335 2331 1327 2331 1327 2330 1328 2330 1330 2329 1331 2326 1331 2314 1330 2313 1328 2312 
1327 2311 1326 2311 1324 2312 1323 2313 1322 2315 1322 2317 36 _pl _cp 
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1346 2313 1346 2315 1346 2329 1350 2329 1350 2331 1346 2331 1346 2337 1345 2337 1344 2335 1343 2334 1342 2333 1341 2332 1340 2331 28 _pl _cp 
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1376 2307 1375 2305 1374 2304 1373 2304 1373 2304 1372 2304 1371 2305 1371 2305 1370 2305 1369 2304 1368 2303 1369 2301 1371 2300 1373 2300 1374 2301 
1375 2302 1376 2303 1386 2326 1387 2329 1389 2330 1389 2331 1382 2331 1382 2330 1383 2330 1384 2329 1384 2328 1384 2328 1384 2328 1384 2328 1384 2327 
1384 2327 1384 2326 47 _pl _cp 
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1394 2331 16 _pl _cp 
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1436 2321 1435 2325 1434 2328 1431 2330 1428 2331 1427 2331 1425 2330 1424 2329 1422 2328 24 _pl _cp 1422 2313 _m
_sp 1422 2313 1424 2311 1426 2311 1429 2312 1431 2313 1432 2316 1432 2319 1432 2323 1431 2326 1429 2328 1426 2329 1423 2328 1422 2325 13 _pl _cp 
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1447 2307 1446 2305 1445 2304 1444 2304 1444 2304 1443 2304 1442 2305 1442 2305 1441 2305 1440 2304 1439 2303 1440 2301 1442 2300 1443 2300 1445 2301 
1446 2302 1447 2303 1457 2326 1458 2329 1460 2330 1460 2331 1453 2331 1453 2330 1454 2330 1455 2329 1455 2328 1455 2328 1455 2328 1455 2328 1455 2327 
1455 2327 1455 2326 47 _pl _cp 
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1481 2315 1483 2312 1486 2310 1489 2310 1491 2310 1494 2311 1496 2312 1497 2314 1498 2316 1498 2319 1499 2322 1499 2326 1499 2327 28 _pl _cp 1484 2328 _m
_sp 1484 2328 1484 2331 1484 2333 1485 2336 1486 2338 1488 2339 1489 2340 1492 2339 1494 2337 1495 2333 1495 2328 11 _pl _cp 1495 2326 _m
_sp 1495 2326 1495 2324 1495 2323 1495 2321 1495 2320 1494 2316 1493 2313 1492 2312 1490 2311 1487 2312 1486 2315 1484 2319 1484 2325 1484 2326 1484 2326 
15 _pl _cp 
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_sp 1173 978 1173 976 1173 974 1174 971 1175 969 1175 968 1176 967 1177 965 1178 964 1180 963 1181 962 1183 962 1184 962 1188 963 1191 965 
1194 968 1195 973 1196 979 1195 985 1194 989 1191 993 1188 995 1184 996 1180 995 1177 993 1175 989 1174 984 27 _pl _cp 1178 979 _m
_sp 1178 979 1178 974 1179 969 1180 966 1182 965 1184 964 1186 964 1188 965 1189 967 1190 970 1191 974 1191 979 1191 984 1190 989 1189 992 
1187 993 1184 994 1182 993 1180 992 1179 989 1178 984 21 _pl _cp 
0 g _f _s _s 
0 g 1354 967 _m
_sp 1354 967 1354 970 1336 978 1354 985 1354 989 1332 979 1332 977 7 _pl _cp 
0 g _f _s _s 
0 g 1386 966 _m
_sp 1386 966 1388 969 1392 972 1393 973 1394 975 1395 976 1396 977 1398 980 1399 982 1400 985 1400 987 1399 991 1398 993 1395 995 1391 996 
1389 996 1387 995 1386 994 1384 993 1383 992 1382 990 1381 989 1381 986 1382 985 1383 988 1384 990 1386 991 1389 992 1392 991 1394 990 
1395 988 1396 985 1396 982 1394 979 1392 976 1389 972 1385 968 1380 963 1380 962 1400 962 1403 969 1402 969 1401 968 1400 967 1400 967 
1398 966 1396 966 47 _pl _cp 
0 g _f _s _s 
0 g 1245 964 _m
_sp 1245 964 1226 964 1226 962 1245 962 4 _pl _cp 1244 986 _m
_sp 1244 986 1226 976 1244 966 1245 967 1229 976 1245 984 6 _pl _cp 
0 g _f _s _s 
0 g 1287 992 _m
_sp 1287 992 1287 964 1285 964 1283 966 1282 968 1282 972 1282 984 1280 984 1278 984 1277 984 1275 984 1275 982 1275 982 1276 982 1277 981 
1278 979 1278 978 1278 972 1278 970 1278 968 1279 966 1280 965 1281 964 1282 963 1284 962 1287 962 1287 952 1291 952 1291 962 1295 963 
1298 964 1300 967 1300 972 1300 978 1300 981 1302 982 1303 982 1303 982 1303 982 1303 982 1303 984 1301 984 1300 984 1298 984 1296 984 
1296 972 1296 969 1295 966 1293 965 1291 964 1291 992 51 _pl _cp 
0 g _f _s _s 
0 g 1431 980 _m
_sp 1431 980 1437 980 1437 984 1423 984 1420 984 1418 983 1417 983 1416 982 1415 981 1413 979 1415 978 1417 980 1420 980 1420 980 1421 980 
1421 973 1421 972 1420 970 1419 969 1418 967 1417 965 1417 964 1418 963 1419 962 1420 963 1422 964 1423 967 1423 970 1423 973 1423 980 
1429 980 1429 970 1429 966 1430 964 1431 962 1433 962 1435 962 1436 964 1437 965 1437 968 1435 968 1434 966 1433 965 1431 966 1431 970 
45 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8217 3905 _m
/Times-BoldR 600 _ff
(\(6.3\))_S /Times-RomanR 600 _ff
1500 3190 _m
(Additionally,)_S 67 _t
(most)_S 67 _t
(underwater)_S 67 _t
(vehicles)_S 67 _t
(must)_S 67 _t
(be)_S 67 _t
(prevented)_S 67 _t
(from)_S 67 _t
(inverting)_S 67 _t
(horizontally)_S 1500 2841 _m
(or)_S 67 _t
(pointing)_S 67 _t
(vertically,)_S 67 _t
(in)_S 67 _t
(order)_S 67 _t
(to)_S 67 _t
(prevent)_S 67 _t
(internal)_S 67 _t
(vehicle)_S 67 _t
(damage)_S 67 _t
(and)_S 67 _t
(uncontrollable)_S 1500 2492 _m
(maneuvering)_S 67 _t
(instabilities.)_S 134 _t
(These)_S 67 _t
(restrictions)_S 67 _t
(add)_S 67 _t
(a)_S 67 _t
(further)_S 67 _t
(constraint)_S 67 _t
(on)_S 67 _t
(roll)_S 67 _t
(angle)_S 67 _t
(for)_S 4950 1288 _m
(105)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(normal)_S 67 _t
(operating)_S 67 _t
(conditions,)_S 67 _t
(but)_S 67 _t
(that)_S 67 _t
(constraint)_S 67 _t
(will)_S 67 _t
(not)_S 67 _t
(be)_S 67 _t
(applied)_S 67 _t
(in)_S 67 _t
(this)_S 67 _t
(model)_S 67 _t
(in)_S 1500 11506 _m
(order)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(able)_S 67 _t
(to)_S 67 _t
(predict)_S 67 _t
(vehicle)_S 67 _t
(motion)_S 67 _t
(under)_S 67 _t
(all)_S 67 _t
(conditions.)_S 1980 11157 _m
(The)_S 67 _t
(order)_S 67 _t
(of)_S 67 _t
(applying)_S 67 _t
(roll,)_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(yaw)_S 67 _t
(matrix)_S 67 _t
(rotations)_S 67 _t
(is)_S 67 _t
(fixed)_S 67 _t
(since)_S 67 _t
(these)_S 1500 10808 _m
(rotations)_S 67 _t
(are)_S 67 _t
(not)_S 67 _t
(commutative.)_S 134 _t
(The)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rotation)_S 67 _t
(matrices)_S 67 _t
(for)_S 67 _t
(converting)_S 67 _t
(from)_S 1500 10459 _m
(body)_S 67 _t
(to)_S 67 _t
(world)_S 67 _t
(coordinates)_S 67 _t
(follow)_S 67 _t
(in)_S 67 _t
(Equation)_S 67 _t
(\(6.4\))_S 67 _t
(\(Fu)_S 67 _t
(87\))_S 67 _t
(\(Cooke)_S 67 _t
(92b\).)_S 134 _t
(Due)_S 67 _t
(to)_S 1500 10110 _m
(typographic)_S 67 _t
(errors)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(number)_S 67 _t
(of)_S 67 _t
(other)_S 67 _t
(references,)_S 67 _t
(matrix)_S 67 _t
(multiplication)_S 67 _t
(results)_S 67 _t
(are)_S 1500 9761 _m
(also)_S 67 _t
(included)_S 67 _t
(in)_S 67 _t
(Equation)_S 67 _t
(\(6.5\).)_S 134 _t
(Finally)_S 67 _t
(it)_S 67 _t
(is)_S 67 _t
(essential)_S 67 _t
(to)_S 67 _t
(note)_S 67 _t
(that,)_S 67 _t
(as)_S 67 _t
(will)_S 67 _t
(be)_S 67 _t
(shown,)_S 1500 9412 _m
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(rotational)_S 67 _t
(velocities)_S 67 _t
/Times-BoldR 600 _ff
(p)_S /Times-RomanR 600 _ff
(,)_S 67 _t
/Times-BoldR 600 _ff
(q)_S /Times-RomanR 600 _ff
67 _t
(and)_S 67 _t
/Times-BoldR 600 _ff
(r)_S /Times-RomanR 600 _ff
67 _t
(are)_S 67 _t
(quite)_S 67 _t
(different)_S 67 _t
(from)_S 67 _t
(the)_S 1500 8867 _m
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rotation)_S 67 _t
(rates)_S 67 _t
5612 8807 _m
5783 8867 _m
(,)_S 67 _t
5900 8795 _m
6054 8867 _m
67 _t
(and)_S 67 _t
6477 8807 _m
6669 8867 _m
(.)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 42 1403 2201 _cw 
_s 1421 2259 _m
_sp 1421 2259 1422 2257 1424 2256 1426 2257 1427 2259 1426 2261 1424 2262 1422 2261 8 _pl _cp 
0 g _f _s _s 
0 g 1426 2242 _m
_sp 1426 2242 1426 2245 1426 2247 1427 2248 1427 2249 1427 2249 1426 2251 1424 2252 1422 2251 1421 2250 1421 2249 1421 2248 1422 2247 1422 2245 1422 2243 
1422 2242 1419 2241 1417 2240 1416 2239 1414 2238 1413 2236 1411 2234 1410 2232 1410 2229 1411 2225 1412 2222 1415 2220 1418 2218 1422 2218 1422 2209 
1426 2209 1426 2218 1430 2218 1433 2220 1435 2223 1436 2226 1437 2230 1436 2234 1435 2237 1433 2239 1430 2241 41 _pl _cp 1422 2240 _m
_sp 1422 2240 1422 2219 1419 2220 1417 2223 1416 2225 1415 2229 1415 2233 1417 2236 1419 2239 9 _pl _cp 1426 2240 _m
_sp 1426 2240 1429 2239 1431 2237 1432 2234 1433 2230 1433 2226 1431 2223 1429 2220 1426 2219 9 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 38 1475 2198 _cw 
_s 1491 2256 _m
_sp 1491 2256 1492 2254 1494 2253 1496 2254 1497 2256 1496 2258 1494 2259 1492 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2234 _m
_sp 1504 2234 1503 2239 1502 2243 1500 2246 1497 2248 1494 2249 1491 2249 1489 2248 1487 2246 1485 2243 1484 2241 1484 2238 1483 2235 1483 2231 1483 2225 
1485 2221 1487 2217 1490 2216 1493 2215 1496 2215 1498 2216 1500 2218 1502 2220 1503 2222 1504 2225 1504 2228 1504 2232 1504 2233 28 _pl _cp 1488 2235 _m
_sp 1488 2235 1488 2238 1488 2240 1489 2243 1490 2245 1492 2246 1493 2247 1496 2246 1498 2244 1499 2240 1500 2235 11 _pl _cp 1500 2233 _m
_sp 1500 2233 1500 2231 1500 2229 1500 2227 1500 2226 1499 2222 1498 2219 1496 2217 1494 2216 1492 2217 1490 2219 1489 2222 1488 2226 1488 2232 1488 2232 
1488 2233 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 85 48 1619 2201 _cw 
_s 1640 2257 _m
_sp 1640 2257 1641 2255 1644 2254 1646 2255 1647 2257 1646 2259 1644 2260 1641 2259 8 _pl _cp 
0 g _f _s _s 
0 g 1641 2248 _m
_sp 1641 2248 1641 2220 1639 2220 1637 2222 1636 2224 1636 2228 1636 2240 1633 2240 1631 2240 1630 2240 1628 2240 1628 2238 1629 2238 1629 2238 1631 2237 
1632 2235 1632 2234 1632 2228 1632 2226 1632 2224 1632 2222 1633 2221 1635 2220 1636 2219 1638 2218 1641 2218 1641 2208 1645 2208 1645 2218 1649 2219 
1651 2220 1653 2223 1653 2228 1653 2234 1654 2237 1656 2238 1656 2238 1656 2238 1657 2238 1657 2238 1657 2240 1655 2240 1653 2240 1652 2240 1650 2240 
1650 2228 1650 2225 1649 2222 1647 2221 1645 2220 1645 2248 51 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 344 1749 400 1684 _cw 
_s 515 2015 _m
_sp 515 2015 515 1974 526 1974 526 1975 523 1975 520 1976 520 1979 520 2009 520 2011 520 2013 523 2013 526 2013 526 2015 13 _pl _cp 
0 g _f _s _s 
0 g 570 1974 _m
_sp 570 1974 570 2015 559 2015 559 2013 562 2013 565 2013 565 2009 565 1980 565 1977 565 1975 562 1975 559 1975 559 1974 13 _pl _cp 
0 g _f _s _s 
0 g 653 2015 _m
_sp 653 2015 653 1974 664 1974 664 1975 661 1975 658 1976 658 1979 658 2009 658 2011 658 2013 661 2013 664 2013 664 2015 13 _pl _cp 
0 g _f _s _s 
0 g 708 1974 _m
_sp 708 1974 708 2015 697 2015 697 2013 700 2013 703 2013 703 2009 703 1980 703 1977 703 1975 700 1975 697 1975 697 1974 13 _pl _cp 
0 g _f _s _s 
0 g 734 1966 _m
_sp 734 1966 734 1966 734 1966 734 1965 733 1963 732 1962 731 1961 731 1961 733 1961 734 1962 736 1964 736 1966 735 1968 733 1969 732 1968 
731 1967 732 1966 733 1966 734 1966 19 _pl _cp 
0 g _f _s _s 
0 g 802 2015 _m
_sp 802 2015 802 1974 814 1974 814 1975 810 1975 807 1976 807 1979 807 2009 807 2011 808 2013 811 2013 814 2013 814 2015 13 _pl _cp 
0 g _f _s _s 
0 g 858 1974 _m
_sp 858 1974 858 2015 846 2015 846 2013 850 2013 853 2013 853 2009 853 1980 853 1977 852 1975 849 1975 846 1975 846 1974 13 _pl _cp 
0 g _f _s _s 
0 g 885 1966 _m
_sp 885 1966 886 1966 886 1966 886 1965 885 1963 883 1962 882 1961 882 1961 884 1961 886 1962 887 1964 887 1966 886 1968 884 1969 883 1968 
882 1967 883 1966 884 1966 885 1966 19 _pl _cp 
0 g _f _s _s 
0 g 947 2015 _m
_sp 947 2015 947 1974 959 1974 959 1975 955 1975 952 1976 952 1979 952 2009 952 2011 953 2013 956 2013 959 2013 959 2015 13 _pl _cp 
0 g _f _s _s 
0 g 1003 1974 _m
_sp 1003 1974 1003 2015 991 2015 991 2013 995 2013 998 2013 998 2009 998 1980 998 1977 997 1975 994 1975 991 1975 991 1974 13 _pl _cp 
0 g _f _s _s 
0 g 1030 1966 _m
_sp 1030 1966 1031 1966 1031 1966 1031 1965 1030 1963 1028 1962 1027 1961 1027 1961 1029 1961 1031 1962 1032 1964 1032 1966 1031 1968 1029 1969 1028 1968 
1027 1967 1028 1966 1029 1966 1030 1966 19 _pl _cp 
0 g _f _s _s 
0 g 685 1870 _m
_sp 685 1870 683 1868 682 1866 680 1865 678 1865 675 1866 672 1868 671 1871 670 1875 671 1878 672 1881 674 1882 677 1883 679 1883 680 1881 
681 1879 683 1878 684 1879 685 1880 684 1882 683 1884 680 1885 677 1885 674 1884 671 1883 668 1880 667 1877 666 1873 667 1869 669 1865 
672 1863 676 1862 678 1862 679 1863 681 1863 682 1864 683 1865 684 1867 685 1868 686 1870 40 _pl _cp 
0 g _f _s _s 
0 g 688 1873 _m
_sp 688 1873 689 1869 691 1865 695 1863 699 1862 703 1862 706 1864 709 1867 710 1870 711 1874 710 1879 708 1882 704 1884 700 1885 696 1884 
693 1883 690 1880 689 1877 18 _pl _cp 693 1875 _m
_sp 693 1875 694 1870 695 1866 697 1864 700 1863 703 1864 705 1866 706 1868 706 1872 705 1877 704 1880 702 1882 699 1883 696 1882 695 1881 
693 1878 693 1875 693 1875 18 _pl _cp 
0 g _f _s _s 
0 g 713 1862 _m
_sp 713 1862 714 1862 715 1863 715 1863 716 1863 718 1862 720 1862 722 1862 725 1862 728 1864 729 1865 730 1868 730 1870 728 1872 727 1873 
726 1874 724 1875 722 1876 720 1877 718 1878 717 1879 717 1880 718 1883 721 1884 724 1884 726 1883 727 1881 728 1878 729 1878 729 1884 
728 1884 727 1884 727 1884 727 1884 726 1884 724 1885 723 1885 721 1885 718 1884 716 1883 714 1881 713 1879 713 1877 715 1875 716 1874 
719 1872 723 1871 726 1869 727 1867 727 1866 726 1864 724 1863 722 1863 720 1864 717 1865 716 1866 716 1867 715 1868 714 1870 713 1870 
60 _pl _cp 
0 g _f _s _s 
0 g 747 1896 _m
_sp 747 1896 744 1894 742 1893 740 1891 739 1889 737 1886 735 1883 734 1879 734 1875 734 1871 735 1867 737 1863 739 1860 740 1858 742 1857 
744 1855 747 1853 747 1854 746 1855 745 1857 744 1858 743 1859 742 1860 742 1861 741 1863 740 1864 739 1866 739 1869 739 1872 739 1875 
739 1878 739 1881 739 1883 740 1885 741 1887 742 1888 742 1890 743 1891 745 1893 747 1895 40 _pl _cp 
0 g _f _s _s 
0 g 786 1853 _m
_sp 786 1853 789 1855 791 1857 793 1858 794 1860 796 1863 798 1867 799 1871 799 1875 799 1879 798 1883 796 1886 794 1889 793 1891 791 1893 
789 1894 786 1896 786 1895 788 1893 790 1891 791 1890 792 1888 792 1887 793 1885 794 1883 794 1881 794 1878 794 1875 794 1872 794 1869 
794 1866 793 1864 792 1863 792 1861 791 1860 790 1859 789 1858 788 1857 787 1855 786 1854 40 _pl _cp 
0 g _f _s _s 
0 g 867 1862 _m
_sp 867 1862 868 1862 869 1863 869 1863 870 1863 872 1862 874 1862 876 1862 879 1862 882 1864 883 1865 884 1868 884 1870 882 1872 881 1873 
880 1874 878 1875 876 1876 874 1877 872 1878 871 1879 871 1880 872 1883 875 1884 878 1884 880 1883 881 1881 882 1878 883 1878 883 1884 
882 1884 881 1884 881 1884 881 1884 880 1884 878 1885 877 1885 875 1885 872 1884 870 1883 868 1881 867 1879 867 1877 869 1875 870 1874 
873 1872 877 1871 880 1869 881 1867 881 1866 880 1864 878 1863 876 1863 874 1864 871 1865 870 1866 870 1867 869 1868 868 1870 867 1870 
60 _pl _cp 
0 g _f _s _s 
0 g 895 1886 _m
_sp 895 1886 894 1886 887 1883 887 1882 887 1882 890 1881 890 1878 890 1867 890 1864 887 1863 887 1863 887 1862 898 1862 898 1863 898 1863 
895 1864 895 1867 17 _pl _cp 889 1894 _m
_sp 889 1894 890 1892 892 1891 894 1892 895 1894 894 1896 892 1897 890 1896 8 _pl _cp 
0 g _f _s _s 
0 g 908 1886 _m
_sp 908 1886 907 1886 900 1883 900 1882 900 1882 903 1881 903 1878 903 1867 903 1864 900 1863 900 1863 900 1862 911 1862 911 1863 911 1863 
908 1864 908 1867 908 1879 909 1881 911 1882 912 1883 913 1883 915 1883 916 1881 916 1879 916 1875 916 1867 916 1864 914 1863 913 1863 
913 1862 925 1862 925 1863 924 1863 921 1864 921 1867 921 1878 920 1881 919 1883 917 1884 915 1885 913 1885 911 1884 910 1883 908 1881 
45 _pl _cp 
0 g _f _s _s 
0 g 940 1896 _m
_sp 940 1896 937 1894 935 1893 933 1891 932 1889 930 1886 928 1883 927 1879 927 1875 927 1871 928 1867 930 1863 932 1860 933 1858 935 1857 
937 1855 940 1853 940 1854 939 1855 938 1857 937 1858 936 1859 935 1860 935 1861 934 1863 933 1864 932 1866 932 1869 932 1872 932 1875 
932 1878 932 1881 932 1883 933 1885 934 1887 935 1888 935 1890 936 1891 938 1893 940 1895 40 _pl _cp 
0 g _f _s _s 
0 g 979 1853 _m
_sp 979 1853 982 1855 984 1857 986 1858 987 1860 989 1863 991 1867 992 1871 992 1875 992 1879 991 1883 989 1886 987 1889 986 1891 984 1893 
982 1894 979 1896 979 1895 981 1893 983 1891 984 1890 985 1888 985 1887 986 1885 987 1883 987 1881 987 1878 987 1875 987 1872 987 1869 
987 1866 986 1864 985 1863 985 1861 984 1860 983 1859 982 1858 981 1857 980 1855 979 1854 40 _pl _cp 
0 g _f _s _s 
0 g 1052 1879 _m
_sp 1052 1879 1052 1876 1053 1874 1053 1872 1054 1870 1055 1869 1056 1867 1056 1866 1057 1864 1059 1863 1060 1862 1062 1862 1063 1862 1067 1863 1070 1865 
1073 1869 1074 1873 1075 1879 1074 1885 1073 1889 1070 1893 1067 1895 1064 1896 1060 1895 1057 1893 1054 1889 1053 1885 27 _pl _cp 1057 1880 _m
_sp 1057 1880 1057 1874 1058 1870 1059 1866 1061 1865 1064 1864 1066 1864 1067 1865 1068 1867 1069 1870 1070 1874 1070 1879 1070 1884 1069 1889 1068 1891 
1066 1893 1064 1894 1061 1893 1059 1891 1057 1886 20 _pl _cp 
0 g _f _s _s 
0 g 670 1782 _m
_sp 670 1782 671 1782 672 1782 672 1782 673 1782 674 1782 677 1781 679 1781 682 1782 685 1783 686 1785 687 1787 686 1790 685 1792 684 1793 
683 1793 681 1794 679 1795 676 1796 675 1798 673 1799 673 1800 673 1801 674 1802 676 1803 678 1803 680 1803 682 1802 683 1800 685 1797 
685 1797 685 1804 685 1804 684 1804 683 1803 683 1804 682 1804 681 1804 680 1804 678 1804 675 1804 672 1803 671 1801 670 1798 670 1796 
672 1795 673 1793 676 1792 680 1790 682 1788 683 1786 682 1783 679 1782 676 1783 674 1784 673 1785 673 1786 672 1787 671 1789 670 1789 
60 _pl _cp 
0 g _f _s _s 
0 g 697 1805 _m
_sp 697 1805 697 1805 689 1802 689 1801 690 1801 692 1800 693 1797 693 1786 693 1783 690 1783 689 1783 689 1782 701 1782 701 1783 700 1783 
698 1783 697 1786 17 _pl _cp 692 1813 _m
_sp 692 1813 693 1811 695 1810 697 1811 698 1813 697 1815 695 1816 693 1815 8 _pl _cp 
0 g _f _s _s 
0 g 710 1805 _m
_sp 710 1805 710 1805 702 1802 702 1801 703 1801 705 1800 706 1797 706 1786 705 1783 703 1783 702 1783 702 1782 714 1782 714 1783 713 1783 
711 1783 710 1786 710 1798 712 1800 713 1801 715 1802 716 1802 717 1802 718 1800 719 1798 719 1795 719 1786 719 1783 716 1783 716 1783 
716 1782 727 1782 727 1783 727 1783 724 1783 724 1786 724 1797 723 1800 722 1802 720 1804 718 1804 716 1804 714 1803 712 1802 710 1800 
45 _pl _cp 
0 g _f _s _s 
0 g 742 1815 _m
_sp 742 1815 739 1813 738 1812 736 1810 734 1808 732 1805 731 1802 730 1798 730 1794 730 1790 731 1786 732 1783 734 1780 736 1778 738 1776 
739 1775 742 1773 743 1774 741 1776 739 1778 738 1779 737 1781 736 1782 736 1783 735 1785 735 1788 735 1791 735 1794 735 1797 735 1800 
735 1803 736 1805 736 1806 737 1807 738 1809 739 1810 741 1812 743 1814 38 _pl _cp 
0 g _f _s _s 
0 g 782 1773 _m
_sp 782 1773 785 1775 787 1776 788 1778 790 1780 792 1783 793 1786 794 1790 794 1794 794 1798 793 1802 792 1805 790 1808 788 1810 787 1812 
785 1813 782 1815 781 1814 783 1813 784 1812 785 1811 786 1810 787 1809 788 1807 788 1806 789 1805 789 1803 790 1800 790 1797 790 1794 
790 1791 790 1788 789 1785 789 1783 788 1782 788 1781 787 1779 786 1778 785 1777 784 1776 783 1775 781 1774 42 _pl _cp 
0 g _f _s _s 
0 g 867 1789 _m
_sp 867 1789 865 1787 864 1786 862 1785 860 1785 857 1786 854 1788 853 1790 852 1794 853 1798 854 1800 856 1802 859 1803 861 1802 862 1800 
863 1798 865 1797 866 1798 867 1799 866 1801 865 1803 862 1804 859 1804 856 1803 852 1802 850 1799 849 1796 848 1792 849 1788 851 1784 
854 1782 858 1781 860 1781 861 1782 863 1783 864 1784 865 1785 866 1786 867 1787 868 1789 40 _pl _cp 
0 g _f _s _s 
0 g 870 1792 _m
_sp 870 1792 871 1788 873 1784 877 1782 881 1781 885 1781 888 1783 891 1786 892 1789 893 1793 892 1798 890 1801 886 1803 882 1804 878 1803 
875 1802 872 1799 871 1796 18 _pl _cp 875 1794 _m
_sp 875 1794 876 1789 877 1786 879 1784 882 1783 885 1784 887 1785 888 1788 888 1791 887 1796 886 1800 884 1802 881 1803 878 1802 877 1801 
875 1798 875 1795 875 1794 18 _pl _cp 
0 g _f _s _s 
0 g 895 1782 _m
_sp 895 1782 896 1782 897 1782 897 1782 898 1782 900 1782 902 1781 904 1781 907 1782 910 1783 911 1785 912 1787 912 1790 910 1792 909 1793 
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1932 1783 1931 1786 17 _pl _cp 1926 1813 _m
_sp 1926 1813 1927 1811 1929 1810 1931 1811 1932 1813 1931 1815 1929 1816 1927 1815 8 _pl _cp 
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1945 1783 1944 1786 1944 1798 1946 1800 1947 1801 1949 1802 1950 1802 1951 1802 1952 1800 1953 1798 1953 1795 1953 1786 1953 1783 1950 1783 1950 1783 
1950 1782 1961 1782 1961 1783 1961 1783 1958 1783 1958 1786 1958 1797 1957 1800 1956 1802 1954 1804 1952 1804 1950 1804 1948 1803 1946 1802 1944 1800 
45 _pl _cp 
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1969 1803 1970 1805 1970 1806 1971 1807 1972 1809 1973 1810 1975 1812 1977 1814 38 _pl _cp 
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2014 1813 2011 1815 2010 1814 2011 1813 2013 1812 2014 1811 2015 1810 2016 1807 2017 1805 2018 1803 2018 1800 2019 1797 2019 1794 2019 1791 2018 1788 
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1638 1732 1635 1731 1633 1729 1631 1724 19 _pl _cp 
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1822 1733 1819 1735 1818 1733 1819 1732 1821 1731 1822 1730 1823 1729 1824 1727 1825 1724 1826 1722 1826 1719 1827 1716 1827 1713 1827 1710 1826 1707 
1826 1704 1825 1702 1824 1700 1823 1697 1822 1696 1821 1695 1819 1694 1818 1693 38 _pl _cp 
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1891 1701 1895 1700 1897 1700 1898 1701 1900 1702 1901 1703 1902 1704 1903 1705 1903 1706 1904 1708 40 _pl _cp 
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1915 1723 1912 1722 1909 1719 1907 1716 19 _pl _cp 1912 1713 _m
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1912 1717 1912 1714 1912 1714 18 _pl _cp 
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1934 1714 1935 1713 1938 1711 1942 1709 1944 1707 1945 1705 1944 1703 1941 1702 1938 1702 1936 1703 1935 1704 1935 1705 1934 1707 1933 1708 1932 1708 
60 _pl _cp 
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553 1988 46 _pl _cp 541 2000 _m
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15 _pl _cp 
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676 1984 675 1985 675 1986 675 1986 676 1987 676 1988 679 1998 682 1998 688 1982 696 1982 696 1983 695 1983 694 1983 693 1984 692 1986 
691 1988 46 _pl _cp 679 2000 _m
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15 _pl _cp 
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719 1978 722 1978 726 1978 718 1969 717 1968 35 _pl _cp 
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824 2013 825 2013 826 2011 826 2010 826 2008 820 1988 819 1986 818 1984 817 1983 816 1983 816 1983 815 1982 828 1982 828 1983 827 1983 
825 1984 825 1985 825 1986 825 1986 825 1987 825 1988 828 1998 831 1998 837 1982 845 1982 846 1983 845 1983 844 1983 843 1984 841 1986 
840 1988 46 _pl _cp 829 2000 _m
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15 _pl _cp 
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868 1961 868 1961 868 1961 868 1961 867 1962 867 1962 866 1962 866 1962 865 1961 866 1960 867 1959 868 1959 869 1960 871 1962 873 1964 
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878 1977 878 1977 878 1976 878 1975 877 1974 877 1973 876 1971 876 1970 875 1969 875 1969 874 1968 874 1969 874 1970 874 1972 873 1974 
873 1976 872 1978 872 1980 871 1981 64 _pl _cp 
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15 _pl _cp 
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1014 1967 1014 1967 1016 1969 1017 1971 1017 1972 1017 1971 1018 1969 1019 1966 1020 1966 1022 1966 1024 1969 1024 1969 1024 1970 1023 1968 1022 1968 
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1022 1980 1021 1979 1019 1977 1019 1976 1019 1978 1018 1980 1017 1981 1016 1981 1014 1980 1013 1980 1013 1979 1014 1979 1014 1979 1015 1979 1016 1978 
1017 1975 61 _pl _cp 
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762 1979 762 1979 762 1979 762 1979 762 1980 760 1980 758 1981 758 1972 758 1970 757 1968 756 1967 754 1967 754 1986 43 _pl _cp 
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_sp 1837 1507 1837 1479 1835 1480 1833 1481 1832 1483 1832 1487 1832 1500 1829 1499 1827 1499 1826 1499 1824 1499 1824 1497 1825 1497 1825 1497 1827 1496 
1828 1494 1828 1493 1828 1487 1828 1485 1828 1483 1828 1481 1829 1480 1831 1479 1832 1478 1834 1477 1837 1477 1837 1468 1841 1468 1841 1477 1845 1478 
1847 1480 1849 1483 1849 1487 1849 1493 1850 1496 1852 1497 1852 1497 1852 1497 1853 1497 1853 1497 1853 1499 1851 1499 1849 1499 1848 1499 1846 1500 
1846 1487 1846 1484 1845 1481 1843 1480 1841 1479 1841 1507 51 _pl _cp 
0 g _f _s _s 
0 g 1996 1501 _m
_sp 1996 1501 1996 1504 1996 1506 1997 1507 1997 1508 1997 1509 1996 1510 1994 1511 1992 1510 1991 1509 1991 1508 1991 1507 1992 1506 1992 1504 1992 1502 
1992 1501 1989 1500 1987 1499 1986 1498 1984 1497 1983 1495 1981 1493 1980 1491 1980 1488 1980 1484 1982 1481 1985 1479 1988 1478 1992 1477 1992 1469 
1996 1469 1996 1477 2000 1478 2003 1479 2005 1482 2006 1485 2007 1489 2006 1493 2005 1496 2003 1499 2000 1500 41 _pl _cp 1992 1499 _m
_sp 1992 1499 1992 1478 1989 1479 1987 1482 1986 1485 1985 1489 1985 1493 1987 1496 1989 1498 9 _pl _cp 1996 1499 _m
_sp 1996 1499 1999 1498 2001 1496 2002 1493 2003 1489 2003 1485 2001 1482 1999 1480 1996 1479 9 _pl _cp 
0 g _f _s _s 
0 g 2113 1507 _m
_sp 2113 1507 2113 1479 2111 1480 2109 1481 2108 1483 2108 1487 2108 1500 2106 1499 2104 1499 2103 1499 2101 1499 2101 1497 2102 1497 2102 1497 2104 1496 
2104 1494 2104 1493 2104 1487 2104 1485 2105 1483 2105 1481 2106 1480 2108 1479 2109 1478 2111 1477 2113 1477 2113 1468 2117 1468 2117 1477 2121 1478 
2124 1480 2126 1483 2126 1487 2126 1493 2127 1496 2129 1497 2129 1497 2129 1497 2129 1497 2130 1497 2130 1499 2128 1499 2126 1499 2124 1499 2122 1500 
2122 1487 2122 1484 2121 1481 2119 1480 2117 1479 2117 1507 51 _pl _cp 
0 g _f _s _s 
0 g 633 1415 _m
_sp 633 1415 632 1420 631 1425 629 1428 626 1430 623 1431 620 1430 617 1429 615 1427 613 1425 612 1423 612 1420 611 1417 611 1413 611 1407 
613 1402 615 1399 618 1397 622 1396 624 1396 626 1397 628 1399 630 1401 631 1403 632 1406 633 1410 633 1414 633 1415 28 _pl _cp 616 1416 _m
_sp 616 1416 616 1419 616 1421 617 1424 618 1427 620 1428 622 1429 624 1428 626 1426 627 1421 628 1416 11 _pl _cp 628 1414 _m
_sp 628 1414 628 1412 628 1410 628 1409 628 1408 627 1403 626 1400 624 1399 622 1398 620 1399 618 1400 617 1403 616 1408 616 1413 616 1414 
616 1414 16 _pl _cp 
0 g _f _s _s 
0 g 739 1426 _m
_sp 739 1426 739 1399 737 1399 735 1401 734 1403 734 1406 734 1419 732 1418 730 1418 729 1418 727 1418 727 1416 728 1416 728 1416 730 1415 
730 1414 730 1412 730 1406 730 1404 731 1402 731 1401 732 1400 734 1399 735 1398 737 1397 739 1397 739 1387 743 1387 743 1397 747 1398 
750 1399 752 1402 752 1406 752 1412 753 1415 755 1416 755 1416 755 1416 755 1416 756 1416 756 1418 754 1418 752 1418 750 1418 748 1419 
748 1406 748 1403 747 1401 745 1399 743 1399 743 1426 51 _pl _cp 
0 g _f _s _s 
0 g 896 1420 _m
_sp 896 1420 896 1422 897 1424 897 1425 897 1426 897 1427 897 1427 897 1428 896 1430 894 1431 893 1430 892 1428 892 1428 892 1427 892 1426 
892 1424 893 1421 893 1420 890 1419 888 1419 886 1418 885 1416 883 1414 882 1412 881 1410 881 1408 881 1404 883 1401 885 1398 888 1397 
892 1396 892 1388 897 1388 897 1396 900 1397 903 1399 906 1402 907 1405 908 1409 907 1412 906 1415 903 1418 900 1419 43 _pl _cp 893 1418 _m
_sp 893 1418 892 1398 889 1399 887 1401 886 1404 885 1408 886 1412 887 1415 890 1417 9 _pl _cp 896 1418 _m
_sp 896 1418 899 1417 902 1415 903 1412 904 1408 903 1404 902 1402 900 1399 897 1398 9 _pl _cp 
0 g _f _s _s 
0 g 1022 1415 _m
_sp 1022 1415 1021 1420 1020 1425 1018 1428 1015 1430 1012 1431 1009 1430 1006 1429 1004 1427 1002 1425 1001 1423 1001 1420 1000 1417 1000 1413 1000 1407 
1002 1402 1004 1399 1007 1397 1011 1396 1013 1396 1015 1397 1017 1399 1019 1401 1020 1403 1021 1406 1022 1410 1022 1414 1022 1415 28 _pl _cp 1005 1416 _m
_sp 1005 1416 1005 1419 1005 1421 1006 1424 1007 1427 1009 1428 1011 1429 1013 1428 1015 1426 1016 1421 1017 1416 11 _pl _cp 1017 1414 _m
_sp 1017 1414 1017 1412 1017 1410 1017 1409 1017 1408 1016 1403 1015 1400 1013 1399 1011 1398 1009 1399 1007 1400 1006 1403 1005 1408 1005 1413 1005 1414 
1005 1414 16 _pl _cp 
0 g _f _s _s 
0 g 1128 1426 _m
_sp 1128 1426 1128 1399 1126 1399 1124 1401 1123 1403 1123 1406 1123 1419 1121 1418 1119 1418 1118 1418 1116 1418 1116 1416 1117 1416 1117 1416 1119 1415 
1119 1414 1119 1412 1119 1406 1119 1404 1120 1402 1120 1401 1121 1400 1123 1399 1124 1398 1126 1397 1128 1397 1128 1387 1132 1387 1132 1397 1136 1398 
1139 1399 1141 1402 1141 1406 1141 1412 1142 1415 1144 1416 1144 1416 1144 1416 1144 1416 1145 1416 1145 1418 1143 1418 1141 1418 1139 1418 1137 1419 
1137 1406 1137 1403 1136 1401 1134 1399 1132 1399 1132 1426 51 _pl _cp 
0 g _f _s _s 
0 g 1301 1420 _m
_sp 1301 1420 1301 1422 1302 1424 1302 1425 1302 1426 1302 1427 1302 1427 1302 1428 1301 1430 1299 1431 1298 1430 1297 1428 1297 1428 1297 1427 1297 1426 
1297 1424 1298 1421 1298 1420 1295 1419 1293 1419 1291 1418 1290 1416 1288 1414 1287 1412 1286 1410 1286 1408 1286 1404 1288 1401 1290 1398 1293 1397 
1297 1396 1297 1388 1302 1388 1302 1396 1305 1397 1308 1399 1311 1402 1312 1405 1313 1409 1312 1412 1311 1415 1308 1418 1305 1419 43 _pl _cp 1298 1418 _m
_sp 1298 1418 1297 1398 1294 1399 1292 1401 1291 1404 1290 1408 1291 1412 1292 1415 1295 1417 9 _pl _cp 1301 1418 _m
_sp 1301 1418 1304 1417 1307 1415 1308 1412 1309 1408 1308 1404 1307 1402 1305 1399 1302 1398 9 _pl _cp 
0 g _f _s _s 
0 g 1427 1426 _m
_sp 1427 1426 1427 1399 1425 1399 1423 1401 1422 1403 1422 1406 1422 1419 1420 1418 1418 1418 1417 1418 1415 1418 1415 1416 1415 1416 1416 1416 1417 1415 
1418 1414 1418 1412 1418 1406 1418 1404 1418 1402 1419 1401 1420 1400 1421 1399 1422 1398 1424 1397 1427 1397 1427 1387 1431 1387 1431 1397 1435 1398 
1438 1399 1440 1402 1440 1406 1440 1412 1440 1415 1442 1416 1443 1416 1443 1416 1443 1416 1443 1416 1443 1418 1441 1418 1440 1418 1438 1418 1436 1419 
1436 1406 1436 1403 1435 1401 1433 1399 1431 1399 1431 1426 51 _pl _cp 
0 g _f _s _s 
0 g 1602 1420 _m
_sp 1602 1420 1602 1422 1602 1424 1602 1425 1602 1426 1603 1427 1603 1427 1603 1428 1602 1430 1600 1431 1598 1430 1597 1428 1597 1428 1597 1427 1598 1426 
1598 1424 1598 1421 1598 1420 1595 1419 1593 1419 1592 1418 1590 1416 1589 1414 1587 1412 1586 1410 1586 1408 1587 1404 1588 1401 1591 1398 1594 1397 
1598 1396 1598 1388 1602 1388 1602 1396 1606 1397 1609 1399 1611 1402 1612 1405 1613 1409 1612 1413 1610 1417 1607 1419 42 _pl _cp 1598 1418 _m
_sp 1598 1418 1598 1398 1595 1399 1593 1401 1592 1404 1591 1408 1591 1412 1593 1415 1595 1417 9 _pl _cp 1602 1418 _m
_sp 1602 1418 1605 1417 1607 1415 1608 1412 1609 1408 1609 1404 1607 1402 1605 1399 1602 1398 9 _pl _cp 
0 g _f _s _s 
0 g 1727 1415 _m
_sp 1727 1415 1726 1420 1725 1425 1723 1428 1720 1430 1717 1431 1714 1430 1712 1429 1710 1427 1708 1425 1707 1423 1707 1420 1706 1417 1706 1413 1706 1407 
1707 1402 1709 1399 1712 1397 1716 1396 1719 1396 1721 1397 1723 1399 1725 1401 1726 1403 1726 1406 1727 1410 1727 1414 1727 1415 28 _pl _cp 1710 1416 _m
_sp 1710 1416 1711 1419 1711 1421 1712 1424 1713 1427 1714 1428 1716 1429 1719 1428 1721 1426 1722 1421 1723 1416 11 _pl _cp 1723 1414 _m
_sp 1723 1414 1723 1412 1723 1410 1723 1409 1723 1408 1722 1403 1721 1400 1719 1399 1717 1398 1715 1399 1713 1400 1711 1403 1710 1408 1710 1413 1710 1414 
1710 1414 16 _pl _cp 
0 g _f _s _s 
0 g 1834 1426 _m
_sp 1834 1426 1834 1399 1832 1399 1830 1401 1829 1403 1829 1406 1829 1419 1827 1418 1825 1418 1824 1418 1822 1418 1822 1416 1822 1416 1822 1416 1824 1415 
1825 1414 1825 1412 1825 1406 1825 1404 1825 1402 1825 1401 1826 1400 1828 1399 1829 1398 1831 1397 1834 1397 1834 1387 1838 1387 1838 1397 1842 1398 
1845 1399 1846 1402 1847 1406 1847 1412 1847 1415 1849 1416 1849 1416 1850 1416 1850 1416 1850 1416 1850 1418 1848 1418 1847 1418 1845 1418 1843 1419 
1843 1406 1843 1403 1842 1401 1840 1399 1838 1399 1838 1426 51 _pl _cp 
0 g _f _s _s 
0 g 1993 1420 _m
_sp 1993 1420 1993 1422 1993 1424 1993 1425 1994 1426 1994 1427 1994 1427 1994 1428 1993 1430 1991 1431 1990 1430 1989 1428 1989 1428 1989 1427 1989 1426 
1989 1424 1989 1421 1989 1420 1986 1419 1984 1419 1983 1418 1981 1416 1980 1414 1979 1412 1978 1410 1978 1408 1978 1404 1980 1401 1982 1398 1985 1397 
1989 1396 1989 1388 1993 1388 1993 1396 1997 1397 2000 1399 2003 1402 2004 1405 2005 1409 2004 1412 2003 1415 2000 1418 1997 1419 43 _pl _cp 1989 1418 _m
_sp 1989 1418 1989 1398 1986 1399 1984 1401 1983 1404 1982 1408 1983 1412 1984 1415 1986 1417 9 _pl _cp 1993 1418 _m
_sp 1993 1418 1996 1417 1998 1415 1999 1412 2000 1408 2000 1404 1998 1402 1996 1399 1993 1398 9 _pl _cp 
0 g _f _s _s 
0 g 2119 1426 _m
_sp 2119 1426 2119 1399 2117 1399 2115 1401 2114 1403 2114 1406 2114 1419 2112 1418 2110 1418 2109 1418 2107 1418 2107 1416 2107 1416 2107 1416 2109 1415 
2110 1414 2110 1412 2110 1406 2110 1404 2110 1402 2110 1401 2111 1400 2113 1399 2114 1398 2116 1397 2119 1397 2119 1387 2123 1387 2123 1397 2127 1398 
2130 1399 2131 1402 2132 1406 2132 1412 2132 1415 2134 1416 2134 1416 2135 1416 2135 1416 2135 1416 2135 1418 2133 1418 2132 1418 2130 1418 2128 1419 
2128 1406 2128 1403 2127 1401 2125 1399 2123 1399 2123 1426 51 _pl _cp 
0 g _f _s _s 
0 g 708 1335 _m
_sp 708 1335 708 1340 706 1344 704 1347 701 1349 698 1350 695 1350 693 1349 691 1347 689 1344 688 1342 688 1339 687 1336 687 1332 687 1326 
689 1321 691 1318 694 1316 697 1315 700 1315 702 1316 704 1318 706 1320 707 1322 708 1325 708 1329 708 1333 708 1334 28 _pl _cp 692 1336 _m
_sp 692 1336 692 1338 692 1340 693 1343 694 1346 696 1347 697 1348 700 1347 702 1345 703 1341 704 1336 11 _pl _cp 704 1334 _m
_sp 704 1334 704 1332 704 1330 704 1328 704 1327 703 1323 702 1320 700 1318 698 1317 696 1318 694 1319 693 1322 692 1327 692 1332 692 1333 
692 1334 16 _pl _cp 
0 g _f _s _s 
0 g 1103 1339 _m
_sp 1103 1339 1104 1341 1104 1343 1104 1344 1104 1345 1104 1346 1104 1347 1104 1347 1103 1349 1102 1350 1100 1349 1099 1347 1099 1347 1099 1346 1099 1345 
1100 1343 1100 1341 1100 1339 1097 1339 1095 1338 1094 1337 1092 1336 1091 1334 1089 1332 1088 1329 1088 1327 1089 1323 1090 1320 1093 1318 1096 1316 
1100 1315 1100 1307 1104 1307 1104 1315 1108 1316 1111 1318 1113 1321 1114 1324 1115 1328 1114 1332 1113 1335 1110 1337 1107 1338 43 _pl _cp 1100 1338 _m
_sp 1100 1338 1100 1317 1097 1318 1095 1321 1093 1323 1093 1327 1093 1331 1095 1334 1097 1337 9 _pl _cp 1104 1338 _m
_sp 1104 1338 1107 1337 1109 1334 1110 1331 1111 1327 1110 1323 1109 1321 1107 1318 1104 1317 9 _pl _cp 
0 g _f _s _s 
0 g 1237 1335 _m
_sp 1237 1335 1236 1340 1235 1344 1233 1347 1230 1349 1227 1350 1224 1350 1222 1349 1220 1347 1218 1344 1217 1342 1217 1339 1216 1336 1216 1332 1216 1326 
1217 1321 1219 1318 1222 1316 1226 1315 1229 1315 1231 1316 1233 1318 1235 1320 1236 1322 1236 1325 1237 1329 1237 1333 1237 1334 28 _pl _cp 1220 1336 _m
_sp 1220 1336 1221 1338 1221 1340 1222 1343 1223 1346 1224 1347 1226 1348 1229 1347 1231 1345 1232 1341 1233 1336 11 _pl _cp 1233 1334 _m
_sp 1233 1334 1233 1332 1233 1330 1233 1328 1233 1327 1232 1323 1231 1320 1229 1318 1227 1317 1225 1318 1223 1319 1221 1322 1220 1327 1220 1332 1220 1333 
1220 1334 16 _pl _cp 
0 g _f _s _s 
0 g 1791 1339 _m
_sp 1791 1339 1791 1341 1791 1343 1791 1344 1792 1345 1792 1346 1792 1347 1792 1347 1791 1349 1789 1350 1788 1349 1787 1347 1787 1347 1787 1346 1787 1345 
1787 1343 1787 1341 1787 1339 1784 1339 1782 1338 1781 1337 1779 1336 1778 1334 1777 1332 1776 1329 1776 1327 1776 1323 1778 1320 1780 1318 1783 1316 
1787 1315 1787 1307 1791 1307 1791 1315 1795 1316 1798 1318 1801 1321 1802 1324 1803 1328 1802 1332 1801 1335 1798 1337 1795 1338 43 _pl _cp 1787 1338 _m
_sp 1787 1338 1787 1317 1784 1318 1782 1321 1781 1323 1780 1327 1781 1331 1782 1334 1784 1337 9 _pl _cp 1791 1338 _m
_sp 1791 1338 1794 1337 1796 1334 1797 1331 1798 1327 1798 1323 1796 1321 1794 1318 1791 1317 9 _pl _cp 
0 g _f _s _s 
0 g 1925 1335 _m
_sp 1925 1335 1924 1340 1923 1344 1921 1347 1918 1349 1915 1350 1912 1350 1909 1349 1907 1347 1905 1344 1904 1342 1904 1339 1903 1336 1903 1332 1903 1326 
1905 1321 1907 1318 1910 1316 1914 1315 1916 1315 1918 1316 1920 1318 1922 1320 1923 1322 1924 1325 1925 1329 1925 1333 1925 1334 28 _pl _cp 1908 1336 _m
_sp 1908 1336 1908 1338 1908 1340 1909 1343 1910 1346 1912 1347 1914 1348 1916 1347 1918 1345 1919 1341 1920 1336 11 _pl _cp 1920 1334 _m
_sp 1920 1334 1920 1332 1920 1330 1920 1328 1920 1327 1919 1323 1918 1320 1916 1318 1914 1317 1912 1318 1910 1319 1909 1322 1908 1327 1908 1332 1908 1333 
1908 1334 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8757 5660 _m
/Times-BoldR 600 _ff
(\(6.5\))_S /Times-RomanR 600 _ff
1500 4576 _m
(Since)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(to)_S 67 _t
(world)_S 67 _t
(rotation)_S 67 _t
(matrix)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(R)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
(is)_S 67 _t
(an)_S 67 _t
(orthogonal)_S 67 _t
(matrix,)_S 67 _t
(it)_S 67 _t
(follows)_S 67 _t
(that)_S 1500 4225 _m
/Times-BoldR 600 _ff
(R)_S /Times-RomanR 600 _ff
67 _t
(inverse)_S 67 _t
(equals)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(R)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
(transpose.)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 71 1749 400 908 _cw 
_s 1142 958 _m
_sp 1142 958 1142 917 1153 917 1153 918 1150 918 1147 919 1147 922 1147 952 1147 954 1147 956 1150 957 1153 957 1153 958 13 _pl _cp 
0 g _f _s _s 
0 g 1203 917 _m
_sp 1203 917 1203 958 1192 958 1192 957 1195 957 1198 956 1198 953 1198 923 1198 921 1198 919 1195 918 1192 918 1192 917 13 _pl _cp 
0 g _f _s _s 
0 g 1231 964 _m
_sp 1231 964 1231 963 1232 964 1233 964 1234 964 1235 963 1235 962 1235 949 1234 946 1232 945 1231 945 1231 945 1241 945 1241 945 1240 945 
1238 946 1237 949 1237 967 18 _pl _cp 
0 g _f _s _s 
0 g 1328 958 _m
_sp 1328 958 1328 917 1339 917 1339 918 1336 918 1333 919 1333 922 1333 952 1333 954 1333 956 1336 957 1339 957 1339 958 13 _pl _cp 
0 g _f _s _s 
0 g 1389 917 _m
_sp 1389 917 1389 958 1377 958 1377 957 1381 957 1384 956 1384 953 1384 923 1384 921 1383 919 1380 918 1377 918 1377 917 13 _pl _cp 
0 g _f _s _s 
0 g 1176 942 _m
_sp 1176 942 1179 942 1181 943 1182 944 1183 945 1184 946 1185 948 1186 949 1186 951 1185 954 1184 956 1182 957 1180 957 1177 958 1174 958 
1163 958 1163 957 1164 957 1165 956 1166 955 1166 954 1165 952 1160 931 1159 929 1158 927 1157 926 1156 926 1156 926 1155 925 1168 925 
1168 926 1167 926 1165 927 1165 928 1165 929 1165 930 1165 931 1165 931 1168 941 1171 941 1177 925 1185 925 1185 926 1185 926 1183 926 
1182 927 1181 929 1180 931 48 _pl _cp 1168 944 _m
_sp 1168 944 1171 944 1174 944 1175 944 1177 945 1178 946 1179 948 1180 951 1180 953 1179 955 1177 956 1174 956 1172 956 1171 955 1170 951 
15 _pl _cp 
0 g _f _s _s 
0 g 1362 942 _m
_sp 1362 942 1365 942 1366 943 1368 944 1369 945 1370 946 1371 948 1371 949 1371 951 1371 954 1369 956 1368 957 1366 957 1363 958 1360 958 
1349 958 1348 957 1350 957 1351 956 1352 955 1352 954 1351 952 1346 931 1345 929 1344 927 1343 926 1342 926 1341 926 1341 925 1353 925 
1354 926 1352 926 1351 927 1350 928 1350 929 1350 930 1351 931 1351 931 1354 941 1357 941 1363 925 1371 925 1371 926 1370 926 1369 926 
1368 927 1367 929 1366 931 48 _pl _cp 1354 944 _m
_sp 1354 944 1357 944 1359 944 1361 944 1362 945 1364 946 1365 948 1366 951 1366 953 1365 955 1363 956 1360 956 1358 956 1357 955 1356 951 
15 _pl _cp 
0 g _f _s _s 
0 g 1397 961 _m
_sp 1397 961 1397 963 1398 964 1400 965 1402 965 1404 965 1400 949 1399 946 1397 945 1396 945 1396 945 1405 945 1406 945 1404 945 1403 946 
1403 947 1403 947 1403 948 1403 949 1408 965 1409 965 1412 964 1413 962 1413 962 1413 962 1413 962 1413 961 1414 961 1415 966 1397 966 
1396 961 31 _pl _cp 
0 g _f _s _s 
0 g 1225 955 _m
_sp 1225 955 1212 955 1212 954 1225 954 4 _pl _cp 
0 g _f _s _s 
0 g 1293 944 _m
_sp 1293 944 1274 944 1274 943 1293 943 4 _pl _cp 1293 937 _m
_sp 1293 937 1274 937 1274 935 1293 935 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8217 3770 _m
/Times-BoldR 600 _ff
(\(6.6\))_S /Times-RomanR 600 _ff
4950 1288 _m
(106)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1980 11855 _m
(The)_S 67 _t
(three)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(translation)_S 67 _t
(rates)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(obtained)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(body)_S 1500 11506 _m
(coordinate)_S 67 _t
(frame)_S 67 _t
(translation)_S 67 _t
(rates)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(following)_S 67 _t
(matrix)_S 67 _t
(equation:)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 215 1749 400 2585 _cw 
_s 1144 2729 _m
_sp 1144 2729 1142 2729 1142 2789 1151 2789 1151 2787 1144 2787 6 _pl _cp 
0 g _f _s _s 
0 g 1144 2709 _m
_sp 1144 2709 1142 2709 1142 2731 1144 2731 4 _pl _cp 
0 g _f _s _s 
0 g 1144 2689 _m
_sp 1144 2689 1142 2689 1142 2711 1144 2711 4 _pl _cp 
0 g _f _s _s 
0 g 1144 2669 _m
_sp 1144 2669 1142 2669 1142 2692 1144 2692 4 _pl _cp 
0 g _f _s _s 
0 g 1144 2650 _m
_sp 1144 2650 1142 2650 1142 2672 1144 2672 4 _pl _cp 
0 g _f _s _s 
0 g 1142 2653 _m
_sp 1142 2653 1144 2653 1144 2590 1151 2590 1151 2588 1142 2588 6 _pl _cp 
0 g _f _s _s 
0 g 1183 2729 _m
_sp 1183 2729 1184 2729 1184 2789 1175 2789 1175 2787 1183 2787 6 _pl _cp 
0 g _f _s _s 
0 g 1184 2709 _m
_sp 1184 2709 1183 2709 1183 2731 1184 2731 4 _pl _cp 
0 g _f _s _s 
0 g 1184 2689 _m
_sp 1184 2689 1183 2689 1183 2711 1184 2711 4 _pl _cp 
0 g _f _s _s 
0 g 1184 2669 _m
_sp 1184 2669 1183 2669 1183 2692 1184 2692 4 _pl _cp 
0 g _f _s _s 
0 g 1184 2650 _m
_sp 1184 2650 1183 2650 1183 2672 1184 2672 4 _pl _cp 
0 g _f _s _s 
0 g 1184 2656 _m
_sp 1184 2656 1183 2656 1183 2592 1175 2592 1175 2590 1184 2590 6 _pl _cp 
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0 g 1355 2729 _m
_sp 1355 2729 1353 2729 1353 2789 1363 2789 1363 2787 1355 2787 6 _pl _cp 
0 g _f _s _s 
0 g 1355 2709 _m
_sp 1355 2709 1353 2709 1353 2731 1355 2731 4 _pl _cp 
0 g _f _s _s 
0 g 1355 2689 _m
_sp 1355 2689 1353 2689 1353 2711 1355 2711 4 _pl _cp 
0 g _f _s _s 
0 g 1355 2669 _m
_sp 1355 2669 1353 2669 1353 2692 1355 2692 4 _pl _cp 
0 g _f _s _s 
0 g 1355 2650 _m
_sp 1355 2650 1353 2650 1353 2672 1355 2672 4 _pl _cp 
0 g _f _s _s 
0 g 1353 2653 _m
_sp 1353 2653 1355 2653 1355 2590 1363 2590 1363 2588 1353 2588 6 _pl _cp 
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1156 2740 1157 2741 1158 2742 1159 2743 1160 2745 1161 2747 1161 2747 1162 2746 1162 2743 1163 2741 1164 2739 1165 2738 1166 2738 1167 2738 1169 2739 
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75 _pl _cp 
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1159 2666 1157 2664 1155 2663 1155 2663 1155 2663 1155 2663 1154 2664 1153 2664 1152 2664 1151 2663 1150 2662 1151 2661 1153 2660 1155 2660 1156 2661 
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1165 2675 1164 2676 1164 2680 1163 2683 1163 2686 1162 2688 1161 2690 1160 2691 1160 2692 1159 2693 70 _pl _cp 
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1168 2603 1167 2602 1167 2602 1168 2601 1168 2601 1168 2601 1168 2600 1167 2600 1165 2601 1163 2603 1162 2604 1160 2605 1159 2606 1157 2606 1171 2623 
1171 2624 1157 2624 1155 2618 1156 2618 1157 2619 1158 2620 1160 2620 1162 2620 1167 2620 1156 2606 1154 2604 41 _pl _cp 
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1286 2701 1288 2701 1288 2699 1288 2698 1288 2696 1282 2676 1281 2674 1280 2672 1279 2671 1278 2671 1278 2671 1278 2670 1290 2670 1290 2671 1289 2671 
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1302 2676 46 _pl _cp 1291 2688 _m
_sp 1291 2688 1293 2688 1296 2688 1298 2689 1299 2690 1301 2691 1302 2693 1302 2695 1302 2698 1301 2700 1299 2701 1297 2701 1294 2701 1294 2700 1293 2696 
15 _pl _cp 
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1377 2761 1370 2760 1369 2759 1371 2759 1372 2758 1372 2757 1372 2756 1372 2755 1369 2745 1369 2744 1369 2743 1368 2742 1368 2741 1369 2739 1371 2738 
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1387 2751 1387 2752 1388 2757 1389 2760 64 _pl _cp 
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1377 2671 1378 2671 1380 2673 1381 2674 1383 2676 1384 2678 1385 2680 1387 2681 1388 2683 1389 2684 1390 2686 1390 2687 1391 2689 1391 2690 1390 2692 
1388 2693 1386 2692 1386 2691 1386 2690 1387 2689 1388 2688 1388 2687 1387 2685 1386 2683 1385 2682 1384 2680 1383 2678 1382 2677 1380 2676 1379 2675 
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0 g _f _s _s 
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_sp 1373 2608 1373 2611 1373 2614 1372 2616 1372 2618 1371 2620 1371 2622 1371 2623 1370 2625 1364 2623 1364 2622 1365 2622 1367 2622 1367 2620 1368 2617 
1369 2613 1369 2609 1369 2606 1370 2602 1370 2601 1380 2618 1382 2602 1383 2602 1386 2605 1388 2608 1391 2611 1393 2614 1394 2616 1395 2618 1396 2619 
1396 2621 1395 2623 1393 2624 1392 2624 1391 2623 1391 2622 1392 2621 1393 2620 1393 2619 1393 2618 1393 2616 1392 2615 1391 2614 1390 2612 1389 2610 
1387 2608 1385 2606 1383 2624 1383 2625 49 _pl _cp 
0 g _f _s _s 
0 g 1235 2689 _m
_sp 1235 2689 1216 2689 1216 2688 1235 2688 4 _pl _cp 1235 2681 _m
_sp 1235 2681 1216 2681 1216 2680 1235 2680 4 _pl _cp 
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_sp 1265 2703 1265 2662 1276 2662 1276 2663 1272 2663 1270 2664 1269 2667 1269 2697 1269 2699 1270 2701 1273 2701 1276 2701 1276 2703 13 _pl _cp 
0 g _f _s _s 
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0 g _f _s 
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_s grestore 8217 10766 _m
/Times-BoldR 600 _ff
(\(6.7\))_S /Times-RomanR 600 _ff
1500 9643 _m
(Inversely,)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(velocities)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
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(coordinate)_S 1500 9294 _m
(frame)_S 67 _t
(velocities)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
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(fashion:)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 234 1749 400 2013 _cw 
_s 1132 2176 _m
_sp 1132 2176 1130 2176 1130 2237 1139 2237 1139 2235 1132 2235 6 _pl _cp 
0 g _f _s _s 
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_sp 1132 2157 1130 2157 1130 2179 1132 2179 4 _pl _cp 
0 g _f _s _s 
0 g 1132 2137 _m
_sp 1132 2137 1130 2137 1130 2159 1132 2159 4 _pl _cp 
0 g _f _s _s 
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_sp 1132 2117 1130 2117 1130 2139 1132 2139 4 _pl _cp 
0 g _f _s _s 
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_sp 1132 2097 1130 2097 1130 2120 1132 2120 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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_sp 1182 2176 1183 2176 1183 2237 1174 2237 1174 2235 1182 2235 6 _pl _cp 
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0 g _f _s _s 
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_sp 1183 2097 1182 2097 1182 2120 1183 2120 4 _pl _cp 
0 g _f _s _s 
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_sp 1183 2078 1182 2078 1182 2100 1183 2100 4 _pl _cp 
0 g _f _s _s 
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_sp 1183 2084 1182 2084 1182 2020 1174 2020 1174 2018 1183 2018 6 _pl _cp 
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_sp 1378 2176 1376 2176 1376 2237 1386 2237 1386 2235 1378 2235 6 _pl _cp 
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_sp 1378 2097 1376 2097 1376 2120 1378 2120 4 _pl _cp 
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_sp 1417 2176 1419 2176 1419 2237 1409 2237 1409 2235 1417 2235 6 _pl _cp 
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_sp 1419 2157 1417 2157 1417 2179 1419 2179 4 _pl _cp 
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_sp 1419 2078 1417 2078 1417 2100 1419 2100 4 _pl _cp 
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_sp 1419 2084 1417 2084 1417 2020 1409 2020 1409 2018 1419 2018 6 _pl _cp 
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1154 2217 1146 2215 1146 2214 1147 2214 1148 2214 1149 2213 1149 2212 1148 2210 1146 2201 1146 2200 1145 2198 1145 2197 1145 2196 1146 2194 1148 2193 
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1165 2196 1167 2199 1166 2200 1165 2199 1164 2197 1163 2196 1162 2196 1161 2196 1161 2197 1161 2198 1161 2199 1162 2200 1162 2201 1163 2203 1163 2205 
1163 2206 1164 2208 1165 2213 1166 2216 64 _pl _cp 
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1154 2112 1155 2113 1157 2115 1158 2116 1160 2118 1161 2120 1162 2122 1164 2123 1165 2125 1166 2126 1167 2129 1168 2131 1167 2134 1165 2135 1163 2134 
1162 2133 1163 2132 1164 2130 1165 2130 1165 2129 1164 2127 1163 2125 1162 2124 1161 2122 1160 2120 1159 2119 1157 2118 1156 2117 1156 2118 1156 2121 
1156 2124 1155 2127 1155 2129 1154 2131 1154 2132 1153 2134 1153 2135 52 _pl _cp 
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1145 2041 1146 2037 1146 2034 1146 2030 1147 2029 1157 2046 1159 2030 1160 2030 1163 2033 1165 2036 1168 2039 1170 2042 1171 2044 1172 2046 1173 2047 
1173 2049 1172 2051 1170 2052 1169 2052 1168 2051 1168 2050 1169 2049 1170 2048 1170 2047 1170 2046 1169 2044 1169 2043 1168 2042 1167 2040 1165 2038 
1164 2036 1162 2034 1160 2052 1159 2053 49 _pl _cp 
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1285 2143 1287 2143 1287 2141 1287 2140 1287 2138 1281 2118 1280 2116 1279 2114 1278 2113 1277 2113 1277 2113 1277 2112 1289 2112 1289 2113 1288 2113 
1287 2114 1286 2115 1286 2116 1286 2116 1286 2117 1287 2118 1289 2128 1293 2128 1299 2112 1306 2112 1307 2113 1306 2113 1305 2113 1304 2114 1302 2116 
1301 2118 46 _pl _cp 1290 2130 _m
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15 _pl _cp 
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1339 2133 1339 2134 1339 2134 1339 2135 1344 2152 1345 2152 1348 2151 1349 2149 1349 2149 1349 2148 1349 2148 1349 2147 1349 2147 1351 2153 1333 2153 
1332 2148 31 _pl _cp 
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1391 2196 1391 2196 1392 2198 1393 2199 1394 2201 1395 2202 1396 2203 1396 2202 1397 2199 1398 2196 1398 2194 1399 2193 1400 2193 1402 2193 1403 2194 
1405 2196 1406 2198 1406 2199 1405 2200 1404 2197 1402 2196 1401 2196 1401 2197 1401 2199 1400 2203 1399 2207 1399 2208 1401 2210 1402 2212 1403 2213 
1404 2213 1404 2213 1405 2213 1406 2213 1406 2213 1407 2213 1408 2215 1407 2216 1406 2217 1404 2217 1403 2215 1401 2213 1399 2210 1398 2210 1398 2212 
1397 2214 1397 2216 1396 2217 1395 2217 1393 2217 1391 2216 1389 2215 1389 2214 1391 2214 1391 2214 1392 2214 1393 2214 1394 2212 1394 2210 1395 2207 
75 _pl _cp 
0 g _f _s _s 
0 g 1386 2133 _m
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1393 2108 1391 2106 1390 2105 1389 2105 1389 2105 1389 2105 1388 2105 1387 2106 1386 2106 1386 2105 1385 2104 1386 2102 1387 2102 1389 2102 1390 2103 
1392 2104 1393 2105 1395 2107 1396 2109 1399 2112 1400 2115 1402 2118 1404 2121 1405 2124 1406 2127 1407 2129 1407 2131 1406 2134 1404 2135 1403 2134 
1402 2132 1402 2132 1403 2131 1405 2130 1405 2129 1405 2128 1405 2127 1404 2126 1404 2124 1403 2122 1401 2120 1401 2119 1400 2117 1400 2117 1399 2116 
1399 2117 1399 2118 1398 2122 1398 2125 1397 2128 1396 2130 1395 2133 1394 2135 68 _pl _cp 
0 g _f _s _s 
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1402 2031 1401 2030 1402 2030 1402 2029 1402 2029 1402 2029 1402 2028 1401 2028 1399 2029 1397 2031 1396 2032 1394 2033 1393 2034 1391 2034 1406 2051 
1405 2052 1391 2052 1389 2046 1391 2046 1392 2048 1396 2048 1402 2048 1390 2034 1388 2032 39 _pl _cp 
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0 g _f _s 
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_s grestore 8217 8514 _m
/Times-BoldR 600 _ff
(\(6.8\))_S /Times-RomanR 600 _ff
1980 7431 _m
(The)_S 67 _t
(three)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
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(Euler)_S 67 _t
(angle)_S 67 _t
(rotation)_S 67 _t
(rates)_S 67 _t
(are)_S 67 _t
(obtained)_S 67 _t
(from)_S 1500 7082 _m
(body)_S 67 _t
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(by)_S 67 _t
(the)_S 67 _t
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(92b\):)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 1749 400 1532 _cw 
_s 855 1590 _m
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856 1573 853 1572 851 1571 850 1570 848 1569 847 1567 845 1565 844 1563 844 1560 845 1556 846 1553 849 1551 852 1549 856 1549 856 1540 
860 1540 860 1549 864 1550 867 1551 869 1554 870 1557 871 1561 870 1565 869 1568 866 1570 863 1572 41 _pl _cp 856 1571 _m
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1171 1573 1168 1572 1166 1571 1165 1570 1163 1569 1162 1567 1161 1565 1160 1563 1160 1560 1161 1555 1163 1552 1166 1550 1171 1549 1171 1540 1175 1540 
1175 1549 1179 1550 1182 1551 1185 1554 1186 1557 1187 1561 1186 1565 1185 1568 1182 1570 1179 1572 40 _pl _cp 1171 1571 _m
_sp 1171 1571 1171 1550 1168 1551 1166 1554 1165 1556 1164 1560 1165 1564 1166 1567 1168 1570 9 _pl _cp 1175 1571 _m
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1299 1555 1301 1551 1304 1550 1308 1549 1310 1549 1312 1550 1314 1552 1316 1554 1317 1556 1318 1559 1319 1562 1319 1566 1319 1567 28 _pl _cp 1302 1569 _m
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_sp 1314 1567 1314 1565 1314 1563 1314 1561 1314 1560 1313 1556 1312 1553 1310 1551 1308 1550 1306 1551 1304 1553 1303 1556 1302 1560 1302 1566 1302 1566 
1302 1567 16 _pl _cp 
0 g _f _s _s 
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1540 1573 1537 1572 1535 1571 1534 1570 1532 1569 1531 1567 1529 1565 1528 1563 1528 1560 1529 1556 1530 1553 1533 1551 1536 1549 1540 1549 1540 1540 
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(\(6.11\))_S /Times-RomanR 600 _ff
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15 _pl _cp 
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45 _pl _cp 
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1424 2328 1422 2325 1421 2322 18 _pl _cp 1424 2320 _m
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60 _pl _cp 
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1520 2311 1519 2309 1518 2308 1518 2306 1517 2305 1516 2304 1515 2303 1514 2302 1513 2300 1512 2299 40 _pl _cp 
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1193 2247 1191 2244 1190 2241 18 _pl _cp 1193 2239 _m
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60 _pl _cp 
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1527 2228 1526 2231 1526 2243 1527 2245 1529 2246 1530 2247 1531 2247 1533 2247 1534 2245 1535 2243 1535 2240 1535 2231 1535 2228 1532 2228 1532 2228 
1532 2227 1543 2227 1543 2228 1542 2228 1540 2228 1539 2231 1539 2242 1539 2245 1538 2247 1536 2249 1533 2249 1531 2249 1530 2248 1528 2247 1526 2245 
45 _pl _cp 
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1555 2220 1558 2218 1559 2219 1558 2220 1557 2221 1555 2222 1554 2223 1553 2226 1552 2228 1551 2230 1551 2233 1550 2236 1550 2239 1550 2242 1551 2245 
1551 2248 1552 2250 1553 2252 1554 2255 1555 2256 1557 2257 1558 2258 1559 2259 38 _pl _cp 
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1596 2258 1593 2260 1592 2259 1594 2257 1596 2255 1597 2254 1598 2252 1598 2251 1599 2250 1600 2248 1600 2245 1600 2242 1600 2239 1600 2236 1600 2233 
1600 2230 1599 2228 1598 2227 1598 2226 1597 2224 1596 2223 1594 2221 1592 2219 38 _pl _cp 
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1064 2152 1065 2157 1066 2163 1065 2169 1064 2173 1062 2177 1059 2179 1055 2180 1051 2179 1048 2177 1045 2173 1044 2168 27 _pl _cp 1048 2163 _m
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1055 2177 1052 2176 1050 2174 1048 2169 19 _pl _cp 
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1116 2157 1114 2158 1112 2159 1109 2160 1108 2162 1106 2163 1106 2164 1106 2165 1107 2166 1109 2167 1111 2167 1113 2167 1115 2166 1116 2164 1118 2161 
1118 2161 1118 2168 1118 2168 1117 2168 1116 2168 1116 2168 1115 2168 1114 2168 1113 2169 1111 2169 1108 2168 1105 2167 1104 2165 1103 2162 1103 2161 
1105 2159 1106 2158 1109 2156 1113 2154 1115 2152 1116 2150 1115 2148 1112 2147 1109 2147 1107 2148 1106 2149 1106 2150 1105 2152 1104 2153 1103 2153 
60 _pl _cp 
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1131 2148 1130 2151 17 _pl _cp 1125 2177 _m
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1144 2148 1143 2151 1143 2162 1145 2164 1146 2165 1148 2166 1149 2166 1150 2166 1151 2164 1152 2162 1152 2159 1152 2151 1152 2148 1149 2147 1149 2147 
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45 _pl _cp 
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1172 2139 1175 2137 1176 2138 1174 2140 1172 2142 1171 2143 1170 2145 1169 2146 1169 2147 1168 2149 1168 2152 1168 2155 1168 2158 1168 2161 1168 2164 
1168 2167 1169 2169 1169 2170 1170 2172 1171 2173 1172 2174 1174 2176 1176 2178 38 _pl _cp 
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1213 2178 1210 2180 1209 2178 1210 2177 1212 2176 1213 2175 1214 2174 1215 2172 1216 2169 1217 2167 1217 2164 1218 2161 1218 2158 1218 2155 1217 2152 
1217 2149 1216 2147 1215 2145 1214 2142 1213 2141 1212 2140 1210 2139 1209 2138 38 _pl _cp 
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1250 2157 1248 2158 1246 2159 1244 2160 1242 2162 1241 2163 1241 2164 1242 2166 1245 2167 1248 2167 1250 2166 1251 2164 1252 2161 1253 2161 1253 2168 
1252 2168 1251 2168 1251 2168 1251 2168 1250 2168 1248 2168 1247 2169 1245 2169 1242 2168 1240 2167 1238 2165 1237 2162 1237 2161 1239 2159 1240 2158 
1243 2156 1247 2154 1250 2152 1251 2150 1251 2149 1250 2148 1248 2147 1246 2147 1244 2147 1241 2148 1240 2149 1240 2150 1239 2152 1238 2153 1237 2153 
60 _pl _cp 
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1273 2147 1275 2150 1277 2154 1276 2154 1275 2152 1273 2150 1271 2149 1268 2148 1265 2149 1263 2151 1262 2155 1261 2159 1261 2159 28 _pl _cp 1271 2161 _m
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1294 2162 1296 2161 1297 2162 1298 2163 1297 2165 1296 2167 1293 2168 1290 2169 1286 2168 1283 2166 1281 2164 1280 2160 1279 2157 1280 2152 1282 2148 
1285 2146 1289 2145 1291 2145 1292 2146 1294 2147 1295 2148 1296 2149 1297 2150 1298 2151 1299 2153 40 _pl _cp 
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1312 2139 1315 2137 1316 2138 1315 2139 1314 2140 1312 2141 1311 2142 1310 2145 1309 2147 1308 2149 1308 2152 1307 2155 1307 2158 1307 2161 1308 2164 
1308 2167 1309 2169 1310 2172 1311 2174 1312 2175 1314 2176 1315 2177 1316 2178 38 _pl _cp 
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1348 2178 1345 2180 1345 2178 1347 2176 1349 2174 1350 2173 1351 2172 1351 2170 1352 2169 1353 2167 1353 2164 1353 2161 1353 2158 1353 2155 1353 2152 
1353 2149 1352 2147 1351 2146 1351 2145 1350 2143 1349 2142 1347 2140 1345 2138 38 _pl _cp 
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_sp 1415 2154 1413 2152 1412 2150 1410 2149 1408 2149 1405 2150 1403 2152 1401 2154 1400 2158 1401 2162 1402 2164 1404 2166 1407 2167 1409 2166 1410 2164 
1411 2162 1413 2161 1414 2162 1415 2163 1414 2165 1413 2167 1411 2168 1408 2169 1404 2168 1401 2166 1398 2164 1397 2160 1396 2157 1397 2152 1399 2148 
1402 2146 1406 2145 1408 2145 1410 2146 1411 2147 1413 2148 1414 2149 1414 2150 1415 2151 1416 2153 40 _pl _cp 
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1426 2168 1423 2167 1421 2164 1419 2161 19 _pl _cp 1423 2158 _m
_sp 1423 2158 1424 2153 1425 2150 1427 2148 1430 2147 1433 2148 1435 2149 1436 2152 1436 2156 1435 2160 1434 2164 1432 2166 1429 2167 1427 2166 1425 2165 
1424 2162 1423 2159 1423 2159 18 _pl _cp 
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1456 2157 1455 2158 1452 2159 1450 2160 1448 2162 1447 2163 1447 2164 1448 2166 1451 2167 1454 2167 1456 2166 1457 2164 1458 2161 1459 2161 1459 2168 
1458 2168 1458 2168 1457 2168 1457 2168 1456 2168 1454 2168 1453 2169 1451 2169 1448 2168 1446 2167 1445 2165 1444 2162 1444 2161 1445 2159 1447 2158 
1449 2156 1453 2154 1456 2152 1457 2150 1457 2149 1456 2148 1454 2147 1452 2147 1450 2147 1447 2148 1446 2150 1445 2153 1444 2153 58 _pl _cp 
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1474 2139 1477 2137 1478 2138 1476 2139 1475 2140 1474 2141 1473 2142 1472 2143 1472 2145 1471 2146 1470 2147 1470 2149 1470 2152 1469 2155 1469 2158 
1469 2161 1470 2164 1470 2167 1470 2169 1471 2170 1472 2172 1472 2173 1473 2174 1474 2175 1475 2176 1476 2177 1478 2178 42 _pl _cp 
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1514 2178 1511 2180 1511 2178 1513 2176 1515 2174 1516 2173 1517 2172 1517 2170 1518 2169 1519 2167 1519 2164 1519 2161 1519 2158 1519 2155 1519 2152 
1519 2149 1518 2147 1517 2146 1517 2145 1516 2143 1515 2142 1513 2140 1511 2138 38 _pl _cp 
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1552 2157 1550 2158 1547 2159 1545 2160 1543 2162 1542 2163 1542 2164 1542 2165 1543 2166 1545 2167 1547 2167 1549 2167 1551 2166 1552 2164 1553 2161 
1554 2161 1554 2168 1553 2168 1553 2168 1552 2168 1552 2168 1551 2168 1549 2168 1548 2169 1547 2169 1544 2168 1541 2167 1540 2165 1539 2162 1539 2161 
1540 2159 1542 2158 1545 2156 1548 2154 1551 2152 1552 2150 1551 2148 1548 2147 1545 2147 1543 2148 1542 2149 1541 2150 1541 2152 1540 2153 1539 2153 
60 _pl _cp 
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1571 2146 1574 2147 1577 2150 1579 2154 1578 2154 1576 2152 1575 2150 1572 2149 1570 2148 1567 2149 1564 2151 1563 2155 1562 2159 1562 2159 29 _pl _cp 1572 2161 _m
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1596 2162 1597 2161 1598 2162 1599 2163 1598 2165 1597 2167 1595 2168 1592 2169 1588 2168 1585 2166 1583 2164 1581 2160 1581 2157 1582 2152 1584 2148 
1586 2146 1590 2145 1592 2145 1594 2146 1595 2147 1597 2148 1598 2149 1599 2150 1599 2151 1600 2153 40 _pl _cp 
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1614 2139 1617 2137 1617 2138 1615 2140 1613 2142 1612 2143 1612 2145 1611 2146 1610 2147 1609 2149 1609 2152 1609 2155 1609 2158 1609 2161 1609 2164 
1609 2167 1610 2169 1611 2170 1612 2172 1612 2173 1613 2174 1615 2176 1617 2178 38 _pl _cp 
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1650 2178 1647 2180 1646 2178 1647 2177 1649 2176 1650 2175 1651 2174 1652 2172 1653 2169 1654 2167 1654 2164 1655 2161 1655 2158 1655 2155 1654 2152 
1654 2149 1653 2147 1652 2145 1651 2142 1650 2141 1649 2140 1647 2139 1646 2138 38 _pl _cp 
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910 2226 910 2228 908 2228 907 2228 906 2230 906 2230 906 2231 907 2233 913 2257 915 2257 918 2257 920 2256 921 2255 921 2253 921 2253 
921 2252 921 2252 921 2251 922 2251 924 2259 897 2259 895 2251 37 _pl _cp 
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1192 2331 1189 2330 1187 2329 1186 2328 1184 2327 1183 2325 1181 2323 1180 2321 1180 2318 1181 2314 1182 2311 1185 2309 1188 2307 1192 2307 1192 2299 
1196 2299 1196 2307 1200 2308 1203 2309 1205 2312 1206 2315 1207 2319 1206 2323 1205 2326 1203 2329 1200 2330 41 _pl _cp 1192 2329 _m
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1320 2313 1322 2310 1325 2308 1328 2307 1331 2307 1333 2308 1335 2310 1337 2312 1338 2314 1339 2317 1339 2321 1339 2325 1339 2326 28 _pl _cp 1323 2327 _m
_sp 1323 2327 1323 2330 1323 2332 1324 2335 1325 2337 1327 2339 1328 2339 1331 2338 1333 2336 1334 2332 1335 2327 11 _pl _cp 1335 2325 _m
_sp 1335 2325 1335 2323 1335 2321 1335 2320 1335 2319 1334 2314 1333 2311 1331 2310 1329 2309 1327 2309 1325 2311 1324 2314 1323 2318 1323 2324 1323 2325 
1323 2325 16 _pl _cp 
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1494 2331 1491 2330 1489 2329 1487 2328 1486 2327 1484 2325 1483 2323 1482 2321 1482 2318 1483 2314 1485 2310 1488 2308 1493 2307 1493 2299 1498 2299 
1498 2307 1501 2308 1504 2309 1507 2312 1508 2315 1509 2319 1508 2323 1507 2326 1504 2329 1501 2330 40 _pl _cp 1494 2329 _m
_sp 1494 2329 1493 2308 1490 2309 1488 2312 1487 2315 1486 2319 1487 2323 1488 2326 1491 2328 9 _pl _cp 1497 2329 _m
_sp 1497 2329 1500 2328 1503 2326 1504 2323 1505 2319 1504 2315 1503 2312 1501 2310 1498 2309 9 _pl _cp 
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1621 2313 1623 2310 1626 2308 1630 2307 1632 2307 1635 2308 1637 2310 1638 2312 1639 2314 1640 2317 1641 2321 1641 2325 1641 2326 28 _pl _cp 1624 2327 _m
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_sp 1636 2325 1636 2323 1636 2321 1636 2320 1636 2319 1636 2314 1635 2311 1633 2310 1631 2309 1628 2309 1626 2311 1625 2314 1624 2318 1624 2324 1624 2325 
1624 2325 16 _pl _cp 
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1262 2254 1263 2251 1263 2250 1260 2249 1258 2249 1256 2248 1255 2246 1253 2244 1252 2242 1251 2240 1251 2238 1251 2234 1253 2231 1255 2228 1258 2226 
1262 2226 1262 2218 1267 2218 1267 2226 1270 2227 1273 2229 1276 2232 1277 2235 1278 2239 1277 2242 1276 2245 1273 2248 1270 2249 43 _pl _cp 1263 2248 _m
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1573 2254 1574 2251 1574 2250 1571 2249 1569 2249 1567 2248 1566 2246 1564 2244 1563 2242 1562 2240 1562 2238 1562 2234 1564 2231 1566 2228 1569 2226 
1573 2226 1573 2218 1578 2218 1578 2226 1581 2227 1584 2229 1587 2232 1588 2235 1589 2239 1588 2242 1587 2245 1584 2248 1581 2249 43 _pl _cp 1574 2248 _m
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1191 2173 1191 2171 1191 2169 1188 2169 1186 2168 1185 2167 1183 2166 1182 2164 1180 2162 1179 2159 1179 2157 1180 2153 1181 2150 1184 2148 1187 2146 
1191 2145 1191 2137 1195 2137 1195 2145 1199 2146 1202 2148 1204 2151 1205 2154 1206 2158 1205 2162 1204 2165 1201 2167 1198 2168 43 _pl _cp 1191 2168 _m
_sp 1191 2168 1191 2147 1188 2148 1186 2151 1184 2153 1184 2157 1184 2161 1186 2164 1188 2167 9 _pl _cp 1195 2168 _m
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1321 2151 1323 2148 1326 2146 1330 2145 1332 2145 1335 2146 1337 2148 1338 2150 1339 2152 1340 2155 1341 2159 1341 2163 1341 2164 28 _pl _cp 1324 2166 _m
_sp 1324 2166 1324 2168 1325 2170 1325 2173 1326 2176 1328 2177 1330 2178 1333 2177 1335 2175 1336 2171 1336 2166 11 _pl _cp 1336 2164 _m
_sp 1336 2164 1336 2162 1336 2160 1336 2158 1336 2157 1336 2153 1335 2150 1333 2148 1331 2147 1328 2148 1326 2149 1325 2152 1324 2157 1324 2162 1324 2163 
1324 2164 16 _pl _cp 
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1492 2173 1492 2171 1492 2169 1489 2169 1487 2168 1486 2167 1484 2166 1483 2164 1482 2162 1481 2159 1481 2157 1481 2153 1483 2150 1485 2148 1488 2146 
1492 2145 1492 2137 1496 2137 1496 2145 1500 2146 1503 2148 1506 2151 1507 2154 1508 2158 1507 2162 1506 2165 1503 2167 1500 2168 43 _pl _cp 1492 2168 _m
_sp 1492 2168 1492 2147 1489 2148 1487 2151 1486 2153 1485 2157 1486 2161 1487 2164 1489 2167 9 _pl _cp 1496 2168 _m
_sp 1496 2168 1499 2167 1501 2164 1502 2161 1503 2157 1503 2153 1501 2151 1499 2148 1496 2147 9 _pl _cp 
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_sp 1642 2165 1641 2170 1640 2174 1638 2177 1635 2179 1632 2180 1629 2180 1627 2179 1625 2177 1623 2174 1622 2172 1622 2169 1621 2166 1621 2162 1621 2156 
1623 2151 1625 2148 1628 2146 1631 2145 1634 2145 1636 2146 1638 2148 1640 2150 1641 2152 1642 2155 1642 2159 1642 2163 1642 2164 28 _pl _cp 1626 2166 _m
_sp 1626 2166 1626 2168 1626 2170 1627 2173 1628 2176 1630 2177 1631 2178 1634 2177 1636 2175 1637 2171 1638 2166 11 _pl _cp 1638 2164 _m
_sp 1638 2164 1638 2162 1638 2160 1638 2158 1638 2157 1637 2153 1636 2150 1634 2148 1632 2147 1630 2148 1628 2149 1627 2152 1626 2157 1626 2162 1626 2163 
1626 2164 16 _pl _cp 
0 g _f _s 
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/Times-BoldR 600 _ff
(\(6.13\))_S /Times-RomanR 600 _ff
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(However)_S 67 _t
(note)_S 67 _t
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/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(T)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
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([)_S /Times-BoldItalicR 600 _ff
(T)_S /Times-BoldR 600 _ff
(])_S /Times-BoldR 360 _ff
5408 7976 _m
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/Times-RomanR 600 _ff
5508 7895 _m
67 _t
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1242 1864 1242 1867 1242 1885 18 _pl _cp 
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0 g _f _s _s 
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1171 1843 1172 1844 1170 1844 1168 1845 1168 1846 1168 1847 1168 1848 1168 1850 1175 1874 1177 1874 1180 1874 1182 1873 1183 1872 1183 1870 1183 1870 
1183 1869 1183 1869 1183 1868 1184 1868 1186 1876 1159 1876 1157 1868 37 _pl _cp 
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_sp 1345 1868 1346 1870 1347 1872 1348 1873 1349 1873 1351 1874 1353 1874 1356 1874 1350 1850 1349 1847 1348 1845 1347 1844 1346 1844 1344 1844 1344 1843 
1358 1843 1358 1844 1356 1844 1355 1845 1354 1846 1354 1847 1354 1848 1355 1850 1362 1874 1364 1874 1366 1874 1368 1873 1369 1872 1369 1870 1369 1870 
1369 1869 1369 1869 1369 1868 1370 1868 1372 1876 1346 1876 1343 1868 37 _pl _cp 
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1405 1865 1405 1865 1405 1866 1405 1867 1410 1883 1411 1883 1414 1882 1415 1880 1415 1880 1415 1880 1415 1880 1415 1879 1415 1879 1417 1884 1399 1884 
1398 1879 31 _pl _cp 
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1277 1855 1277 1853 1284 1853 1281 1847 1282 1846 20 _pl _cp 
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/Times-BoldR 600 _ff
(\(6.14\))_S /Times-RomanR 600 _ff
1500 6730 _m
(Instead)_S 67 _t
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1096 1443 1094 1443 1093 1443 1093 1444 1093 1445 1093 1445 1093 1447 1095 1452 1097 1451 1098 1451 1100 1451 1103 1452 1106 1454 1108 1456 1110 1459 
1112 1462 1113 1465 1113 1468 1113 1471 1112 1473 1110 1474 1108 1474 1105 1474 1103 1473 1101 1471 40 _pl _cp 1096 1456 _m
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1104 1471 1101 1470 1100 1468 1099 1466 1098 1464 1097 1461 21 _pl _cp 
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1202 1479 1202 1476 1202 1475 1199 1474 1197 1474 1196 1473 1194 1471 1193 1469 1191 1467 1190 1465 1190 1463 1191 1459 1192 1456 1195 1453 1198 1452 
1202 1451 1202 1443 1206 1443 1206 1451 1210 1452 1213 1454 1215 1457 1216 1460 1217 1464 1216 1468 1214 1472 1211 1474 42 _pl _cp 1202 1473 _m
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1301 1468 1301 1467 1301 1461 1301 1459 1301 1457 1301 1455 1302 1454 1304 1453 1305 1452 1307 1451 1310 1451 1310 1441 1314 1441 1314 1451 1318 1452 
1321 1453 1322 1456 1323 1461 1323 1467 1323 1470 1325 1471 1325 1471 1326 1471 1326 1471 1326 1471 1326 1473 1324 1473 1323 1473 1321 1473 1319 1473 
1319 1461 1319 1458 1318 1455 1316 1454 1314 1453 1314 1481 51 _pl _cp 
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1421 1457 1423 1454 1426 1452 1429 1451 1432 1451 1434 1452 1436 1454 1438 1456 1439 1458 1440 1461 1440 1465 1440 1469 1440 1470 28 _pl _cp 1424 1471 _m
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_sp 1436 1469 1436 1467 1436 1465 1436 1464 1436 1463 1435 1458 1434 1455 1432 1454 1430 1453 1428 1454 1426 1455 1425 1458 1424 1463 1424 1468 1424 1469 
1424 1469 16 _pl _cp 
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1355 1463 1353 1464 1351 1465 1349 1466 1347 1468 1346 1469 1346 1470 1347 1472 1350 1473 1353 1473 1355 1472 1356 1470 1357 1467 1358 1467 1358 1474 
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60 _pl _cp 
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1370 1453 1370 1456 17 _pl _cp 1364 1483 _m
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1383 1453 1383 1456 1383 1468 1384 1470 1386 1471 1387 1472 1388 1472 1390 1472 1391 1470 1391 1468 1391 1465 1391 1456 1391 1453 1389 1453 1388 1453 
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45 _pl _cp 
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1412 1445 1415 1443 1415 1444 1413 1446 1411 1448 1410 1449 1410 1451 1409 1452 1408 1453 1407 1455 1407 1458 1407 1461 1407 1464 1407 1467 1407 1470 
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1448 1483 1445 1485 1444 1484 1445 1483 1447 1482 1448 1481 1449 1480 1450 1477 1451 1475 1452 1473 1452 1470 1453 1467 1453 1464 1453 1461 1452 1458 
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(\(6.15\))_S /Times-RomanR 600 _ff
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957 1184 958 1185 960 1186 961 1187 963 1189 964 1191 961 1180 960 1177 958 1176 957 1176 956 1175 968 1175 968 1176 966 1176 965 1176 
965 1177 965 1178 965 1180 973 1207 969 1207 35 _pl _cp 954 1191 _m
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958 1200 956 1197 955 1194 954 1191 954 1191 20 _pl _cp 
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1052 1190 1054 1187 1057 1185 1061 1184 1063 1184 1066 1185 1068 1187 1069 1189 1070 1191 1071 1194 1072 1198 1072 1202 1072 1203 28 _pl _cp 1055 1204 _m
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_sp 1067 1202 1067 1200 1067 1198 1067 1197 1067 1196 1067 1191 1066 1188 1064 1187 1062 1186 1059 1187 1057 1188 1056 1191 1055 1196 1055 1201 1055 1202 
1055 1202 16 _pl _cp 
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1183 1212 1183 1209 1183 1208 1180 1207 1178 1207 1177 1206 1175 1204 1174 1202 1172 1200 1171 1198 1171 1196 1172 1192 1173 1189 1176 1186 1179 1185 
1183 1184 1183 1176 1187 1176 1187 1184 1191 1185 1194 1187 1196 1190 1197 1193 1198 1197 1197 1201 1195 1205 1192 1207 42 _pl _cp 1183 1206 _m
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1299 1206 1299 1205 1299 1199 1299 1197 1299 1195 1299 1193 1300 1192 1302 1191 1303 1190 1305 1189 1308 1189 1308 1179 1312 1179 1312 1189 1316 1190 
1318 1191 1320 1194 1320 1199 1320 1205 1321 1208 1323 1209 1323 1209 1323 1209 1324 1209 1324 1209 1324 1211 1322 1211 1320 1211 1319 1211 1317 1211 
1317 1199 1317 1196 1316 1193 1314 1192 1312 1191 1312 1219 51 _pl _cp 
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1428 1212 1428 1209 1428 1208 1425 1207 1423 1207 1422 1206 1420 1204 1419 1202 1417 1200 1416 1198 1416 1196 1417 1192 1418 1189 1421 1186 1424 1185 
1428 1184 1428 1176 1432 1176 1432 1184 1436 1185 1439 1187 1441 1190 1442 1193 1443 1197 1442 1200 1441 1203 1438 1206 1435 1207 43 _pl _cp 1428 1206 _m
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1561 1190 1563 1187 1566 1185 1570 1184 1572 1184 1574 1185 1576 1187 1578 1189 1579 1191 1580 1194 1581 1198 1581 1202 1581 1203 28 _pl _cp 1564 1204 _m
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_sp 1576 1202 1576 1200 1576 1198 1576 1197 1576 1196 1575 1191 1574 1188 1572 1187 1570 1186 1568 1187 1566 1188 1565 1191 1564 1196 1564 1201 1564 1202 
1564 1202 16 _pl _cp 
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1102 1201 1104 1200 1105 1201 1106 1202 1105 1204 1104 1206 1101 1207 1098 1207 1095 1206 1091 1205 1089 1202 1088 1199 1087 1195 1088 1191 1090 1187 
1093 1185 1097 1184 1099 1184 1100 1185 1102 1186 1103 1187 1104 1188 1105 1189 1106 1190 1107 1192 40 _pl _cp 
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1114 1201 1114 1198 1114 1197 18 _pl _cp 
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1147 1196 1145 1197 1143 1198 1141 1199 1139 1201 1138 1202 1138 1203 1139 1205 1142 1206 1145 1206 1147 1205 1148 1203 1149 1200 1150 1200 1150 1207 
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1140 1195 1144 1193 1147 1191 1148 1189 1148 1188 1147 1186 1145 1185 1143 1185 1141 1186 1138 1187 1137 1188 1137 1189 1136 1190 1135 1192 1134 1192 
60 _pl _cp 
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1165 1178 1168 1176 1168 1177 1166 1179 1164 1181 1163 1182 1163 1184 1162 1185 1161 1186 1160 1188 1160 1191 1160 1194 1160 1197 1160 1200 1160 1203 
1160 1206 1161 1208 1162 1209 1163 1210 1163 1212 1164 1213 1166 1215 1168 1217 38 _pl _cp 
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1205 1216 1202 1218 1201 1217 1203 1216 1204 1215 1205 1214 1206 1213 1207 1212 1208 1210 1208 1209 1209 1208 1209 1206 1210 1203 1210 1200 1210 1197 
1210 1194 1210 1191 1209 1188 1209 1186 1208 1185 1208 1184 1207 1182 1206 1181 1205 1180 1204 1179 1203 1178 1201 1177 42 _pl _cp 
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1353 1196 1351 1197 1349 1198 1346 1199 1345 1201 1343 1202 1343 1203 1343 1204 1344 1205 1346 1206 1348 1206 1350 1206 1352 1205 1353 1203 1355 1200 
1355 1200 1355 1207 1355 1207 1354 1207 1353 1206 1353 1207 1352 1207 1351 1207 1350 1207 1348 1207 1345 1207 1342 1206 1341 1204 1340 1201 1340 1199 
1342 1198 1343 1196 1346 1195 1350 1193 1352 1191 1353 1189 1352 1186 1349 1185 1346 1186 1344 1187 1343 1188 1343 1189 1342 1190 1341 1192 1340 1192 
60 _pl _cp 
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(\(6.17\))_S /Times-RomanR 600 _ff
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(the)_S 67 _t
(following)_S 67 _t
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1213 2330 1217 2328 1220 2326 1221 2324 1221 2323 1220 2322 1218 2321 1216 2321 1214 2321 1211 2322 1210 2323 1210 2324 1209 2326 1208 2327 1207 2327 
60 _pl _cp 
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1235 2322 1235 2325 17 _pl _cp 1229 2351 _m
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1248 2322 1248 2325 1248 2336 1249 2338 1251 2339 1252 2340 1253 2340 1255 2340 1256 2338 1256 2336 1256 2333 1256 2325 1256 2322 1254 2321 1253 2321 
1253 2320 1265 2320 1265 2321 1264 2321 1261 2322 1261 2325 1261 2336 1260 2339 1259 2341 1257 2342 1255 2343 1253 2343 1251 2342 1250 2341 1248 2339 
45 _pl _cp 
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1277 2313 1280 2311 1280 2312 1278 2314 1276 2316 1275 2317 1275 2319 1274 2320 1273 2321 1272 2323 1272 2326 1272 2329 1272 2332 1272 2335 1272 2338 
1272 2341 1273 2343 1274 2344 1275 2346 1275 2347 1276 2348 1278 2350 1280 2352 38 _pl _cp 
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1317 2352 1314 2354 1313 2352 1315 2351 1316 2350 1317 2349 1318 2348 1319 2347 1320 2346 1320 2344 1321 2343 1321 2341 1322 2338 1322 2335 1322 2332 
1322 2329 1322 2326 1321 2323 1321 2321 1320 2320 1320 2319 1319 2317 1318 2316 1317 2315 1316 2314 1315 2313 1313 2312 42 _pl _cp 
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1382 2336 1383 2335 1384 2336 1385 2337 1384 2339 1383 2341 1381 2342 1378 2343 1374 2342 1371 2340 1369 2338 1367 2334 1367 2331 1368 2326 1370 2322 
1372 2320 1376 2319 1378 2319 1380 2320 1381 2321 1383 2322 1384 2323 1385 2324 1385 2325 1386 2327 40 _pl _cp 
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1396 2342 1393 2341 1391 2338 1390 2335 19 _pl _cp 1393 2332 _m
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1394 2336 1393 2333 1393 2333 18 _pl _cp 
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1427 2331 1425 2332 1422 2333 1420 2334 1418 2336 1417 2337 1417 2338 1417 2339 1418 2340 1420 2341 1422 2341 1424 2341 1426 2340 1427 2338 1428 2335 
1429 2335 1429 2342 1428 2342 1428 2342 1427 2342 1427 2342 1426 2342 1424 2342 1423 2343 1422 2343 1419 2342 1416 2341 1415 2339 1414 2336 1414 2335 
1415 2333 1417 2332 1420 2330 1423 2328 1426 2326 1427 2324 1426 2322 1423 2321 1420 2321 1418 2322 1417 2323 1416 2324 1416 2326 1415 2327 1414 2327 
60 _pl _cp 
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1444 2313 1447 2311 1448 2312 1447 2313 1446 2314 1444 2315 1443 2316 1442 2319 1441 2321 1440 2323 1440 2326 1439 2329 1439 2332 1439 2335 1440 2338 
1440 2341 1441 2343 1442 2346 1443 2348 1444 2349 1446 2350 1447 2351 1448 2352 38 _pl _cp 
0 g _f _s _s 
0 g 1482 2311 _m
_sp 1482 2311 1485 2313 1486 2315 1488 2316 1490 2318 1492 2321 1493 2324 1494 2328 1494 2332 1494 2336 1493 2340 1492 2343 1490 2346 1488 2349 1486 2350 
1485 2352 1482 2354 1481 2352 1483 2350 1485 2348 1486 2347 1487 2346 1487 2344 1488 2343 1489 2341 1489 2338 1489 2335 1489 2332 1489 2329 1489 2326 
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1519 2336 1520 2335 1521 2336 1522 2337 1521 2339 1520 2341 1518 2342 1515 2343 1511 2342 1508 2340 1506 2338 1504 2334 1504 2331 1505 2326 1507 2322 
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1533 2342 1530 2341 1528 2338 1526 2335 19 _pl _cp 1530 2332 _m
_sp 1530 2332 1531 2327 1533 2324 1535 2322 1538 2321 1540 2322 1542 2323 1543 2326 1544 2330 1543 2334 1542 2338 1539 2340 1536 2341 1534 2340 1532 2339 
1531 2336 1530 2333 1530 2333 18 _pl _cp 
0 g _f _s _s 
0 g 1551 2320 _m
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1564 2331 1562 2332 1559 2333 1557 2334 1555 2336 1554 2337 1554 2338 1554 2339 1555 2340 1557 2341 1559 2341 1561 2341 1563 2340 1564 2338 1565 2335 
1566 2335 1566 2342 1565 2342 1565 2342 1564 2342 1564 2342 1563 2342 1561 2342 1560 2343 1559 2343 1556 2342 1553 2341 1552 2339 1551 2336 1551 2335 
1552 2333 1554 2332 1557 2330 1560 2328 1563 2326 1564 2324 1563 2322 1560 2321 1557 2321 1555 2322 1554 2323 1553 2324 1553 2326 1552 2327 1551 2327 
60 _pl _cp 
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0 g 1584 2354 _m
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1581 2313 1584 2311 1585 2312 1584 2313 1583 2314 1581 2315 1580 2316 1579 2319 1578 2321 1577 2323 1577 2326 1576 2329 1576 2332 1576 2335 1577 2338 
1577 2341 1578 2343 1579 2346 1580 2348 1581 2349 1583 2350 1584 2351 1585 2352 38 _pl _cp 
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1617 2352 1614 2354 1614 2352 1616 2350 1618 2348 1619 2347 1620 2346 1620 2344 1621 2343 1622 2341 1622 2338 1622 2335 1622 2332 1622 2329 1622 2326 
1622 2323 1621 2321 1620 2320 1620 2319 1619 2317 1618 2316 1616 2314 1614 2312 38 _pl _cp 
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931 2400 932 2402 930 2402 928 2402 928 2404 928 2404 928 2405 928 2407 935 2431 937 2431 940 2431 942 2430 943 2429 943 2427 943 2427 
943 2426 943 2426 943 2425 944 2425 946 2433 919 2433 917 2425 37 _pl _cp 
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_sp 1086 2466 1084 2466 1084 2527 1093 2527 1093 2525 1086 2525 6 _pl _cp 
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_sp 1086 2368 1084 2368 1084 2390 1086 2390 4 _pl _cp 
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_sp 1651 2387 1650 2387 1650 2410 1651 2410 4 _pl _cp 
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_sp 1651 2374 1650 2374 1650 2310 1642 2310 1642 2308 1651 2308 6 _pl _cp 
0 g _f _s _s 
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_sp 1555 2500 1554 2505 1553 2509 1551 2512 1548 2514 1545 2515 1542 2515 1539 2514 1537 2512 1536 2509 1535 2507 1534 2505 1534 2502 1534 2498 1534 2492 
1535 2487 1537 2484 1540 2482 1544 2481 1546 2481 1549 2482 1551 2484 1552 2486 1553 2488 1554 2491 1555 2495 1555 2499 1555 2500 28 _pl _cp 1538 2501 _m
_sp 1538 2501 1538 2504 1539 2506 1539 2509 1540 2511 1542 2513 1544 2513 1547 2512 1549 2510 1550 2506 1550 2501 11 _pl _cp 1550 2499 _m
_sp 1550 2499 1550 2497 1550 2495 1550 2494 1550 2493 1550 2488 1549 2485 1547 2484 1545 2483 1542 2483 1540 2485 1539 2488 1538 2492 1538 2498 1538 2499 
1538 2499 16 _pl _cp 
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1296 2428 1297 2425 1297 2424 1294 2423 1292 2423 1290 2422 1289 2420 1287 2418 1286 2416 1285 2414 1285 2412 1285 2408 1287 2405 1289 2402 1292 2400 
1296 2400 1296 2392 1301 2392 1301 2400 1304 2401 1307 2403 1310 2406 1311 2409 1312 2413 1311 2416 1310 2419 1307 2422 1304 2423 43 _pl _cp 1297 2422 _m
_sp 1297 2422 1296 2402 1293 2403 1291 2405 1290 2408 1289 2412 1290 2416 1291 2419 1294 2421 9 _pl _cp 1300 2422 _m
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0 g 1465 2424 _m
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1461 2428 1461 2425 1461 2424 1458 2423 1456 2423 1455 2422 1453 2420 1452 2418 1450 2416 1449 2414 1449 2412 1450 2408 1451 2405 1454 2402 1457 2400 
1461 2400 1461 2392 1465 2392 1465 2400 1469 2401 1472 2403 1474 2406 1475 2409 1476 2413 1475 2417 1473 2421 1470 2423 42 _pl _cp 1461 2422 _m
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_sp 1465 2422 1468 2421 1470 2419 1471 2416 1472 2412 1472 2408 1470 2406 1468 2403 1465 2402 9 _pl _cp 
0 g _f _s _s 
0 g 1608 2419 _m
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1589 2406 1591 2403 1594 2401 1597 2400 1600 2400 1602 2401 1604 2403 1606 2405 1607 2407 1608 2410 1608 2414 1608 2418 1608 2419 28 _pl _cp 1592 2420 _m
_sp 1592 2420 1592 2423 1592 2425 1593 2428 1594 2431 1596 2432 1597 2433 1600 2432 1602 2430 1603 2425 1604 2420 11 _pl _cp 1604 2418 _m
_sp 1604 2418 1604 2416 1604 2414 1604 2413 1604 2412 1603 2407 1602 2404 1600 2403 1598 2402 1596 2402 1594 2404 1593 2407 1592 2411 1592 2417 1592 2418 
1592 2418 16 _pl _cp 
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0 g 1299 2343 _m
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1295 2347 1295 2345 1295 2343 1292 2343 1290 2342 1289 2341 1287 2340 1286 2338 1284 2336 1283 2333 1283 2331 1284 2327 1285 2324 1288 2321 1291 2320 
1295 2319 1295 2311 1299 2311 1299 2319 1303 2320 1306 2322 1308 2325 1309 2328 1310 2332 1309 2337 1307 2340 1304 2342 42 _pl _cp 1295 2342 _m
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1462 2347 1463 2345 1463 2343 1460 2343 1458 2342 1456 2341 1455 2340 1453 2338 1452 2336 1451 2333 1451 2331 1451 2327 1453 2324 1455 2321 1458 2320 
1462 2319 1462 2311 1467 2311 1467 2319 1470 2320 1473 2322 1476 2325 1477 2328 1478 2332 1477 2336 1476 2339 1473 2341 1470 2342 43 _pl _cp 1463 2342 _m
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_sp 1466 2342 1469 2341 1472 2338 1473 2335 1474 2331 1473 2327 1472 2325 1470 2322 1467 2321 9 _pl _cp 
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1590 2325 1592 2322 1595 2320 1599 2319 1601 2319 1604 2320 1606 2322 1607 2324 1608 2326 1609 2329 1610 2333 1610 2337 1610 2338 28 _pl _cp 1593 2340 _m
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_sp 1605 2338 1605 2336 1605 2334 1605 2332 1605 2331 1605 2327 1604 2324 1602 2322 1600 2321 1597 2321 1595 2323 1594 2326 1593 2330 1593 2336 1593 2337 
1593 2338 16 _pl _cp 
0 g _f _s 
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_s grestore 8117 9677 _m
/Times-BoldR 600 _ff
(\(6.19\))_S /Times-RomanR 600 _ff
1980 8594 _m
(The)_S 67 _t
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1391 767 1393 770 1393 774 1393 780 1394 783 1396 784 1396 784 1396 784 1397 784 1397 784 1397 786 1395 786 1393 786 1392 786 1390 787 
1390 774 1390 771 1389 768 1387 767 1385 766 1385 794 51 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 3852 _m
/Times-BoldR 600 _ff
(\(6.21\))_S /Times-RomanR 600 _ff
4950 1288 _m
(109)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(Matrix)_S 67 _t
(conversion)_S 67 _t
(from)_S 67 _t
(body)_S 67 _t
(to)_S 67 _t
(world)_S 67 _t
(velocities)_S 67 _t
(is)_S 67 _t
(thus:)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 358 1749 400 2529 _cw 
_s 901 2685 _m
_sp 901 2685 901 2734 909 2734 909 2733 902 2733 902 2686 909 2686 909 2685 8 _pl _cp 
0 g _f _s _s 
0 g 960 2685 _m
_sp 960 2685 960 2734 952 2734 952 2733 958 2733 958 2686 952 2686 952 2685 8 _pl _cp 
0 g _f _s _s 
0 g 1121 2797 _m
_sp 1121 2797 1119 2797 1119 2857 1129 2857 1129 2855 1121 2855 6 _pl _cp 
0 g _f _s _s 
0 g 1121 2777 _m
_sp 1121 2777 1119 2777 1119 2799 1121 2799 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2757 _m
_sp 1121 2757 1119 2757 1119 2779 1121 2779 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2737 _m
_sp 1121 2737 1119 2737 1119 2760 1121 2760 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2718 _m
_sp 1121 2718 1119 2718 1119 2740 1121 2740 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2698 _m
_sp 1121 2698 1119 2698 1119 2720 1121 2720 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2678 _m
_sp 1121 2678 1119 2678 1119 2700 1121 2700 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2658 _m
_sp 1121 2658 1119 2658 1119 2681 1121 2681 4 _pl _cp 
0 g _f _s _s 
0 g 1121 2639 _m
_sp 1121 2639 1119 2639 1119 2661 1121 2661 4 _pl _cp 
0 g _f _s _s 
0 g 1119 2642 _m
_sp 1119 2642 1121 2642 1121 2579 1129 2579 1129 2577 1119 2577 6 _pl _cp 
0 g _f _s _s 
0 g 1493 2797 _m
_sp 1493 2797 1494 2797 1494 2857 1485 2857 1485 2855 1493 2855 6 _pl _cp 
0 g _f _s _s 
0 g 1494 2777 _m
_sp 1494 2777 1493 2777 1493 2799 1494 2799 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2757 _m
_sp 1494 2757 1493 2757 1493 2779 1494 2779 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2737 _m
_sp 1494 2737 1493 2737 1493 2760 1494 2760 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2718 _m
_sp 1494 2718 1493 2718 1493 2740 1494 2740 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2698 _m
_sp 1494 2698 1493 2698 1493 2720 1494 2720 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2678 _m
_sp 1494 2678 1493 2678 1493 2700 1494 2700 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2658 _m
_sp 1494 2658 1493 2658 1493 2681 1494 2681 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2639 _m
_sp 1494 2639 1493 2639 1493 2661 1494 2661 4 _pl _cp 
0 g _f _s _s 
0 g 1494 2645 _m
_sp 1494 2645 1493 2645 1493 2581 1485 2581 1485 2579 1494 2579 6 _pl _cp 
0 g _f _s _s 
0 g 1308 2826 _m
_sp 1308 2826 1306 2826 1306 2751 1308 2751 4 _pl _cp 
0 g _f _s _s 
0 g 1151 2716 _m
_sp 1151 2716 1151 2714 1260 2714 1260 2716 4 _pl _cp 
0 g _f _s _s 
0 g 1352 2716 _m
_sp 1352 2716 1352 2714 1461 2714 1461 2716 4 _pl _cp 
0 g _f _s _s 
0 g 1308 2669 _m
_sp 1308 2669 1306 2669 1306 2594 1308 2594 4 _pl _cp 
0 g _f _s _s 
0 g 1520 2685 _m
_sp 1520 2685 1520 2734 1528 2734 1528 2733 1521 2733 1521 2686 1528 2686 1528 2685 8 _pl _cp 
0 g _f _s _s 
0 g 1579 2685 _m
_sp 1579 2685 1579 2734 1571 2734 1571 2733 1577 2733 1577 2686 1571 2686 1571 2685 8 _pl _cp 
0 g _f _s _s 
0 g 923 2707 _m
_sp 923 2707 923 2725 923 2729 925 2730 926 2730 927 2732 915 2732 914 2730 915 2730 917 2729 917 2725 918 2698 919 2698 939 2725 941 2727 
942 2729 943 2730 944 2730 945 2732 936 2732 936 2730 937 2730 938 2730 938 2729 938 2727 936 2725 26 _pl _cp 
0 g _f _s _s 
0 g 973 2687 _m
_sp 973 2687 972 2689 972 2690 972 2692 972 2693 971 2696 971 2698 967 2697 966 2696 967 2696 969 2696 969 2695 970 2692 970 2689 970 2686 
970 2683 971 2682 978 2693 979 2683 980 2683 982 2685 983 2687 985 2689 986 2691 987 2693 988 2695 987 2697 986 2698 985 2697 985 2696 
985 2696 985 2695 986 2694 986 2694 986 2693 986 2692 985 2690 983 2688 982 2687 981 2686 980 2697 979 2698 42 _pl _cp 
0 g _f _s _s 
0 g 989 2687 _m
_sp 989 2687 989 2685 990 2683 992 2682 994 2682 996 2682 997 2683 999 2684 1000 2685 1001 2687 1003 2689 1004 2690 1004 2692 1003 2694 1002 2696 
1000 2697 998 2698 997 2698 995 2697 994 2696 992 2695 991 2693 990 2691 989 2689 989 2687 989 2687 26 _pl _cp 992 2686 _m
_sp 992 2686 993 2684 995 2683 997 2684 999 2686 1000 2688 1000 2690 1001 2691 1001 2693 1000 2696 998 2697 996 2696 994 2693 993 2691 993 2690 
992 2688 992 2686 992 2686 18 _pl _cp 
0 g _f _s _s 
0 g 1006 2683 _m
_sp 1006 2683 1009 2683 1009 2686 1010 2688 1010 2689 1012 2691 1013 2693 1014 2694 1015 2695 1015 2695 1015 2695 1016 2694 1017 2694 1018 2695 1018 2696 
1017 2697 1016 2698 1015 2697 1014 2696 1013 2695 1012 2693 1011 2693 1011 2692 1012 2698 1007 2697 1007 2696 1008 2696 1009 2696 1009 2695 1009 2695 
1009 2694 31 _pl _cp 
0 g _f _s _s 
0 g 1028 2706 _m
_sp 1028 2706 1022 2705 1022 2704 1023 2704 1024 2704 1024 2703 1024 2702 1024 2701 1020 2687 1019 2685 1019 2684 1020 2683 1021 2682 1023 2683 1024 2684 
1025 2685 1026 2686 1026 2687 1025 2686 1024 2684 1022 2684 1022 2684 1022 2684 1022 2685 1022 2686 25 _pl _cp 
0 g _f _s _s 
0 g 1037 2686 _m
_sp 1037 2686 1037 2686 1037 2685 1037 2684 1037 2683 1038 2682 1039 2682 1041 2683 1042 2684 1043 2686 1043 2686 1042 2686 1041 2684 1040 2684 1040 2684 
1040 2685 1040 2686 1040 2686 1045 2706 1040 2705 1039 2704 1041 2704 1042 2704 1042 2703 1042 2702 1041 2701 1040 2696 1039 2697 1037 2698 1036 2698 
1034 2697 1033 2696 1031 2694 1030 2692 1028 2690 1027 2688 1027 2686 1028 2683 1031 2682 1034 2683 1036 2684 1037 2685 42 _pl _cp 1030 2686 _m
_sp 1030 2686 1031 2685 1033 2684 1035 2685 1037 2687 1038 2688 1038 2689 1039 2691 1039 2692 1039 2694 1039 2695 1038 2696 1037 2697 1035 2696 1033 2693 
1032 2691 1031 2690 1030 2688 1030 2686 1030 2686 20 _pl _cp 
0 g _f _s _s 
0 g 1209 2794 _m
_sp 1209 2794 1212 2794 1214 2795 1215 2796 1216 2797 1217 2798 1218 2800 1219 2801 1219 2803 1218 2806 1217 2808 1215 2809 1213 2809 1210 2810 1207 2810 
1196 2810 1196 2809 1197 2809 1198 2808 1199 2807 1199 2806 1198 2804 1193 2783 1192 2781 1191 2779 1190 2778 1189 2778 1189 2778 1188 2777 1201 2777 
1201 2778 1200 2778 1198 2779 1198 2780 1198 2781 1198 2782 1198 2783 1198 2783 1201 2793 1204 2793 1210 2777 1218 2777 1218 2778 1218 2778 1216 2778 
1215 2779 1214 2781 1213 2783 48 _pl _cp 1201 2796 _m
_sp 1201 2796 1204 2796 1207 2796 1208 2796 1210 2797 1211 2798 1212 2800 1213 2803 1213 2805 1212 2807 1210 2808 1207 2808 1205 2808 1204 2807 1203 2803 
15 _pl _cp 
0 g _f _s _s 
0 g 1392 2645 _m
_sp 1392 2645 1394 2647 1395 2649 1396 2650 1397 2650 1399 2651 1401 2651 1404 2651 1397 2627 1396 2624 1396 2622 1395 2621 1393 2621 1392 2621 1391 2620 
1406 2620 1406 2621 1404 2621 1403 2622 1402 2623 1402 2624 1402 2625 1403 2627 1409 2651 1411 2651 1414 2651 1416 2650 1417 2649 1417 2647 1417 2647 
1417 2646 1417 2646 1417 2645 1418 2645 1420 2653 1393 2653 1391 2645 37 _pl _cp 
0 g _f _s _s 
0 g 1542 2707 _m
_sp 1542 2707 1542 2725 1542 2727 1542 2729 1543 2730 1545 2730 1546 2730 1546 2732 1534 2732 1534 2730 1534 2730 1535 2730 1536 2729 1537 2727 1537 2725 
1537 2698 1538 2698 1558 2725 1560 2727 1561 2729 1563 2730 1564 2730 1564 2732 1555 2732 1555 2730 1556 2730 1557 2730 1557 2729 1557 2727 1555 2725 
30 _pl _cp 
0 g _f _s _s 
0 g 1592 2693 _m
_sp 1592 2693 1595 2706 1589 2705 1589 2704 1590 2704 1591 2704 1591 2703 1591 2702 1591 2701 1587 2686 1586 2684 1586 2684 1586 2684 1586 2684 1587 2684 
1589 2683 1591 2682 1593 2682 1595 2683 1596 2684 1598 2686 1599 2688 1600 2690 1601 2691 1601 2693 1601 2695 1600 2697 1599 2698 1598 2698 1597 2698 
1596 2697 1594 2696 32 _pl _cp 1589 2684 _m
_sp 1589 2684 1590 2684 1591 2683 1593 2684 1595 2685 1596 2687 1597 2689 1598 2691 1598 2693 1598 2695 1596 2696 1595 2695 1593 2694 1592 2692 1591 2690 
1590 2688 1590 2687 1589 2685 18 _pl _cp 
0 g _f _s _s 
0 g 1603 2687 _m
_sp 1603 2687 1603 2685 1604 2683 1606 2682 1608 2682 1610 2682 1611 2683 1613 2684 1614 2685 1615 2687 1616 2689 1617 2690 1617 2692 1617 2694 1616 2696 
1614 2697 1612 2698 1611 2698 1609 2697 1608 2696 1606 2695 1605 2693 1604 2691 1603 2689 1603 2687 1603 2687 26 _pl _cp 1606 2686 _m
_sp 1606 2686 1607 2684 1609 2683 1611 2684 1612 2686 1613 2688 1614 2690 1614 2691 1614 2693 1613 2696 1612 2697 1611 2697 1610 2696 1608 2694 1607 2693 
1607 2691 1607 2690 1606 2688 1606 2686 1606 2686 20 _pl _cp 
0 g _f _s _s 
0 g 1629 2686 _m
_sp 1629 2686 1628 2686 1628 2685 1628 2684 1629 2683 1630 2682 1631 2682 1632 2683 1633 2684 1635 2686 1634 2686 1634 2686 1632 2684 1632 2684 1631 2684 
1631 2685 1631 2686 1631 2686 1637 2706 1631 2705 1631 2704 1632 2704 1633 2704 1633 2703 1633 2702 1633 2701 1631 2696 1630 2697 1629 2698 1628 2698 
1626 2697 1625 2696 1623 2694 1621 2692 1620 2690 1619 2688 1619 2686 1620 2683 1623 2682 1625 2683 1627 2684 1628 2685 42 _pl _cp 1622 2686 _m
_sp 1622 2686 1623 2685 1624 2684 1626 2685 1628 2687 1629 2688 1629 2689 1630 2691 1630 2692 1631 2694 1631 2695 1630 2696 1629 2697 1628 2697 1627 2696 
1625 2694 1624 2693 1623 2691 1623 2690 1622 2688 1622 2686 1622 2686 22 _pl _cp 
0 g _f _s _s 
0 g 1636 2697 _m
_sp 1636 2697 1636 2696 1637 2696 1637 2696 1638 2696 1639 2694 1640 2692 1640 2691 1641 2689 1641 2687 1642 2685 1642 2683 1641 2681 1640 2680 1639 2679 
1638 2678 1638 2678 1638 2678 1637 2678 1637 2678 1637 2679 1636 2679 1635 2678 1635 2677 1635 2676 1636 2676 1638 2676 1639 2677 1641 2679 1642 2681 
1644 2683 1645 2685 1646 2686 1647 2689 1648 2691 1649 2693 1650 2694 1650 2695 1649 2697 1648 2698 1647 2697 1646 2696 1647 2696 1647 2695 1648 2695 
1648 2694 1648 2693 1648 2693 1648 2692 1647 2691 1647 2690 1646 2688 1646 2687 1645 2686 1645 2686 1644 2685 1644 2686 1644 2686 1643 2689 1643 2691 
1643 2693 1642 2695 1641 2697 1641 2698 64 _pl _cp 
0 g _f _s _s 
0 g 1092 2718 _m
_sp 1092 2718 1073 2718 1073 2716 1092 2716 4 _pl _cp 1092 2710 _m
_sp 1092 2710 1073 2710 1073 2708 1092 2708 4 _pl _cp 
0 g _f _s _s 
0 g 1175 2810 _m
_sp 1175 2810 1175 2769 1186 2769 1186 2770 1183 2770 1180 2771 1180 2774 1180 2804 1180 2806 1180 2808 1183 2809 1186 2809 1186 2810 13 _pl _cp 
0 g _f _s _s 
0 g 1236 2769 _m
_sp 1236 2769 1236 2810 1225 2810 1225 2809 1228 2809 1231 2808 1231 2805 1231 2775 1231 2773 1231 2771 1228 2770 1225 2770 1225 2769 13 _pl _cp 
0 g _f _s _s 
0 g 1395 2793 _m
_sp 1395 2793 1395 2791 1396 2789 1396 2786 1397 2784 1398 2783 1399 2782 1399 2780 1400 2779 1402 2778 1403 2777 1405 2777 1406 2777 1410 2778 1413 2780 
1416 2783 1417 2788 1418 2794 1417 2799 1416 2804 1413 2808 1410 2810 1407 2811 1403 2810 1400 2808 1397 2804 1396 2799 27 _pl _cp 1400 2794 _m
_sp 1400 2794 1400 2788 1401 2784 1402 2781 1404 2779 1407 2779 1409 2779 1410 2780 1411 2782 1412 2785 1413 2789 1413 2794 1413 2799 1412 2803 1411 2806 
1409 2808 1407 2809 1404 2808 1402 2806 1401 2803 1400 2799 21 _pl _cp 
0 g _f _s _s 
0 g 1194 2636 _m
_sp 1194 2636 1194 2634 1195 2632 1195 2629 1196 2627 1197 2626 1198 2625 1198 2623 1199 2622 1201 2621 1202 2620 1204 2620 1205 2620 1209 2621 1212 2623 
1215 2626 1216 2631 1217 2637 1216 2642 1215 2647 1212 2651 1209 2653 1206 2654 1202 2653 1199 2651 1196 2647 1195 2642 27 _pl _cp 1199 2637 _m
_sp 1199 2637 1199 2631 1200 2627 1201 2624 1203 2622 1206 2622 1208 2622 1209 2623 1210 2625 1211 2628 1212 2632 1212 2637 1212 2642 1211 2646 1210 2649 
1208 2651 1206 2652 1203 2651 1201 2649 1200 2646 1199 2642 21 _pl _cp 
0 g _f _s _s 
0 g 1375 2653 _m
_sp 1375 2653 1375 2612 1386 2612 1386 2613 1382 2613 1380 2614 1379 2617 1379 2647 1379 2649 1380 2651 1383 2652 1386 2652 1386 2653 13 _pl _cp 
0 g _f _s _s 
0 g 1438 2612 _m
_sp 1438 2612 1438 2653 1427 2653 1427 2652 1430 2652 1433 2651 1433 2648 1433 2618 1433 2616 1433 2614 1430 2613 1427 2613 1427 2612 13 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 10827 _m
/Times-BoldR 600 _ff
(\(6.22\))_S /Times-RomanR 600 _ff
1500 9526 _m
(and)_S 67 _t
(inversely:)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 359 1749 400 1946 _cw 
_s 897 2102 _m
_sp 897 2102 897 2151 905 2151 905 2150 898 2150 898 2103 905 2103 905 2102 8 _pl _cp 
0 g _f _s _s 
0 g 956 2102 _m
_sp 956 2102 956 2151 948 2151 948 2150 954 2150 954 2103 948 2103 948 2102 8 _pl _cp 
0 g _f _s _s 
0 g 1104 2214 _m
_sp 1104 2214 1102 2214 1102 2274 1112 2274 1112 2272 1104 2272 6 _pl _cp 
0 g _f _s _s 
0 g 1104 2194 _m
_sp 1104 2194 1102 2194 1102 2216 1104 2216 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2174 _m
_sp 1104 2174 1102 2174 1102 2196 1104 2196 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2154 _m
_sp 1104 2154 1102 2154 1102 2177 1104 2177 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2135 _m
_sp 1104 2135 1102 2135 1102 2157 1104 2157 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2115 _m
_sp 1104 2115 1102 2115 1102 2137 1104 2137 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2095 _m
_sp 1104 2095 1102 2095 1102 2117 1104 2117 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2075 _m
_sp 1104 2075 1102 2075 1102 2098 1104 2098 4 _pl _cp 
0 g _f _s _s 
0 g 1104 2056 _m
_sp 1104 2056 1102 2056 1102 2078 1104 2078 4 _pl _cp 
0 g _f _s _s 
0 g 1102 2059 _m
_sp 1102 2059 1104 2059 1104 1996 1112 1996 1112 1994 1102 1994 6 _pl _cp 
0 g _f _s _s 
0 g 1476 2214 _m
_sp 1476 2214 1477 2214 1477 2274 1468 2274 1468 2272 1476 2272 6 _pl _cp 
0 g _f _s _s 
0 g 1477 2194 _m
_sp 1477 2194 1476 2194 1476 2216 1477 2216 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2174 _m
_sp 1477 2174 1476 2174 1476 2196 1477 2196 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2154 _m
_sp 1477 2154 1476 2154 1476 2177 1477 2177 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2135 _m
_sp 1477 2135 1476 2135 1476 2157 1477 2157 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2115 _m
_sp 1477 2115 1476 2115 1476 2137 1477 2137 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2095 _m
_sp 1477 2095 1476 2095 1476 2117 1477 2117 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2075 _m
_sp 1477 2075 1476 2075 1476 2098 1477 2098 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2056 _m
_sp 1477 2056 1476 2056 1476 2078 1477 2078 4 _pl _cp 
0 g _f _s _s 
0 g 1477 2062 _m
_sp 1477 2062 1476 2062 1476 1998 1468 1998 1468 1996 1477 1996 6 _pl _cp 
0 g _f _s _s 
0 g 1291 2243 _m
_sp 1291 2243 1289 2243 1289 2168 1291 2168 4 _pl _cp 
0 g _f _s _s 
0 g 1134 2133 _m
_sp 1134 2133 1134 2131 1243 2131 1243 2133 4 _pl _cp 
0 g _f _s _s 
0 g 1335 2133 _m
_sp 1335 2133 1335 2131 1444 2131 1444 2133 4 _pl _cp 
0 g _f _s _s 
0 g 1291 2086 _m
_sp 1291 2086 1289 2086 1289 2011 1291 2011 4 _pl _cp 
0 g _f _s _s 
0 g 919 2124 _m
_sp 919 2124 919 2142 919 2146 921 2147 922 2147 923 2149 911 2149 910 2147 911 2147 913 2146 913 2142 914 2115 915 2115 935 2142 937 2144 
938 2146 939 2147 940 2147 941 2149 932 2149 932 2147 933 2147 934 2147 934 2146 934 2144 932 2142 26 _pl _cp 
0 g _f _s _s 
0 g 968 2110 _m
_sp 968 2110 972 2123 966 2122 966 2121 967 2121 968 2121 968 2120 968 2119 968 2118 963 2103 963 2101 963 2101 963 2101 963 2101 963 2101 
965 2100 967 2099 969 2099 971 2100 973 2101 975 2103 976 2105 977 2107 978 2108 978 2110 978 2112 977 2114 976 2115 974 2115 974 2115 
973 2114 972 2114 971 2113 969 2112 34 _pl _cp 966 2101 _m
_sp 966 2101 967 2101 968 2100 970 2101 972 2102 973 2104 974 2106 975 2108 975 2110 974 2112 973 2113 972 2112 970 2111 969 2109 968 2107 
967 2105 967 2104 966 2102 18 _pl _cp 
0 g _f _s _s 
0 g 980 2104 _m
_sp 980 2104 980 2102 981 2100 983 2099 985 2099 987 2099 988 2100 990 2101 991 2102 992 2104 993 2106 994 2107 994 2109 994 2111 993 2113 
991 2114 989 2115 988 2115 986 2114 985 2113 983 2112 982 2110 981 2108 980 2106 980 2104 980 2104 26 _pl _cp 983 2103 _m
_sp 983 2103 984 2101 985 2100 987 2101 989 2103 990 2105 990 2107 991 2108 991 2110 990 2113 989 2114 988 2114 986 2113 985 2111 984 2110 
983 2108 983 2107 983 2105 983 2103 983 2103 20 _pl _cp 
0 g _f _s _s 
0 g 1005 2103 _m
_sp 1005 2103 1005 2103 1005 2102 1005 2101 1006 2100 1006 2099 1007 2099 1009 2100 1010 2101 1012 2103 1011 2103 1010 2103 1009 2101 1008 2101 1008 2101 
1008 2102 1008 2103 1008 2103 1013 2123 1008 2122 1008 2121 1009 2121 1010 2121 1010 2120 1010 2119 1010 2118 1008 2113 1007 2114 1006 2115 1005 2115 
1003 2114 1002 2113 1000 2111 998 2109 997 2107 996 2105 996 2103 997 2100 999 2099 1002 2100 1004 2101 1005 2102 42 _pl _cp 999 2103 _m
_sp 999 2103 1000 2102 1001 2101 1003 2102 1005 2104 1006 2105 1006 2106 1007 2108 1007 2109 1007 2111 1007 2112 1007 2113 1006 2114 1005 2114 1004 2113 
1002 2111 1001 2110 1000 2108 1000 2107 999 2105 999 2103 999 2103 22 _pl _cp 
0 g _f _s _s 
0 g 1012 2114 _m
_sp 1012 2114 1013 2113 1013 2113 1014 2113 1015 2113 1016 2111 1017 2109 1017 2108 1018 2106 1018 2104 1019 2102 1019 2100 1018 2098 1017 2097 1016 2096 
1015 2095 1015 2095 1014 2095 1014 2095 1014 2095 1013 2096 1013 2096 1012 2095 1012 2094 1012 2093 1013 2093 1014 2093 1015 2094 1017 2096 1019 2098 
1021 2100 1022 2102 1023 2103 1024 2106 1025 2108 1026 2110 1026 2111 1026 2112 1026 2114 1024 2115 1024 2114 1023 2113 1023 2113 1024 2112 1025 2112 
1025 2111 1025 2110 1025 2110 1025 2109 1024 2108 1023 2107 1022 2105 1022 2104 1022 2103 1021 2103 1021 2102 1021 2103 1021 2103 1020 2106 1020 2108 
1020 2110 1019 2112 1018 2114 1017 2115 64 _pl _cp 
0 g _f _s _s 
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_sp 1254 2621 1254 2619 1300 2619 1300 2621 4 _pl _cp 
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1078 2639 1080 2638 1082 2637 1082 2636 1082 2636 1082 2636 1082 2635 1082 2634 1083 2634 54 _pl _cp 
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_sp 1105 2597 1105 2599 1105 2600 1105 2602 1104 2603 1104 2606 1103 2608 1099 2607 1099 2606 1100 2606 1101 2606 1101 2605 1102 2602 1102 2599 1103 2596 
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1117 2606 1118 2605 1119 2605 1119 2604 1119 2603 1118 2603 1117 2601 1116 2599 1114 2597 1114 2596 1112 2607 1112 2608 42 _pl _cp 
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1125 2601 1125 2600 1125 2598 1125 2597 1125 2597 20 _pl _cp 
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1141 2604 31 _pl _cp 
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1158 2595 1159 2597 1158 2597 1158 2597 1156 2595 1155 2594 1155 2594 1154 2595 1155 2595 1155 2596 25 _pl _cp 
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1172 2595 1172 2596 1172 2597 1178 2616 1172 2615 1172 2614 1173 2614 1174 2614 1174 2613 1174 2613 1174 2612 1172 2606 1171 2608 1170 2608 1169 2608 
1167 2607 1166 2606 1164 2605 1162 2603 1161 2601 1160 2599 1160 2597 1161 2594 1164 2593 1166 2593 1168 2595 1169 2596 42 _pl _cp 1163 2596 _m
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1164 2602 1164 2600 1163 2599 1163 2597 1163 2597 20 _pl _cp 
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1281 2641 46 _pl _cp 1272 2642 _m
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1280 2658 1279 2657 1277 2655 1275 2653 1274 2650 1273 2647 1272 2644 1272 2642 1272 2642 24 _pl _cp 
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0 g 1275 2574 _m
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1278 2573 1278 2574 1279 2575 1287 2604 1278 2602 1278 2601 1280 2601 1281 2601 1281 2600 1281 2599 1281 2598 1279 2590 1277 2591 1275 2592 1273 2592 
1271 2591 1268 2589 1266 2587 1263 2584 1262 2581 1260 2578 1260 2575 1260 2572 1262 2571 1263 2569 1266 2569 1268 2569 1269 2569 1271 2570 1273 2572 
1274 2573 46 _pl _cp 1265 2575 _m
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1273 2590 1272 2589 1270 2587 1268 2585 1267 2583 1266 2580 1265 2577 1265 2575 1265 2575 24 _pl _cp 
0 g _f _s _s 
0 g 1291 2589 _m
_sp 1291 2589 1287 2575 1287 2573 1286 2571 1287 2570 1289 2569 1291 2569 1293 2570 1294 2571 1295 2572 1295 2573 1296 2575 1295 2575 1293 2572 1291 2571 
1291 2571 1290 2572 1291 2573 1291 2574 1291 2576 1295 2589 1299 2589 1300 2591 1295 2591 1297 2597 1296 2597 1294 2594 1292 2593 1291 2592 1290 2591 
1288 2591 1287 2590 1287 2589 33 _pl _cp 
0 g _f _s _s 
0 g 1330 2638 _m
_sp 1330 2638 1324 2615 1323 2613 1322 2611 1321 2610 1320 2610 1319 2610 1319 2609 1329 2609 1329 2610 1328 2610 1326 2611 1326 2612 1326 2613 1326 2613 
1326 2614 1326 2615 1331 2635 1335 2609 1336 2609 1353 2636 1348 2615 1347 2613 1346 2611 1345 2610 1344 2610 1344 2610 1343 2609 1355 2609 1356 2610 
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1335 2642 1327 2642 1326 2640 1327 2640 1329 2640 50 _pl _cp 
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0 g 1386 2617 _m
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0 g 1436 2597 _m
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1448 2606 1448 2605 1449 2605 1449 2604 1449 2603 1449 2603 1448 2601 1446 2599 1445 2597 1444 2596 1443 2607 1442 2608 42 _pl _cp 
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0 g 1452 2597 _m
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1463 2608 1461 2608 1460 2608 1458 2607 1457 2606 1455 2605 1454 2603 1453 2602 1452 2600 1452 2598 1452 2598 26 _pl _cp 1455 2596 _m
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1455 2598 1455 2597 1455 2597 18 _pl _cp 
0 g _f _s _s 
0 g 1469 2593 _m
_sp 1469 2593 1472 2593 1472 2596 1473 2598 1473 2599 1475 2601 1476 2603 1477 2605 1478 2605 1478 2605 1478 2605 1479 2604 1480 2604 1481 2605 1481 2606 
1480 2607 1479 2608 1478 2607 1477 2606 1476 2605 1475 2603 1474 2603 1474 2602 1475 2608 1470 2607 1470 2606 1471 2606 1472 2606 1472 2606 1472 2605 
1472 2604 31 _pl _cp 
0 g _f _s _s 
0 g 1491 2616 _m
_sp 1491 2616 1485 2615 1485 2614 1486 2614 1487 2614 1487 2613 1487 2613 1487 2612 1483 2598 1482 2595 1482 2594 1483 2593 1484 2593 1486 2593 1487 2594 
1488 2595 1489 2597 1489 2597 1488 2597 1487 2595 1485 2594 1485 2594 1485 2595 1485 2595 1485 2596 25 _pl _cp 
0 g _f _s _s 
0 g 1500 2596 _m
_sp 1500 2596 1500 2596 1500 2595 1500 2594 1500 2593 1501 2593 1502 2593 1504 2593 1505 2594 1506 2596 1506 2597 1505 2596 1504 2594 1503 2594 1503 2595 
1503 2595 1503 2596 1503 2597 1508 2616 1503 2615 1502 2614 1504 2614 1505 2614 1505 2613 1505 2613 1504 2612 1503 2606 1502 2608 1500 2608 1499 2608 
1497 2607 1496 2606 1494 2605 1493 2603 1491 2601 1490 2599 1490 2597 1491 2594 1494 2593 1497 2593 1499 2595 1500 2596 42 _pl _cp 1493 2596 _m
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1493 2599 1493 2597 1493 2597 18 _pl _cp 
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/Times-BoldItalicR 600 _ff
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30 _pl _cp 
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678 1106 677 1105 675 1103 673 1101 672 1099 671 1097 671 1095 672 1092 674 1091 677 1092 679 1093 680 1094 42 _pl _cp 674 1095 _m
_sp 674 1095 675 1094 676 1093 678 1094 680 1096 681 1097 681 1098 682 1100 682 1101 682 1103 682 1104 682 1105 681 1106 680 1106 679 1105 
677 1103 676 1102 675 1100 675 1099 674 1097 674 1095 674 1095 22 _pl _cp 
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796 1139 796 1140 797 1141 804 1170 796 1169 796 1168 798 1168 799 1167 799 1166 799 1165 799 1164 797 1156 795 1157 793 1158 791 1158 
789 1157 786 1155 784 1153 781 1150 780 1147 778 1144 778 1141 778 1138 779 1137 781 1135 783 1135 785 1135 787 1136 789 1137 791 1138 
792 1140 46 _pl _cp 782 1141 _m
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791 1157 790 1156 788 1154 786 1151 785 1149 783 1146 782 1143 782 1141 782 1141 24 _pl _cp 
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789 1071 789 1072 790 1074 797 1102 789 1101 789 1100 791 1100 792 1100 792 1099 792 1098 792 1096 790 1088 788 1090 786 1091 784 1091 
782 1090 779 1088 777 1086 774 1083 773 1080 771 1076 771 1073 771 1071 772 1069 774 1068 776 1067 778 1067 780 1068 782 1069 784 1071 
785 1072 46 _pl _cp 775 1073 _m
_sp 775 1073 776 1071 779 1070 781 1070 782 1071 784 1073 785 1075 786 1077 787 1078 788 1080 788 1082 789 1084 789 1086 788 1088 786 1089 
784 1089 783 1088 781 1086 779 1084 778 1082 776 1079 775 1076 775 1074 775 1073 24 _pl _cp 
0 g _f _s _s 
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801 1072 801 1073 802 1074 806 1088 810 1088 810 1090 806 1090 808 1095 807 1095 804 1093 803 1091 801 1090 798 1089 798 1088 29 _pl _cp 
0 g _f _s _s 
0 g 928 1203 _m
_sp 928 1203 931 1203 932 1204 934 1205 935 1206 936 1207 937 1209 937 1210 937 1212 937 1215 935 1217 934 1218 932 1218 929 1219 926 1219 
915 1219 914 1218 916 1218 917 1217 918 1216 918 1215 917 1213 912 1192 911 1190 910 1188 909 1187 908 1187 907 1187 907 1186 919 1186 
920 1187 918 1187 917 1188 916 1189 916 1190 916 1191 917 1192 917 1192 920 1202 923 1202 929 1186 937 1186 937 1187 936 1187 935 1187 
934 1188 933 1190 932 1192 48 _pl _cp 920 1205 _m
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15 _pl _cp 
0 g _f _s _s 
0 g 1111 1054 _m
_sp 1111 1054 1112 1056 1113 1058 1115 1059 1116 1059 1118 1060 1119 1060 1123 1060 1116 1036 1115 1033 1114 1031 1113 1030 1112 1030 1111 1030 1110 1029 
1124 1029 1125 1030 1123 1030 1121 1031 1121 1032 1121 1033 1121 1034 1121 1036 1128 1060 1130 1060 1133 1060 1135 1059 1136 1058 1136 1056 1136 1056 
1136 1055 1136 1055 1136 1054 1137 1054 1139 1062 1112 1062 1110 1054 37 _pl _cp 
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1280 1138 1281 1139 1282 1139 1283 1141 1274 1141 1274 1139 1275 1139 1276 1139 1276 1138 1276 1136 1274 1134 26 _pl _cp 
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1307 1092 1309 1091 1311 1091 1313 1092 1315 1093 1317 1095 1318 1097 1319 1099 1320 1100 1320 1102 1320 1104 1319 1106 1318 1107 1316 1107 1316 1107 
1315 1106 1314 1106 1313 1105 1311 1104 34 _pl _cp 1308 1093 _m
_sp 1308 1093 1309 1093 1310 1092 1312 1093 1314 1094 1315 1096 1316 1098 1317 1100 1317 1102 1316 1104 1315 1105 1314 1104 1312 1103 1311 1101 1310 1099 
1309 1097 1309 1096 1308 1094 18 _pl _cp 
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_sp 1322 1096 1322 1094 1323 1092 1325 1091 1327 1091 1329 1091 1330 1092 1332 1093 1333 1094 1334 1096 1335 1098 1336 1099 1336 1101 1336 1103 1335 1105 
1333 1106 1331 1107 1330 1107 1328 1106 1327 1105 1325 1104 1324 1102 1323 1100 1322 1098 1322 1096 1322 1096 26 _pl _cp 1325 1095 _m
_sp 1325 1095 1326 1093 1327 1092 1329 1093 1331 1095 1332 1097 1332 1099 1333 1100 1333 1102 1332 1105 1331 1106 1330 1106 1328 1105 1327 1103 1326 1102 
1325 1100 1325 1099 1325 1097 1325 1095 1325 1095 20 _pl _cp 
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1350 1094 1350 1095 1350 1095 1355 1115 1350 1114 1350 1113 1351 1113 1352 1113 1352 1112 1352 1111 1352 1110 1350 1105 1349 1106 1348 1107 1347 1107 
1345 1106 1344 1105 1342 1103 1340 1101 1339 1099 1338 1097 1338 1095 1339 1092 1341 1091 1344 1092 1346 1093 1347 1094 42 _pl _cp 1341 1095 _m
_sp 1341 1095 1342 1094 1343 1093 1345 1094 1347 1096 1348 1097 1348 1098 1349 1100 1349 1101 1349 1103 1349 1104 1349 1105 1348 1106 1347 1106 1346 1105 
1344 1103 1343 1102 1342 1100 1342 1099 1341 1097 1341 1095 1341 1095 22 _pl _cp 
0 g _f _s _s 
0 g 1354 1106 _m
_sp 1354 1106 1355 1105 1355 1105 1356 1105 1357 1105 1358 1103 1359 1101 1359 1100 1360 1098 1360 1096 1361 1094 1361 1092 1360 1090 1359 1089 1358 1088 
1357 1087 1357 1087 1356 1087 1356 1087 1356 1087 1355 1088 1355 1088 1354 1087 1354 1086 1354 1085 1355 1085 1356 1085 1357 1086 1359 1088 1361 1090 
1363 1092 1364 1094 1365 1095 1366 1098 1367 1100 1368 1102 1368 1103 1368 1104 1368 1106 1366 1107 1366 1106 1365 1105 1365 1105 1366 1104 1367 1104 
1367 1103 1367 1102 1367 1102 1367 1101 1366 1100 1365 1099 1364 1097 1364 1096 1364 1095 1363 1095 1363 1094 1363 1095 1363 1095 1362 1098 1362 1100 
1362 1102 1361 1104 1360 1106 1359 1107 64 _pl _cp 
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1521 1219 1521 1218 1522 1218 1523 1217 1524 1216 1524 1215 1523 1213 1518 1192 1517 1190 1516 1188 1515 1187 1514 1187 1514 1187 1513 1186 1526 1186 
1526 1187 1525 1187 1523 1188 1523 1189 1523 1190 1523 1191 1523 1192 1523 1192 1526 1202 1529 1202 1535 1186 1543 1186 1543 1187 1543 1187 1541 1187 
1540 1188 1539 1190 1538 1192 48 _pl _cp 1526 1205 _m
_sp 1526 1205 1529 1205 1532 1205 1533 1205 1535 1206 1536 1207 1537 1209 1538 1212 1538 1214 1537 1216 1535 1217 1532 1217 1530 1217 1529 1216 1528 1212 
15 _pl _cp 
0 g _f _s _s 
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_sp 1717 1054 1719 1056 1720 1058 1721 1059 1722 1059 1724 1060 1726 1060 1729 1060 1722 1036 1721 1033 1721 1031 1720 1030 1718 1030 1717 1030 1716 1029 
1731 1029 1731 1030 1729 1030 1728 1031 1727 1032 1727 1033 1727 1034 1728 1036 1734 1060 1736 1060 1739 1060 1741 1059 1742 1058 1742 1056 1742 1056 
1742 1055 1742 1055 1742 1054 1743 1054 1745 1062 1718 1062 1716 1054 37 _pl _cp 
0 g _f _s _s 
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1878 1139 1878 1140 1879 1141 1887 1170 1878 1169 1878 1168 1880 1168 1881 1167 1881 1166 1881 1165 1881 1164 1879 1156 1877 1157 1875 1158 1873 1158 
1871 1157 1868 1155 1866 1153 1863 1150 1862 1147 1860 1144 1860 1141 1860 1138 1862 1137 1863 1135 1866 1135 1868 1135 1869 1136 1871 1137 1873 1138 
1874 1140 46 _pl _cp 1865 1141 _m
_sp 1865 1141 1866 1138 1868 1137 1870 1137 1871 1139 1873 1140 1874 1143 1875 1145 1876 1146 1877 1148 1877 1150 1878 1152 1878 1153 1877 1156 1875 1157 
1873 1157 1872 1156 1870 1154 1868 1151 1867 1149 1866 1146 1865 1143 1865 1141 1865 1141 24 _pl _cp 
0 g _f _s _s 
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1871 1071 1871 1072 1872 1074 1880 1102 1871 1101 1871 1100 1873 1100 1874 1100 1874 1099 1874 1098 1874 1096 1872 1088 1870 1090 1868 1091 1866 1091 
1864 1090 1861 1088 1859 1086 1856 1083 1855 1080 1853 1076 1853 1073 1853 1071 1855 1069 1856 1068 1859 1067 1861 1067 1862 1068 1864 1069 1866 1071 
1867 1072 46 _pl _cp 1858 1073 _m
_sp 1858 1073 1859 1071 1861 1070 1863 1070 1864 1071 1866 1073 1867 1075 1868 1077 1869 1078 1870 1080 1870 1082 1871 1084 1871 1086 1870 1088 1868 1089 
1866 1089 1865 1088 1863 1086 1861 1084 1860 1082 1859 1079 1858 1076 1858 1074 1858 1073 24 _pl _cp 
0 g _f _s _s 
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1884 1072 1884 1073 1884 1074 1888 1088 1892 1088 1893 1090 1888 1090 1890 1095 1889 1095 1887 1093 1885 1091 1883 1090 1880 1089 1880 1088 29 _pl _cp 
0 g _f _s _s 
0 g 1942 1116 _m
_sp 1942 1116 1942 1134 1942 1136 1943 1138 1944 1139 1945 1139 1946 1139 1946 1141 1934 1141 1934 1139 1934 1139 1936 1139 1937 1138 1937 1136 1937 1134 
1937 1107 1939 1107 1959 1134 1961 1136 1962 1138 1963 1139 1964 1139 1965 1141 1956 1141 1955 1139 1956 1139 1957 1139 1958 1138 1957 1136 1956 1134 
30 _pl _cp 
0 g _f _s _s 
0 g 1992 1102 _m
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1989 1092 1991 1091 1993 1091 1995 1092 1996 1093 1998 1095 2000 1097 2001 1099 2002 1100 2002 1102 2002 1104 2001 1106 1999 1107 1998 1107 1997 1107 
1996 1106 1994 1105 32 _pl _cp 1990 1093 _m
_sp 1990 1093 1990 1093 1992 1092 1994 1093 1995 1094 1997 1096 1998 1098 1999 1100 1999 1102 1998 1104 1997 1105 1996 1104 1994 1103 1993 1101 1991 1099 
1990 1097 1990 1096 1990 1094 18 _pl _cp 
0 g _f _s _s 
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2015 1106 2013 1107 2011 1107 2009 1106 2008 1105 2006 1104 2005 1102 2004 1100 2003 1098 2003 1096 2003 1096 26 _pl _cp 2006 1095 _m
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2006 1097 2006 1095 2006 1095 18 _pl _cp 
0 g _f _s _s 
0 g 2029 1095 _m
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2032 1094 2032 1095 2032 1095 2037 1115 2032 1114 2031 1113 2033 1113 2034 1113 2034 1112 2034 1111 2033 1110 2032 1105 2031 1106 2029 1107 2028 1107 
2026 1106 2025 1105 2023 1103 2022 1101 2020 1099 2019 1097 2019 1095 2020 1092 2023 1091 2026 1092 2028 1093 2029 1094 42 _pl _cp 2022 1095 _m
_sp 2022 1095 2023 1094 2025 1093 2027 1094 2029 1096 2030 1097 2030 1098 2031 1100 2031 1101 2031 1103 2031 1104 2030 1105 2029 1106 2027 1105 2025 1102 
2024 1100 2023 1099 2022 1097 2022 1095 2022 1095 20 _pl _cp 
0 g _f _s _s 
0 g 2036 1106 _m
_sp 2036 1106 2036 1105 2037 1105 2038 1105 2039 1105 2040 1103 2041 1101 2041 1100 2041 1098 2042 1096 2042 1094 2043 1092 2042 1090 2041 1089 2040 1088 
2038 1087 2038 1087 2038 1087 2038 1087 2037 1087 2037 1088 2036 1088 2036 1087 2035 1086 2036 1085 2037 1085 2038 1085 2039 1086 2041 1088 2043 1090 
2044 1092 2046 1094 2047 1095 2048 1098 2049 1100 2049 1102 2050 1103 2050 1104 2049 1106 2048 1107 2047 1106 2047 1105 2047 1105 2048 1104 2049 1104 
2049 1103 2049 1102 2049 1102 2048 1101 2048 1100 2047 1099 2046 1097 2046 1096 2045 1095 2045 1095 2045 1094 2045 1095 2045 1095 2044 1098 2044 1100 
2043 1102 2043 1104 2042 1106 2041 1107 64 _pl _cp 
0 g _f _s _s 
0 g 736 1127 _m
_sp 736 1127 717 1127 717 1125 736 1125 4 _pl _cp 736 1119 _m
_sp 736 1119 717 1119 717 1117 736 1117 4 _pl _cp 
0 g _f _s _s 
0 g 1407 1131 _m
_sp 1407 1131 1407 1123 1398 1123 1398 1121 1407 1121 1407 1113 1409 1113 1409 1121 1417 1121 1417 1123 1409 1123 1409 1131 12 _pl _cp 
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0 g _f _s _s 
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0 g _f _s _s 
0 g 1114 1202 _m
_sp 1114 1202 1114 1200 1114 1198 1115 1195 1116 1193 1116 1192 1117 1191 1118 1189 1119 1188 1121 1187 1122 1186 1124 1186 1125 1186 1129 1187 1132 1189 
1135 1192 1136 1197 1137 1203 1136 1209 1135 1213 1132 1217 1129 1219 1125 1220 1122 1219 1118 1217 1116 1213 1115 1208 27 _pl _cp 1119 1203 _m
_sp 1119 1203 1119 1198 1120 1193 1121 1190 1123 1189 1125 1188 1127 1188 1129 1189 1130 1191 1131 1194 1132 1198 1132 1203 1132 1208 1131 1213 1130 1216 
1128 1217 1125 1218 1123 1217 1121 1216 1120 1213 1119 1208 21 _pl _cp 
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934 1035 935 1040 936 1046 935 1052 934 1056 931 1060 928 1062 924 1063 921 1062 917 1060 915 1056 914 1051 27 _pl _cp 918 1046 _m
_sp 918 1046 918 1041 919 1036 920 1033 922 1032 924 1031 926 1031 928 1032 929 1034 930 1037 931 1041 931 1046 931 1051 930 1056 929 1059 
927 1060 924 1061 922 1060 920 1059 919 1056 918 1051 21 _pl _cp 
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1741 1192 1742 1197 1743 1203 1742 1209 1741 1213 1738 1217 1735 1219 1732 1220 1728 1219 1725 1217 1722 1213 1720 1208 27 _pl _cp 1725 1203 _m
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1734 1217 1732 1218 1729 1217 1727 1216 1726 1213 1725 1208 21 _pl _cp 
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1540 1035 1541 1040 1542 1046 1541 1052 1540 1056 1537 1060 1534 1062 1531 1063 1527 1062 1524 1060 1521 1056 1520 1051 27 _pl _cp 1524 1046 _m
_sp 1524 1046 1524 1041 1525 1036 1526 1033 1528 1032 1531 1031 1533 1031 1534 1032 1535 1034 1536 1037 1537 1041 1537 1046 1537 1051 1536 1056 1535 1059 
1533 1060 1531 1061 1528 1060 1526 1059 1525 1056 1524 1051 21 _pl _cp 
0 g _f _s _s 
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0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 4620 _m
/Times-BoldR 600 _ff
(\(6.26\))_S /Times-RomanR 600 _ff
4950 1288 _m
(114)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1500 11854 _m
(Substituting)_S 67 _t
(acceleration)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(A)_S /Times-RomanR 600 _ff
(])_S 67 _t
(for)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-RomanR 600 _ff
(])_S 67 _t
(\(as)_S 67 _t
(always)_S 67 _t
(in)_S 67 _t
(the)_S 1500 11504 _m
(appropriate)_S 67 _t
(coordinate)_S 67 _t
(frames\))_S 67 _t
(results)_S 67 _t
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701 2577 701 2578 701 2578 706 2598 701 2597 701 2596 702 2596 703 2596 703 2595 703 2594 703 2593 701 2588 700 2589 699 2590 698 2590 
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814 2622 814 2623 815 2624 822 2653 814 2652 814 2651 816 2651 817 2650 817 2649 817 2648 817 2647 815 2639 813 2640 811 2641 809 2641 
807 2640 804 2638 802 2636 799 2633 798 2630 796 2627 796 2624 796 2621 797 2620 799 2618 801 2618 803 2618 805 2619 807 2620 809 2621 
810 2623 46 _pl _cp 800 2624 _m
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809 2640 808 2639 806 2637 804 2634 803 2632 801 2629 800 2626 800 2624 800 2624 24 _pl _cp 
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807 2554 807 2555 808 2557 815 2585 807 2584 807 2583 809 2583 810 2583 810 2582 810 2581 810 2579 808 2571 806 2573 804 2574 802 2574 
800 2573 797 2571 795 2569 792 2566 791 2563 789 2559 789 2556 789 2554 790 2552 792 2551 794 2550 796 2550 798 2551 800 2552 802 2554 
803 2555 46 _pl _cp 793 2556 _m
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802 2572 801 2571 799 2569 797 2567 796 2565 794 2562 793 2559 793 2557 793 2556 24 _pl _cp 
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819 2555 819 2556 820 2557 824 2571 828 2571 828 2573 824 2573 826 2578 825 2578 822 2576 821 2574 819 2573 816 2572 816 2571 29 _pl _cp 
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933 2702 932 2701 934 2701 935 2700 936 2699 936 2698 935 2696 930 2675 929 2673 928 2671 927 2670 926 2670 925 2670 925 2669 937 2669 
938 2670 936 2670 935 2671 934 2672 934 2673 934 2674 935 2675 935 2675 938 2685 941 2685 947 2669 955 2669 955 2670 954 2670 953 2670 
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15 _pl _cp 
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1142 2512 1143 2513 1141 2513 1139 2514 1139 2515 1139 2516 1139 2517 1139 2519 1146 2543 1148 2543 1151 2543 1153 2542 1154 2541 1154 2539 1154 2539 
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1298 2621 1299 2622 1300 2622 1301 2624 1292 2624 1292 2622 1293 2622 1294 2622 1294 2621 1294 2619 1292 2617 26 _pl _cp 
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1325 2575 1327 2574 1329 2574 1331 2575 1333 2576 1335 2578 1336 2580 1337 2582 1338 2583 1338 2585 1338 2587 1337 2589 1336 2590 1334 2590 1334 2590 
1333 2589 1332 2589 1331 2588 1329 2587 34 _pl _cp 1326 2576 _m
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1327 2580 1327 2579 1326 2577 18 _pl _cp 
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1351 2589 1349 2590 1348 2590 1346 2589 1345 2588 1343 2587 1342 2585 1341 2583 1340 2581 1340 2579 1340 2579 26 _pl _cp 1343 2578 _m
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1343 2583 1343 2582 1343 2580 1343 2578 1343 2578 20 _pl _cp 
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1368 2577 1368 2578 1368 2578 1373 2598 1368 2597 1368 2596 1369 2596 1370 2596 1370 2595 1370 2594 1370 2593 1368 2588 1367 2589 1366 2590 1365 2590 
1363 2589 1362 2588 1360 2586 1358 2584 1357 2582 1356 2580 1356 2578 1357 2575 1359 2574 1362 2575 1364 2576 1365 2577 42 _pl _cp 1359 2578 _m
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1362 2586 1361 2585 1360 2583 1360 2582 1359 2580 1359 2578 1359 2578 22 _pl _cp 
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1375 2570 1375 2570 1374 2570 1374 2570 1374 2570 1373 2571 1373 2571 1372 2570 1372 2569 1372 2568 1373 2568 1374 2568 1375 2569 1377 2571 1379 2573 
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1385 2586 1385 2585 1385 2585 1385 2584 1384 2583 1383 2582 1382 2580 1382 2579 1382 2578 1381 2578 1381 2577 1381 2578 1381 2578 1380 2581 1380 2583 
1380 2585 1379 2587 1378 2589 1377 2590 64 _pl _cp 
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1539 2702 1539 2701 1540 2701 1541 2700 1542 2699 1542 2698 1541 2696 1536 2675 1535 2673 1534 2671 1533 2670 1532 2670 1532 2670 1531 2669 1544 2669 
1544 2670 1543 2670 1541 2671 1541 2672 1541 2673 1541 2674 1541 2675 1541 2675 1544 2685 1547 2685 1553 2669 1561 2669 1561 2670 1561 2670 1559 2670 
1558 2671 1557 2673 1556 2675 48 _pl _cp 1544 2688 _m
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15 _pl _cp 
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1749 2512 1749 2513 1747 2513 1746 2514 1745 2515 1745 2516 1745 2517 1746 2519 1752 2543 1754 2543 1757 2543 1759 2542 1760 2541 1760 2539 1760 2539 
1760 2538 1760 2538 1760 2537 1761 2537 1763 2545 1736 2545 1734 2537 37 _pl _cp 
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1895 2602 1895 2597 1896 2596 1896 2595 1896 2595 1896 2595 1895 2593 1893 2592 1892 2592 1891 2591 1904 2591 1904 2592 1904 2592 1902 2593 1901 2595 
1900 2597 1899 2624 32 _pl _cp 1887 2604 _m
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1932 2575 1934 2574 1936 2574 1938 2575 1939 2576 1941 2578 1942 2580 1943 2582 1944 2583 1944 2585 1944 2587 1943 2589 1942 2590 1941 2590 1940 2590 
1939 2589 1937 2588 32 _pl _cp 1932 2576 _m
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1933 2580 1933 2579 1932 2577 18 _pl _cp 
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1957 2589 1955 2590 1954 2590 1952 2589 1951 2588 1949 2587 1948 2585 1947 2583 1946 2581 1946 2579 1946 2579 26 _pl _cp 1949 2578 _m
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1950 2583 1950 2582 1949 2580 1949 2578 1949 2578 20 _pl _cp 
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1974 2577 1974 2578 1974 2578 1980 2598 1974 2597 1974 2596 1975 2596 1976 2596 1976 2595 1976 2594 1976 2593 1974 2588 1973 2589 1972 2590 1971 2590 
1969 2589 1968 2588 1966 2586 1964 2584 1963 2582 1962 2580 1962 2578 1963 2575 1966 2574 1968 2575 1970 2576 1971 2577 42 _pl _cp 1965 2578 _m
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1968 2586 1967 2585 1966 2583 1966 2582 1965 2580 1965 2578 1965 2578 22 _pl _cp 
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1981 2570 1981 2570 1981 2570 1980 2570 1980 2570 1980 2571 1979 2571 1978 2570 1978 2569 1978 2568 1979 2568 1981 2568 1982 2569 1984 2571 1985 2573 
1987 2575 1988 2577 1989 2578 1990 2581 1991 2583 1992 2585 1993 2586 1993 2587 1992 2589 1991 2590 1990 2589 1989 2588 1990 2588 1990 2587 1991 2587 
1991 2586 1991 2585 1991 2585 1991 2584 1990 2583 1990 2582 1989 2580 1989 2579 1988 2578 1988 2578 1987 2577 1987 2578 1987 2578 1986 2581 1986 2583 
1986 2585 1985 2587 1984 2589 1984 2590 64 _pl _cp 
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1153 2675 1154 2680 1155 2686 1154 2691 1153 2696 1150 2700 1147 2702 1143 2703 1139 2702 1136 2700 1134 2696 1133 2691 27 _pl _cp 1137 2686 _m
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1146 2700 1143 2701 1141 2700 1139 2698 1138 2695 1137 2691 21 _pl _cp 
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952 2518 953 2523 954 2529 953 2534 952 2539 949 2543 946 2545 942 2546 939 2545 935 2543 933 2539 932 2534 27 _pl _cp 936 2529 _m
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945 2543 942 2544 940 2543 938 2541 937 2538 936 2534 21 _pl _cp 
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1759 2675 1760 2680 1761 2686 1760 2691 1759 2696 1756 2700 1753 2702 1750 2703 1746 2702 1743 2700 1740 2696 1738 2691 27 _pl _cp 1743 2686 _m
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1752 2700 1750 2701 1747 2700 1745 2698 1744 2695 1743 2691 21 _pl _cp 
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1558 2518 1559 2523 1560 2529 1559 2534 1558 2539 1555 2543 1552 2545 1549 2546 1545 2545 1542 2543 1539 2539 1538 2534 27 _pl _cp 1542 2529 _m
_sp 1542 2529 1542 2523 1543 2519 1544 2516 1546 2514 1549 2514 1551 2514 1552 2515 1553 2517 1554 2520 1555 2524 1555 2529 1555 2534 1554 2538 1553 2541 
1551 2543 1549 2544 1546 2543 1544 2541 1543 2538 1542 2534 21 _pl _cp 
0 g _f _s _s 
0 g 1718 2545 _m
_sp 1718 2545 1718 2504 1729 2504 1729 2505 1725 2505 1723 2506 1722 2509 1722 2539 1722 2541 1723 2543 1726 2544 1729 2544 1729 2545 13 _pl _cp 
0 g _f _s _s 
0 g 1781 2504 _m
_sp 1781 2504 1781 2545 1770 2545 1770 2544 1773 2544 1776 2543 1776 2540 1776 2510 1776 2508 1776 2506 1773 2505 1770 2505 1770 2504 13 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 10436 _m
/Times-BoldR 600 _ff
(\(6.27\))_S /Times-RomanR 600 _ff
1500 9175 _m
(Inspection)_S 67 _t
(of)_S 67 _t
(Equation)_S 67 _t
(\(6.27\))_S 67 _t
(makes)_S 67 _t
(it)_S 67 _t
(clear)_S 67 _t
(that)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 1500 8825 _m
(accelerations)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(A)_S /Times-RomanR 600 _ff
(])_S /Times-BoldItalicR 360 _ff
2878 8780 _m
(world)_S 3158 8780 _m
/Times-RomanR 600 _ff
3158 8825 _m
67 _t
(and)_S 67 _t
(rotated)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(accelerations)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(A)_S /Times-RomanR 600 _ff
(])_S /Times-BoldItalicR 360 _ff
7492 8780 _m
(body)_S 7725 8780 _m
/Times-RomanR 600 _ff
7725 8825 _m
67 _t
(are)_S 67 _t
(not)_S 1500 8475 _m
(equivalent)_S 67 _t
(unless)_S 67 _t
(the)_S 67 _t
(transformation)_S 67 _t
(matrix)_S 67 _t
(between)_S 67 _t
(coordinate)_S 67 _t
(frames)_S 67 _t
(is)_S 67 _t
(unchanging,)_S 1500 8126 _m
(or)_S 67 _t
(all)_S 67 _t
(body)_S 67 _t
(velocities)_S 67 _t
(are)_S 67 _t
(zero)_S 67 _t
(\(Greenwood)_S 67 _t
(88\).)_S 134 _t
(It)_S 67 _t
(is)_S 67 _t
(possible)_S 67 _t
(to)_S 67 _t
(examine)_S 67 _t
(accelerations)_S 1500 7777 _m
(acting)_S 67 _t
(upon)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(from)_S 67 _t
(a)_S 67 _t
(perspective)_S 67 _t
(within)_S 67 _t
(the)_S 67 _t
(rotating)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame,)_S 67 _t
(but)_S 1500 7428 _m
(they)_S 67 _t
(cannot)_S 67 _t
(be)_S 67 _t
(directly)_S 67 _t
(integrated)_S 67 _t
(into)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(accelerations.)_S 2400 7079 _m
(It)_S 67 _t
(is)_S 67 _t
(possible)_S 67 _t
(to)_S 67 _t
(numerically)_S 67 _t
(integrate)_S 67 _t
(the)_S 67 _t
(six)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(with)_S 1500 6730 _m
(respect)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(and)_S 67 _t
(determine)_S 67 _t
(new)_S 67 _t
(velocity)_S 67 _t
(values.)_S 134 _t
(This)_S 67 _t
(dynamics)_S 67 _t
(equation)_S 67 _t
(integration)_S 1500 6381 _m
(must)_S 67 _t
(be)_S 67 _t
(performed)_S 67 _t
(using)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(variables.)_S 134 _t
(Once)_S 67 _t
(new)_S 67 _t
(values)_S 67 _t
(for)_S 67 _t
(body)_S 1500 6032 _m
(velocities)_S 67 _t
(are)_S 67 _t
(thereby)_S 67 _t
(obtained,)_S 67 _t
(the)_S 67 _t
(six)_S 67 _t
(Euler)_S 67 _t
(kinematic)_S 67 _t
(constraint)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 1500 5683 _m
(\(6.22\))_S 67 _t
(are)_S 67 _t
(utilized)_S 67 _t
(to)_S 67 _t
(produce)_S 67 _t
(linear)_S 67 _t
(and)_S 67 _t
(angular)_S 67 _t
(world)_S 67 _t
(velocities.)_S 134 _t
(Finally)_S 67 _t
(posture)_S 67 _t
(is)_S 1500 5334 _m
(determined)_S 67 _t
(within)_S 67 _t
(the)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(system)_S 67 _t
(using)_S 67 _t
(world)_S 67 _t
(velocities.)_S 134 _t
1980 4912 _m
/Times-BoldR 600 _ff
(4.)_S 2400 4912 _m
(Time)_S 67 _t
(Dependencies)_S /Times-RomanR 600 _ff
2400 4563 _m
(During)_S 67 _t
(operation)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(vehicle)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
_U (virtual)_S 67 _t
(world)_S _u (,)_S 67 _t
(forces)_S 67 _t
(acting)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(robot)_S 1500 4214 _m
(can)_S 67 _t
(be)_S 67 _t
(estimated)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(state)_S 67 _t
(vector)_S 67 _t
(while)_S 67 _t
(velocities)_S 67 _t
(and)_S 67 _t
(body)_S 67 _t
(accelerations)_S 1500 3865 _m
(are)_S 67 _t
(analytically)_S 67 _t
(derived.)_S 134 _t
(During)_S 67 _t
(operation)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
_U (real)_S 67 _t
(world)_S _u (,)_S 67 _t
(forces)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(similarly)_S 1500 3516 _m
(estimated)_S 67 _t
(while)_S 67 _t
(accurate)_S 67 _t
(velocity)_S 67 _t
(and)_S 67 _t
(body)_S 67 _t
(acceleration)_S 67 _t
(information)_S 67 _t
(may)_S 67 _t
(\(or)_S 67 _t
(may)_S 67 _t
(not\))_S 1500 3167 _m
(be)_S 67 _t
(available)_S 67 _t
(from)_S 67 _t
(flow)_S 67 _t
(and)_S 67 _t
(inertial)_S 67 _t
(navigation)_S 67 _t
(sensors.)_S 134 _t
(In)_S 67 _t
(either)_S 67 _t
(world,)_S 67 _t
(good)_S 67 _t
(estimates)_S 1500 2818 _m
(of)_S 67 _t
(changes)_S 67 _t
(in)_S 67 _t
(body)_S 67 _t
(frame)_S 67 _t
(velocities)_S 67 _t
(are)_S 67 _t
(a)_S 67 _t
(primary)_S 67 _t
(robot)_S 67 _t
(requirement)_S 67 _t
(so)_S 67 _t
(that)_S 67 _t
(velocity)_S 1500 2469 _m
(and)_S 67 _t
(posture)_S 67 _t
(estimates)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(cumulatively)_S 67 _t
(integrated)_S 67 _t
(over)_S 67 _t
(time.)_S 134 _t
(Accurately)_S 67 _t
(estimating)_S 1500 2120 _m
(body)_S 67 _t
(frame)_S 67 _t
(velocity)_S 67 _t
(changes)_S 67 _t
(at)_S 67 _t
(suitably)_S 67 _t
(short)_S 67 _t
(time)_S 67 _t
(intervals)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(key)_S 67 _t
(to)_S 67 _t
(properly)_S 4950 1288 _m
(115)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1500 11855 _m
(modeling)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(response.)_S 134 _t
(Thus)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 1500 11506 _m
(must)_S 67 _t
(be)_S 67 _t
(written)_S 67 _t
(to)_S 67 _t
(produce)_S 67 _t
(time)_S 67 _t
(rates)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(velocities)_S 67 _t
(as)_S 67 _t
(the)_S 67 _t
(dependent)_S 1500 11157 _m
(variables,)_S 67 _t
(obtained)_S 67 _t
(through)_S 67 _t
(calculations)_S 67 _t
(that)_S 67 _t
(solely)_S 67 _t
(involve)_S 67 _t
(vehicle)_S 67 _t
(variables)_S 67 _t
(\(such)_S 67 _t
(as)_S 1500 10808 _m
(posture,)_S 67 _t
(propellers,)_S 67 _t
(thrusters)_S 67 _t
(and)_S 67 _t
(plane)_S 67 _t
(surfaces\))_S 67 _t
(which)_S 67 _t
(are)_S 67 _t
(continuously)_S 67 _t
(known)_S 67 _t
(to)_S 67 _t
(the)_S 1500 10459 _m
(robot.)_S 2400 10110 _m
(The)_S 67 _t
(Newton-Euler)_S 67 _t
(formulation)_S 67 _t
(of)_S 67 _t
(Newton's)_S 67 _t
(Second)_S 67 _t
(Law)_S 67 _t
(from)_S 1500 9761 _m
(Equation)_S 67 _t
(\(6.24\))_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(expanded)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(chain)_S 67 _t
(rule)_S 67 _t
(to)_S 67 _t
(produce)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 149 1749 400 2215 _cw 
_s 696 2258 _m
_sp 696 2258 696 2307 704 2307 704 2306 697 2306 697 2260 704 2260 704 2258 8 _pl _cp 
0 g _f _s _s 
0 g 755 2258 _m
_sp 755 2258 755 2307 747 2307 747 2306 753 2306 753 2260 747 2260 747 2258 8 _pl _cp 
0 g _f _s _s 
0 g 904 2284 _m
_sp 904 2284 904 2282 949 2282 949 2284 4 _pl _cp 
0 g _f _s _s 
0 g 969 2293 _m
_sp 969 2293 966 2293 966 2305 966 2310 966 2314 966 2318 967 2323 967 2327 968 2330 969 2334 970 2337 972 2340 974 2344 976 2347 980 2352 
980 2352 977 2347 975 2343 973 2339 972 2335 971 2332 970 2329 970 2325 969 2320 969 2316 969 2312 969 2308 969 2304 28 _pl _cp 
0 g _f _s _s 
0 g 969 2293 _m
_sp 969 2293 966 2293 966 2279 966 2275 966 2270 966 2266 967 2262 967 2258 968 2254 969 2251 970 2247 972 2244 974 2240 976 2237 980 2233 
980 2233 977 2238 975 2242 973 2245 972 2249 971 2253 970 2256 970 2260 969 2264 969 2268 969 2273 969 2277 969 2281 28 _pl _cp 
0 g _f _s _s 
0 g 982 2258 _m
_sp 982 2258 982 2307 990 2307 990 2306 984 2306 984 2260 990 2260 990 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1052 2258 _m
_sp 1052 2258 1052 2307 1044 2307 1044 2306 1051 2306 1051 2260 1044 2260 1044 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1171 2258 _m
_sp 1171 2258 1171 2307 1179 2307 1179 2306 1172 2306 1172 2260 1179 2260 1179 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1230 2258 _m
_sp 1230 2258 1230 2307 1222 2307 1222 2306 1228 2306 1228 2260 1222 2260 1222 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1314 2293 _m
_sp 1314 2293 1317 2293 1317 2305 1317 2310 1317 2314 1316 2318 1316 2323 1315 2327 1315 2330 1314 2334 1313 2337 1311 2340 1309 2344 1307 2347 1303 2352 
1302 2352 1305 2347 1308 2343 1310 2339 1311 2335 1312 2332 1313 2329 1313 2325 1314 2320 1314 2316 1314 2312 1314 2308 1314 2304 28 _pl _cp 
0 g _f _s _s 
0 g 1314 2293 _m
_sp 1314 2293 1317 2293 1317 2279 1317 2275 1317 2270 1316 2266 1316 2262 1315 2258 1315 2254 1314 2251 1313 2247 1311 2244 1309 2240 1307 2237 1303 2233 
1302 2233 1305 2238 1308 2242 1310 2245 1311 2249 1312 2253 1313 2256 1313 2260 1314 2264 1314 2268 1314 2273 1314 2277 1314 2281 28 _pl _cp 
0 g _f _s _s 
0 g 1395 2284 _m
_sp 1395 2284 1395 2282 1511 2282 1511 2284 4 _pl _cp 
0 g _f _s _s 
0 g 1438 2286 _m
_sp 1438 2286 1438 2335 1446 2335 1446 2334 1439 2334 1439 2287 1446 2287 1446 2286 8 _pl _cp 
0 g _f _s _s 
0 g 1508 2286 _m
_sp 1508 2286 1508 2335 1500 2335 1500 2334 1506 2334 1506 2287 1500 2287 1500 2286 8 _pl _cp 
0 g _f _s _s 
0 g 1522 2258 _m
_sp 1522 2258 1522 2307 1530 2307 1530 2306 1524 2306 1524 2260 1530 2260 1530 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1581 2258 _m
_sp 1581 2258 1581 2307 1573 2307 1573 2306 1580 2306 1580 2260 1573 2260 1573 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1659 2258 _m
_sp 1659 2258 1659 2307 1667 2307 1667 2306 1660 2306 1660 2260 1667 2260 1667 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1729 2258 _m
_sp 1729 2258 1729 2307 1721 2307 1721 2306 1727 2306 1727 2260 1721 2260 1721 2258 8 _pl _cp 
0 g _f _s _s 
0 g 1746 2284 _m
_sp 1746 2284 1746 2282 1851 2282 1851 2284 4 _pl _cp 
0 g _f _s _s 
0 g 1789 2286 _m
_sp 1789 2286 1789 2335 1797 2335 1797 2334 1790 2334 1790 2287 1797 2287 1797 2286 8 _pl _cp 
0 g _f _s _s 
0 g 1848 2286 _m
_sp 1848 2286 1848 2335 1840 2335 1840 2334 1846 2334 1846 2287 1840 2287 1840 2286 8 _pl _cp 
0 g _f _s _s 
0 g 737 2305 _m
_sp 737 2305 712 2305 712 2303 713 2303 715 2303 715 2301 715 2301 715 2300 715 2298 709 2278 708 2276 707 2274 706 2273 705 2273 705 2273 
704 2272 717 2272 718 2273 716 2273 714 2274 714 2275 714 2276 714 2276 714 2277 714 2278 717 2288 720 2288 723 2288 725 2288 726 2287 
726 2285 726 2285 725 2284 725 2284 725 2283 726 2283 730 2295 729 2295 728 2293 726 2291 725 2290 722 2290 718 2290 721 2302 727 2302 
730 2302 732 2301 734 2300 734 2299 734 2299 734 2299 734 2298 734 2297 735 2297 54 _pl _cp 
0 g _f _s _s 
0 g 768 2267 _m
_sp 768 2267 771 2279 765 2278 765 2277 766 2277 767 2277 767 2276 767 2276 767 2275 763 2259 762 2258 762 2258 762 2257 762 2257 763 2257 
765 2256 767 2256 769 2256 771 2257 772 2258 774 2259 775 2261 776 2263 777 2264 777 2266 777 2268 776 2270 775 2271 774 2271 773 2271 
772 2271 770 2269 32 _pl _cp 765 2258 _m
_sp 765 2258 766 2257 767 2256 769 2257 771 2258 772 2260 773 2263 774 2265 774 2267 774 2268 772 2269 771 2269 769 2268 768 2266 767 2264 
766 2262 766 2260 765 2259 18 _pl _cp 
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_sp 779 2260 779 2258 780 2257 782 2256 784 2256 786 2256 787 2256 789 2257 790 2259 791 2261 792 2262 793 2264 793 2266 793 2268 792 2270 
790 2271 788 2271 787 2271 785 2270 784 2269 782 2268 781 2266 780 2265 779 2263 779 2261 779 2261 26 _pl _cp 782 2259 _m
_sp 782 2259 783 2257 785 2256 787 2257 788 2260 789 2262 790 2263 790 2265 790 2266 789 2269 788 2270 787 2270 786 2269 784 2268 783 2266 
783 2264 783 2263 782 2261 782 2260 782 2260 20 _pl _cp 
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0 g 805 2259 _m
_sp 805 2259 804 2259 804 2258 804 2257 805 2256 806 2256 807 2256 808 2256 809 2257 811 2259 810 2260 810 2259 808 2257 808 2257 807 2258 
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_sp 798 2259 799 2258 800 2257 802 2258 804 2261 805 2262 805 2263 806 2266 807 2268 806 2269 805 2270 804 2270 803 2269 801 2268 800 2266 
799 2265 799 2263 798 2262 798 2260 798 2260 20 _pl _cp 
0 g _f _s _s 
0 g 812 2270 _m
_sp 812 2270 812 2269 813 2269 813 2269 814 2269 815 2267 816 2265 816 2264 817 2262 817 2260 818 2258 818 2256 817 2254 816 2253 815 2252 
814 2251 814 2251 814 2251 813 2251 813 2252 813 2252 812 2252 811 2252 811 2251 811 2250 812 2249 814 2249 815 2250 817 2252 818 2254 
820 2256 821 2258 822 2260 823 2262 824 2264 825 2266 826 2267 826 2269 825 2270 824 2271 823 2270 822 2269 823 2269 823 2268 824 2268 
824 2267 824 2267 824 2266 824 2265 823 2264 823 2263 822 2261 822 2260 821 2259 821 2259 820 2258 820 2259 820 2260 819 2262 819 2264 
819 2266 818 2268 817 2270 817 2271 64 _pl _cp 
0 g _f _s _s 
0 g 931 2305 _m
_sp 931 2305 931 2304 931 2303 931 2302 932 2300 933 2299 935 2299 936 2300 938 2302 941 2305 940 2305 939 2304 937 2302 936 2302 935 2302 
935 2303 935 2304 936 2305 943 2334 935 2333 935 2332 937 2332 938 2332 938 2331 938 2330 938 2328 936 2320 934 2322 932 2322 930 2322 
928 2321 925 2319 923 2317 920 2314 919 2311 917 2308 917 2305 917 2302 918 2301 920 2299 922 2299 924 2299 926 2300 928 2301 930 2302 
931 2304 46 _pl _cp 921 2305 _m
_sp 921 2305 922 2303 925 2302 927 2302 928 2303 930 2305 931 2307 932 2309 933 2310 934 2312 934 2314 935 2316 935 2318 934 2320 932 2321 
930 2321 929 2320 927 2318 925 2316 924 2313 922 2310 921 2307 921 2305 921 2305 24 _pl _cp 
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0 g 924 2237 _m
_sp 924 2237 924 2237 924 2235 924 2234 925 2232 926 2232 928 2232 929 2233 931 2235 934 2237 933 2238 932 2237 930 2235 929 2234 928 2235 
928 2236 928 2237 929 2238 936 2267 928 2265 928 2264 930 2264 931 2264 931 2263 931 2262 931 2261 929 2253 927 2254 925 2255 923 2255 
921 2254 918 2252 916 2250 913 2247 912 2244 910 2241 910 2238 910 2235 911 2234 913 2232 915 2232 917 2232 919 2232 921 2233 923 2235 
924 2236 46 _pl _cp 914 2238 _m
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923 2253 922 2252 920 2250 918 2248 917 2246 915 2243 914 2240 914 2238 914 2238 24 _pl _cp 
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0 g 941 2252 _m
_sp 941 2252 937 2238 936 2236 936 2234 937 2233 939 2232 941 2232 943 2233 944 2234 945 2235 945 2236 946 2238 945 2238 943 2235 941 2234 
941 2234 940 2235 940 2236 940 2237 941 2239 945 2252 949 2252 949 2254 945 2254 947 2260 946 2260 943 2257 942 2256 941 2255 940 2254 
938 2254 937 2253 937 2252 33 _pl _cp 
0 g _f _s _s 
0 g 1001 2301 _m
_sp 1001 2301 995 2278 994 2276 993 2274 992 2273 991 2273 991 2273 990 2272 1000 2272 1000 2273 999 2273 998 2274 997 2275 997 2276 997 2276 
997 2277 998 2278 1003 2298 1006 2272 1007 2272 1025 2299 1019 2278 1018 2276 1017 2274 1016 2273 1015 2273 1015 2273 1014 2272 1027 2272 1027 2273 
1026 2273 1024 2274 1024 2275 1024 2276 1024 2276 1024 2278 1029 2298 1030 2300 1031 2302 1032 2303 1033 2303 1034 2303 1034 2305 1025 2305 1010 2280 
1006 2305 998 2305 998 2303 998 2303 1000 2303 50 _pl _cp 
0 g _f _s _s 
0 g 1065 2267 _m
_sp 1065 2267 1068 2279 1063 2278 1063 2277 1064 2277 1065 2277 1065 2276 1065 2276 1065 2275 1060 2259 1060 2258 1060 2258 1060 2257 1060 2257 1060 2257 
1062 2256 1064 2256 1066 2256 1068 2257 1069 2258 1071 2259 1073 2261 1074 2263 1075 2264 1075 2266 1075 2268 1074 2270 1072 2271 1071 2271 1070 2271 
1069 2271 1067 2269 32 _pl _cp 1063 2258 _m
_sp 1063 2258 1063 2257 1065 2256 1067 2257 1068 2258 1070 2260 1071 2263 1072 2265 1072 2267 1071 2268 1070 2269 1069 2269 1067 2268 1066 2266 1064 2264 
1063 2262 1063 2260 1063 2259 18 _pl _cp 
0 g _f _s _s 
0 g 1076 2260 _m
_sp 1076 2260 1076 2258 1077 2257 1079 2256 1081 2256 1083 2256 1085 2256 1086 2257 1088 2259 1089 2261 1090 2262 1091 2264 1091 2266 1091 2268 1090 2270 
1088 2271 1086 2271 1084 2271 1082 2270 1081 2269 1079 2268 1078 2266 1077 2265 1076 2263 1076 2261 1076 2261 26 _pl _cp 1079 2259 _m
_sp 1079 2259 1080 2257 1082 2256 1084 2257 1086 2260 1087 2262 1087 2263 1088 2265 1088 2266 1087 2269 1085 2270 1083 2269 1081 2266 1080 2264 1080 2263 
1079 2261 1079 2260 1079 2260 18 _pl _cp 
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1105 2258 1105 2259 1105 2260 1110 2279 1105 2278 1104 2277 1106 2277 1107 2277 1107 2276 1107 2276 1106 2275 1105 2269 1104 2271 1102 2271 1101 2271 
1099 2270 1098 2269 1096 2268 1095 2266 1093 2264 1092 2262 1092 2260 1093 2257 1096 2256 1099 2256 1101 2258 1102 2259 42 _pl _cp 1095 2259 _m
_sp 1095 2259 1096 2258 1098 2257 1100 2258 1102 2261 1103 2262 1103 2263 1104 2266 1104 2268 1103 2269 1102 2270 1100 2269 1098 2266 1097 2265 1096 2263 
1095 2262 1095 2260 1095 2260 18 _pl _cp 
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_sp 1109 2270 1109 2269 1110 2269 1111 2269 1112 2269 1113 2267 1114 2265 1114 2264 1114 2262 1115 2260 1115 2258 1116 2256 1115 2254 1114 2253 1113 2252 
1111 2251 1111 2251 1111 2251 1111 2251 1110 2252 1110 2252 1109 2252 1109 2252 1108 2251 1109 2250 1110 2249 1111 2249 1112 2250 1114 2252 1116 2254 
1117 2256 1119 2258 1120 2260 1121 2262 1122 2264 1122 2266 1123 2267 1123 2269 1122 2270 1121 2271 1120 2270 1120 2269 1120 2269 1121 2268 1122 2268 
1122 2267 1122 2267 1122 2266 1121 2265 1121 2264 1120 2263 1119 2261 1119 2260 1118 2259 1118 2259 1118 2258 1118 2259 1118 2260 1117 2262 1117 2264 
1116 2266 1116 2268 1115 2270 1114 2271 64 _pl _cp 
0 g _f _s _s 
0 g 1193 2280 _m
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1212 2302 1213 2303 1214 2303 1215 2305 1206 2305 1206 2303 1207 2303 1208 2303 1208 2302 1208 2301 1206 2298 26 _pl _cp 
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1239 2256 1241 2256 1243 2256 1245 2257 1247 2258 1249 2259 1250 2261 1251 2263 1252 2264 1252 2266 1252 2268 1251 2270 1250 2271 1248 2271 1248 2271 
1247 2271 1246 2270 1245 2269 1243 2268 34 _pl _cp 1240 2258 _m
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1241 2262 1241 2260 1240 2259 18 _pl _cp 
0 g _f _s _s 
0 g 1254 2260 _m
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1265 2271 1263 2271 1262 2271 1260 2270 1259 2269 1257 2268 1256 2266 1255 2265 1254 2263 1254 2261 1254 2261 26 _pl _cp 1257 2259 _m
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1257 2264 1257 2263 1257 2261 1257 2260 1257 2260 20 _pl _cp 
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1282 2258 1282 2259 1282 2260 1287 2279 1282 2278 1282 2277 1283 2277 1284 2277 1284 2276 1284 2276 1284 2275 1282 2269 1281 2271 1280 2271 1279 2271 
1277 2270 1276 2269 1274 2268 1272 2266 1271 2264 1270 2262 1270 2260 1271 2257 1273 2256 1276 2256 1278 2258 1279 2259 42 _pl _cp 1273 2259 _m
_sp 1273 2259 1274 2258 1275 2257 1277 2258 1279 2261 1280 2262 1280 2263 1281 2266 1281 2268 1281 2269 1280 2270 1279 2270 1278 2269 1276 2268 1275 2266 
1274 2265 1274 2263 1273 2262 1273 2260 1273 2260 20 _pl _cp 
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1289 2251 1289 2251 1288 2251 1288 2251 1288 2252 1287 2252 1287 2252 1286 2252 1286 2251 1286 2250 1287 2249 1288 2249 1289 2250 1291 2252 1293 2254 
1295 2256 1296 2258 1297 2260 1298 2262 1299 2264 1300 2266 1300 2267 1300 2269 1300 2270 1298 2271 1298 2270 1297 2269 1297 2269 1298 2268 1299 2268 
1299 2267 1299 2267 1299 2266 1299 2265 1298 2264 1297 2263 1296 2261 1296 2260 1296 2259 1295 2259 1295 2258 1295 2259 1295 2260 1294 2262 1294 2264 
1294 2266 1293 2268 1292 2270 1291 2271 64 _pl _cp 
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1419 2303 1419 2304 1419 2305 1427 2334 1419 2333 1419 2332 1420 2332 1421 2332 1422 2331 1422 2330 1421 2328 1419 2320 1418 2322 1416 2322 1414 2322 
1411 2321 1408 2319 1406 2317 1404 2314 1402 2311 1401 2308 1401 2305 1401 2302 1402 2301 1404 2299 1406 2299 1408 2299 1410 2300 1411 2301 1413 2302 
1414 2304 46 _pl _cp 1405 2305 _m
_sp 1405 2305 1406 2303 1408 2302 1410 2302 1412 2303 1413 2305 1415 2307 1416 2309 1416 2310 1417 2312 1417 2314 1418 2316 1418 2318 1417 2320 1415 2321 
1414 2321 1412 2320 1411 2318 1409 2316 1408 2313 1406 2310 1405 2307 1405 2305 1405 2305 24 _pl _cp 
0 g _f _s _s 
0 g 1457 2329 _m
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1453 2305 1453 2306 1458 2326 1461 2300 1462 2300 1480 2327 1475 2306 1474 2304 1473 2302 1472 2301 1471 2301 1470 2301 1470 2300 1482 2300 1483 2301 
1481 2301 1480 2302 1479 2303 1479 2304 1479 2304 1480 2306 1485 2326 1486 2328 1487 2330 1488 2331 1489 2331 1489 2331 1489 2333 1481 2333 1465 2308 
1462 2333 1453 2333 1453 2331 1453 2331 1456 2331 50 _pl _cp 
0 g _f _s _s 
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1454 2236 1454 2237 1455 2238 1462 2267 1454 2265 1454 2264 1456 2264 1457 2264 1457 2263 1457 2262 1457 2261 1455 2253 1453 2254 1451 2255 1449 2255 
1447 2254 1444 2252 1442 2250 1439 2247 1438 2244 1436 2241 1436 2238 1436 2235 1437 2234 1439 2232 1441 2232 1443 2232 1445 2232 1447 2233 1449 2235 
1450 2236 46 _pl _cp 1440 2238 _m
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1449 2253 1448 2252 1446 2250 1444 2248 1443 2246 1441 2243 1440 2240 1440 2238 1440 2238 24 _pl _cp 
0 g _f _s _s 
0 g 1467 2252 _m
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1467 2234 1466 2235 1466 2236 1466 2237 1467 2239 1471 2252 1475 2252 1475 2254 1471 2254 1473 2260 1472 2260 1469 2257 1468 2256 1467 2255 1466 2254 
1464 2254 1463 2253 1463 2252 33 _pl _cp 
0 g _f _s _s 
0 g 1544 2280 _m
_sp 1544 2280 1544 2298 1544 2300 1545 2302 1546 2303 1547 2303 1548 2303 1548 2305 1536 2305 1536 2303 1536 2303 1537 2303 1538 2302 1539 2300 1539 2298 
1539 2271 1541 2271 1560 2298 1562 2300 1563 2302 1565 2303 1566 2303 1566 2305 1557 2305 1557 2303 1558 2303 1559 2303 1560 2302 1559 2301 1557 2298 
30 _pl _cp 
0 g _f _s _s 
0 g 1678 2301 _m
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1674 2277 1674 2278 1679 2298 1682 2272 1683 2272 1701 2299 1696 2278 1695 2276 1694 2274 1693 2273 1692 2273 1691 2273 1691 2272 1703 2272 1704 2273 
1702 2273 1701 2274 1700 2275 1700 2276 1700 2276 1701 2278 1706 2298 1707 2300 1708 2302 1709 2303 1710 2303 1710 2303 1710 2305 1702 2305 1686 2280 
1683 2305 1674 2305 1674 2303 1674 2303 1677 2303 50 _pl _cp 
0 g _f _s _s 
0 g 1766 2305 _m
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1770 2303 1770 2304 1770 2305 1778 2334 1770 2333 1770 2332 1771 2332 1772 2332 1773 2331 1773 2330 1772 2328 1770 2320 1769 2322 1767 2322 1765 2322 
1762 2321 1759 2319 1757 2317 1755 2314 1753 2311 1752 2308 1752 2305 1752 2302 1753 2301 1755 2299 1757 2299 1759 2299 1761 2300 1762 2301 1764 2302 
1765 2304 46 _pl _cp 1756 2305 _m
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1765 2321 1763 2320 1762 2318 1760 2316 1759 2313 1757 2310 1756 2307 1756 2305 1756 2305 24 _pl _cp 
0 g _f _s _s 
0 g 1811 2308 _m
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1830 2330 1831 2331 1832 2331 1833 2333 1824 2333 1824 2331 1825 2331 1826 2331 1826 2330 1826 2328 1824 2326 26 _pl _cp 
0 g _f _s _s 
0 g 1796 2237 _m
_sp 1796 2237 1796 2237 1795 2235 1795 2234 1796 2232 1798 2232 1799 2232 1801 2233 1803 2235 1805 2237 1804 2238 1803 2237 1801 2235 1800 2234 1800 2235 
1800 2236 1800 2237 1800 2238 1808 2267 1800 2265 1799 2264 1801 2264 1802 2264 1803 2263 1803 2262 1802 2261 1800 2253 1798 2254 1796 2255 1794 2255 
1792 2254 1789 2252 1787 2250 1785 2247 1783 2244 1782 2241 1781 2238 1782 2235 1783 2234 1785 2232 1787 2232 1789 2232 1790 2232 1792 2233 1794 2235 
1795 2236 46 _pl _cp 1786 2238 _m
_sp 1786 2238 1787 2235 1789 2234 1791 2234 1793 2235 1794 2237 1796 2239 1797 2241 1797 2242 1798 2244 1798 2246 1799 2248 1799 2250 1798 2252 1796 2253 
1795 2253 1793 2252 1792 2250 1790 2248 1788 2246 1787 2243 1786 2240 1786 2238 1786 2238 24 _pl _cp 
0 g _f _s _s 
0 g 1812 2252 _m
_sp 1812 2252 1808 2238 1808 2236 1807 2234 1808 2233 1810 2232 1812 2232 1814 2233 1815 2234 1816 2235 1817 2236 1818 2238 1817 2238 1815 2235 1813 2234 
1812 2234 1812 2235 1812 2236 1812 2237 1812 2239 1816 2252 1820 2252 1821 2254 1817 2254 1818 2260 1817 2260 1815 2257 1813 2256 1812 2255 1811 2254 
1810 2254 1808 2253 1808 2252 33 _pl _cp 
0 g _f _s _s 
0 g 875 2291 _m
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_sp 875 2283 856 2283 856 2282 875 2282 4 _pl _cp 
0 g _f _s _s 
0 g 1141 2289 _m
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0 g _f _s _s 
0 g 1365 2291 _m
_sp 1365 2291 1346 2291 1346 2290 1365 2290 4 _pl _cp 1365 2283 _m
_sp 1365 2283 1346 2283 1346 2282 1365 2282 4 _pl _cp 
0 g _f _s _s 
0 g 1621 2296 _m
_sp 1621 2296 1621 2287 1613 2287 1613 2286 1621 2286 1621 2277 1623 2277 1623 2286 1632 2286 1632 2287 1623 2287 1623 2296 12 _pl _cp 
0 g _f _s 
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_s grestore 8117 9152 _m
/Times-BoldR 600 _ff
(\(6.28\))_S /Times-RomanR 600 _ff
2400 8363 _m
(Within)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(the)_S 67 _t
(mass)_S 67 _t
(matrix)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(M)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
(is)_S 67 _t
(unchanging.)_S 67 _t
1500 8012 _m
(Differentiation)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(velocity)_S 67 _t
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/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
(reveals)_S 67 _t
(effects)_S 67 _t
(that)_S 67 _t
(are)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
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(coordinate)_S 67 _t
(frame)_S 67 _t
(rotating)_S 67 _t
(with)_S 67 _t
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5435 7623 _m
5638 7623 _m
67 _t
(with)_S 67 _t
(respect)_S 67 _t
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(coordinate)_S gsave 4 4 scale 16 _sr 
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_sp 1381 1918 1381 1913 1381 1910 1380 1909 1379 1907 1377 1907 1375 1908 1374 1909 1373 1912 1373 1916 1373 1919 1374 1922 1376 1924 1378 1926 1377 1928 
1373 1926 1370 1923 1369 1920 1368 1916 1369 1912 1371 1908 1373 1906 1377 1905 1379 1905 1380 1906 1382 1907 1383 1908 1384 1907 1385 1906 1387 1905 
1389 1905 1392 1906 1395 1908 1397 1912 1398 1916 1397 1920 1396 1923 1393 1926 1389 1928 1388 1926 1390 1925 1391 1923 1392 1921 1392 1920 1393 1918 
1393 1916 1393 1912 1392 1910 1390 1908 1389 1907 1387 1907 1386 1909 1385 1910 1385 1913 1385 1918 55 _pl _cp 
0 g _f _s 
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(frame)_S 67 _t
(\(Fossen)_S 67 _t
(94\):)_S gsave 4 4 scale 16 _sr 
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0 g _f _s _s 
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1199 1662 1201 1656 1203 1650 1202 1650 1200 1654 1198 1659 1197 1663 1195 1668 1194 1673 1194 1678 1193 1682 1193 1687 1193 1692 1194 1697 1195 1702 
1196 1707 1197 1712 1198 1717 1200 1721 1202 1725 35 _pl _cp 
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0 g 1649 1725 _m
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1653 1662 1651 1656 1649 1650 1650 1650 1652 1654 1654 1659 1655 1663 1656 1668 1657 1673 1658 1678 1659 1682 1659 1687 1659 1692 1658 1697 1657 1702 
1656 1707 1655 1712 1654 1717 1652 1721 1650 1725 35 _pl _cp 
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900 1676 913 1676 913 1677 912 1677 910 1678 910 1679 910 1680 910 1681 910 1682 910 1682 913 1693 916 1693 918 1693 920 1692 921 1691 
921 1689 921 1689 921 1689 921 1688 921 1687 922 1687 925 1699 924 1699 923 1697 922 1696 920 1695 917 1695 913 1695 917 1707 923 1707 
926 1707 928 1706 930 1705 930 1703 930 1703 930 1703 930 1702 930 1701 931 1701 54 _pl _cp 
0 g _f _s _s 
0 g 963 1671 _m
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960 1660 962 1660 964 1660 966 1661 968 1662 970 1663 971 1665 972 1667 973 1669 973 1671 972 1674 969 1675 969 1675 968 1675 967 1674 
966 1673 964 1672 32 _pl _cp 961 1662 _m
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962 1666 962 1664 961 1663 18 _pl _cp 
0 g _f _s _s 
0 g 975 1665 _m
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986 1675 984 1675 983 1675 981 1674 980 1673 978 1672 977 1670 976 1669 975 1667 975 1665 975 1665 26 _pl _cp 978 1664 _m
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978 1669 978 1667 978 1666 978 1664 978 1664 20 _pl _cp 
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1003 1662 1003 1663 1003 1664 1008 1683 1003 1682 1003 1682 1004 1682 1005 1682 1005 1681 1005 1680 1005 1679 1003 1674 1002 1675 1001 1675 1000 1675 
998 1674 997 1673 995 1672 993 1670 992 1668 991 1666 991 1664 992 1661 994 1660 997 1660 999 1662 1000 1663 42 _pl _cp 994 1664 _m
_sp 994 1664 995 1662 996 1661 998 1662 1000 1665 1001 1666 1001 1667 1002 1670 1002 1672 1002 1673 1001 1674 1000 1674 999 1673 997 1672 996 1671 
995 1669 995 1668 994 1666 994 1664 994 1664 20 _pl _cp 
0 g _f _s _s 
0 g 1007 1674 _m
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1010 1655 1010 1655 1009 1656 1009 1656 1009 1656 1008 1656 1008 1656 1007 1656 1007 1655 1007 1654 1008 1653 1009 1654 1010 1654 1012 1656 1014 1658 
1016 1661 1017 1662 1018 1664 1019 1666 1020 1669 1021 1670 1021 1672 1021 1673 1021 1674 1019 1675 1019 1675 1018 1674 1018 1673 1019 1673 1020 1672 
1020 1671 1020 1671 1020 1670 1020 1669 1019 1668 1018 1667 1017 1665 1017 1665 1017 1664 1016 1663 1016 1663 1016 1664 1016 1664 1015 1666 1015 1668 
1015 1670 1014 1672 1013 1674 1012 1675 64 _pl _cp 
0 g _f _s _s 
0 g 1116 1706 _m
_sp 1116 1706 1110 1682 1109 1680 1108 1678 1107 1677 1106 1677 1106 1677 1105 1676 1115 1676 1116 1677 1114 1677 1113 1678 1112 1679 1112 1680 1112 1681 
1113 1681 1113 1683 1118 1702 1121 1676 1122 1676 1140 1703 1134 1682 1133 1680 1132 1678 1131 1677 1130 1677 1130 1677 1130 1676 1142 1676 1142 1677 
1141 1677 1140 1678 1139 1680 1139 1680 1139 1681 1140 1683 1145 1703 1146 1705 1146 1707 1147 1708 1148 1708 1149 1708 1149 1709 1141 1709 1125 1685 
1122 1709 1113 1709 1113 1708 1113 1708 1115 1707 50 _pl _cp 
0 g _f _s _s 
0 g 1237 1684 _m
_sp 1237 1684 1237 1703 1237 1705 1238 1707 1239 1708 1240 1708 1241 1708 1241 1709 1229 1709 1229 1708 1229 1708 1230 1708 1231 1707 1232 1705 1232 1703 
1232 1676 1234 1676 1253 1703 1255 1705 1256 1707 1258 1707 1259 1708 1259 1709 1250 1709 1250 1708 1251 1708 1252 1708 1253 1707 1252 1705 1250 1703 
30 _pl _cp 
0 g _f _s _s 
0 g 1287 1671 _m
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1284 1660 1286 1660 1288 1660 1290 1661 1291 1662 1293 1663 1294 1665 1296 1667 1297 1669 1297 1671 1296 1674 1293 1675 1292 1675 1291 1675 1289 1673 
30 _pl _cp 1285 1662 _m
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1285 1666 1285 1664 1285 1663 18 _pl _cp 
0 g _f _s _s 
0 g 1298 1665 _m
_sp 1298 1665 1298 1663 1299 1661 1301 1660 1303 1660 1305 1660 1306 1661 1308 1662 1309 1663 1310 1665 1312 1667 1313 1668 1313 1670 1312 1672 1311 1674 
1309 1675 1307 1675 1306 1675 1304 1674 1303 1673 1301 1672 1300 1670 1299 1669 1298 1667 1298 1665 1298 1665 26 _pl _cp 1301 1664 _m
_sp 1301 1664 1302 1662 1304 1661 1306 1662 1308 1664 1309 1666 1309 1668 1310 1669 1310 1671 1309 1673 1307 1674 1305 1673 1303 1670 1302 1669 1302 1667 
1301 1666 1301 1664 1301 1664 18 _pl _cp 
0 g _f _s _s 
0 g 1324 1664 _m
_sp 1324 1664 1324 1663 1324 1662 1324 1661 1324 1660 1325 1660 1326 1660 1327 1660 1328 1661 1330 1663 1329 1664 1329 1663 1327 1662 1327 1662 1327 1662 
1326 1662 1326 1663 1327 1664 1332 1683 1326 1682 1326 1682 1327 1682 1328 1682 1328 1681 1328 1680 1328 1679 1327 1674 1326 1675 1324 1675 1323 1675 
1321 1674 1320 1673 1318 1672 1317 1670 1315 1668 1314 1666 1314 1664 1315 1661 1318 1660 1320 1660 1323 1662 1323 1663 42 _pl _cp 1317 1664 _m
_sp 1317 1664 1318 1662 1319 1661 1320 1661 1322 1662 1323 1664 1324 1665 1324 1666 1325 1667 1326 1670 1326 1672 1325 1673 1324 1674 1322 1673 1320 1671 
1319 1669 1318 1668 1317 1666 1317 1664 1317 1664 20 _pl _cp 
0 g _f _s _s 
0 g 1331 1674 _m
_sp 1331 1674 1331 1674 1332 1674 1332 1674 1334 1673 1335 1671 1335 1670 1336 1668 1336 1666 1337 1664 1337 1662 1337 1660 1337 1659 1336 1658 1335 1656 
1333 1655 1333 1655 1333 1656 1333 1656 1332 1656 1332 1656 1331 1656 1331 1656 1330 1655 1331 1654 1332 1653 1333 1654 1334 1654 1336 1656 1338 1658 
1339 1661 1340 1662 1341 1664 1342 1666 1343 1669 1344 1670 1345 1672 1345 1673 1344 1674 1343 1675 1342 1675 1342 1674 1342 1673 1342 1673 1343 1672 
1343 1671 1343 1671 1343 1670 1343 1669 1342 1668 1342 1667 1341 1665 1341 1665 1340 1664 1340 1663 1339 1663 1339 1664 1339 1664 1339 1666 1338 1668 
1338 1670 1337 1672 1337 1674 1336 1675 64 _pl _cp 
0 g _f _s _s 
0 g 1529 1684 _m
_sp 1529 1684 1529 1703 1529 1707 1531 1708 1532 1708 1533 1709 1521 1709 1520 1708 1521 1708 1523 1707 1523 1703 1524 1676 1525 1676 1545 1703 1547 1705 
1548 1707 1549 1707 1550 1708 1551 1709 1542 1709 1542 1708 1543 1708 1544 1708 1544 1707 1544 1705 1542 1703 26 _pl _cp 
0 g _f _s _s 
0 g 1578 1671 _m
_sp 1578 1671 1582 1683 1576 1682 1576 1682 1577 1682 1578 1682 1578 1681 1578 1680 1578 1679 1573 1663 1573 1662 1573 1662 1573 1662 1573 1661 1573 1661 
1575 1660 1577 1660 1579 1660 1581 1661 1583 1662 1585 1663 1586 1665 1587 1667 1588 1669 1588 1671 1587 1674 1584 1675 1584 1675 1583 1675 1582 1674 
1581 1673 1579 1672 32 _pl _cp 1576 1662 _m
_sp 1576 1662 1577 1661 1578 1661 1580 1661 1582 1663 1583 1665 1584 1667 1585 1669 1585 1671 1584 1672 1583 1673 1582 1673 1580 1672 1579 1670 1578 1668 
1577 1666 1577 1664 1576 1663 18 _pl _cp 
0 g _f _s _s 
0 g 1590 1665 _m
_sp 1590 1665 1590 1663 1591 1661 1593 1660 1595 1660 1597 1660 1598 1661 1600 1662 1601 1663 1602 1665 1603 1667 1604 1668 1604 1670 1604 1672 1603 1674 
1601 1675 1599 1675 1598 1675 1596 1674 1595 1673 1593 1672 1592 1670 1591 1669 1590 1667 1590 1665 1590 1665 26 _pl _cp 1593 1664 _m
_sp 1593 1664 1594 1662 1595 1661 1597 1662 1599 1664 1600 1666 1600 1668 1601 1669 1601 1671 1600 1673 1599 1674 1598 1674 1596 1673 1595 1672 1594 1670 
1593 1669 1593 1667 1593 1666 1593 1664 1593 1664 20 _pl _cp 
0 g _f _s _s 
0 g 1615 1664 _m
_sp 1615 1664 1615 1663 1615 1662 1615 1661 1616 1660 1616 1660 1617 1660 1619 1660 1620 1661 1622 1663 1621 1664 1620 1663 1619 1662 1618 1662 1618 1662 
1618 1662 1618 1663 1618 1664 1623 1683 1618 1682 1618 1682 1619 1682 1620 1682 1620 1681 1620 1680 1620 1679 1618 1674 1617 1675 1616 1675 1615 1675 
1613 1674 1612 1673 1610 1672 1608 1670 1607 1668 1606 1666 1606 1664 1607 1661 1609 1660 1612 1660 1614 1662 1615 1663 42 _pl _cp 1609 1664 _m
_sp 1609 1664 1610 1662 1611 1661 1613 1662 1615 1665 1616 1666 1616 1667 1617 1670 1617 1672 1617 1673 1616 1674 1615 1674 1614 1673 1612 1672 1611 1671 
1610 1669 1610 1668 1609 1666 1609 1664 1609 1664 20 _pl _cp 
0 g _f _s _s 
0 g 1622 1674 _m
_sp 1622 1674 1623 1674 1623 1674 1624 1674 1625 1673 1626 1671 1627 1670 1627 1668 1628 1666 1628 1664 1629 1662 1629 1660 1628 1659 1627 1658 1626 1656 
1625 1655 1625 1655 1624 1656 1624 1656 1624 1656 1623 1656 1623 1656 1622 1656 1622 1655 1622 1654 1623 1653 1624 1654 1625 1654 1627 1656 1629 1658 
1631 1661 1632 1662 1633 1664 1634 1666 1635 1669 1636 1670 1636 1672 1636 1673 1636 1674 1634 1675 1634 1675 1633 1674 1633 1673 1634 1673 1635 1672 
1635 1671 1635 1671 1635 1670 1635 1669 1634 1668 1633 1667 1632 1665 1632 1665 1632 1664 1631 1663 1631 1663 1631 1664 1631 1664 1630 1666 1630 1668 
1630 1670 1629 1672 1628 1674 1627 1675 64 _pl _cp 
0 g _f _s _s 
0 g 1070 1695 _m
_sp 1070 1695 1051 1695 1051 1694 1070 1694 4 _pl _cp 1070 1688 _m
_sp 1070 1688 1051 1688 1051 1686 1070 1686 4 _pl _cp 
0 g _f _s _s 
0 g 1383 1700 _m
_sp 1383 1700 1383 1692 1375 1692 1375 1690 1383 1690 1383 1681 1385 1681 1385 1690 1394 1690 1394 1692 1385 1692 1385 1700 12 _pl _cp 
0 g _f _s _s 
0 g 1470 1696 _m
_sp 1470 1696 1479 1687 1470 1677 1471 1676 1481 1686 1490 1676 1491 1678 1482 1687 1491 1696 1490 1698 1481 1688 1471 1697 12 _pl _cp 
0 g _f _s _s 
0 g 1242 1717 _m
_sp 1242 1717 1243 1715 1245 1714 1247 1715 1248 1717 1247 1719 1245 1720 1243 1719 8 _pl _cp 
0 g _f _s _s 
0 g 1437 1689 _m
_sp 1437 1689 1437 1684 1437 1681 1436 1680 1435 1678 1433 1678 1431 1679 1430 1680 1429 1683 1429 1687 1429 1690 1430 1693 1432 1695 1434 1697 1433 1699 
1429 1697 1426 1694 1425 1691 1424 1687 1425 1683 1427 1679 1429 1677 1433 1676 1435 1676 1436 1677 1438 1678 1439 1679 1440 1678 1441 1677 1443 1676 
1445 1676 1448 1677 1451 1679 1453 1683 1454 1687 1453 1691 1452 1694 1449 1697 1445 1699 1444 1697 1446 1696 1447 1694 1448 1692 1448 1691 1449 1689 
1449 1687 1449 1683 1448 1681 1446 1679 1445 1678 1443 1678 1442 1680 1441 1681 1441 1684 1441 1689 55 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 6759 _m
/Times-BoldR 600 _ff
(\(6.29\))_S /Times-RomanR 600 _ff
2400 5857 _m
(Since)_S 67 _t
(matrix)_S 67 _t
(multiplication)_S 67 _t
(is)_S 67 _t
(associative)_S 67 _t
(but)_S 67 _t
(not)_S 67 _t
(commutative,)_S 67 _t
(both)_S 67 _t
(sides)_S 1500 5508 _m
(of)_S 67 _t
(matrix)_S 67 _t
(Equation)_S 67 _t
(\(6.29\))_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(multiplied)_S 67 _t
(by)_S 67 _t
(a)_S 67 _t
(single)_S 67 _t
(matrix)_S 67 _t
(as)_S 67 _t
(long)_S 67 _t
(as)_S 67 _t
(order)_S 67 _t
(of)_S 1500 5159 _m
(multiplication)_S 67 _t
(is)_S 67 _t
(carefully)_S 67 _t
(preserved.)_S 134 _t
(In)_S 67 _t
(this)_S 67 _t
(case)_S 67 _t
(both)_S 67 _t
(sides)_S 67 _t
(of)_S 67 _t
(Equation)_S 67 _t
(\(6.29\))_S 67 _t
(are)_S 1500 4809 _m
(multiplied)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(mass)_S 67 _t
(matrix)_S 67 _t
(inverse)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(M)_S /Times-RomanR 600 _ff
(])_S /Times-BoldR 360 _ff
4980 4891 _m
(-1)_S 5080 4891 _m
/Times-RomanR 600 _ff
5080 4809 _m
(.)_S 134 _t
(Transposing)_S 67 _t
(the)_S 67 _t
(result)_S 67 _t
(yields)_S 1500 4459 _m
(Equation)_S 67 _t
(\(6.30\):)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 86 1699 425 952 _cw 
_s 884 967 _m
_sp 884 967 884 1027 892 1027 892 1026 885 1026 885 969 892 969 892 967 8 _pl _cp 
0 g _f _s _s 
0 g 943 967 _m
_sp 943 967 943 1027 935 1027 935 1026 941 1026 941 969 935 969 935 967 8 _pl _cp 
0 g _f _s _s 
0 g 1089 968 _m
_sp 1089 968 1089 1016 1097 1016 1097 1015 1091 1015 1091 969 1097 969 1097 968 8 _pl _cp 
0 g _f _s _s 
0 g 1160 968 _m
_sp 1160 968 1160 1016 1152 1016 1152 1015 1158 1015 1158 969 1152 969 1152 968 8 _pl _cp 
0 g _f _s _s 
0 g 1245 968 _m
_sp 1245 968 1245 1016 1253 1016 1253 1015 1247 1015 1247 969 1253 969 1253 968 8 _pl _cp 
0 g _f _s _s 
0 g 1304 968 _m
_sp 1304 968 1304 1016 1296 1016 1296 1015 1303 1015 1303 969 1296 969 1296 968 8 _pl _cp 
0 g _f _s _s 
0 g 1537 968 _m
_sp 1537 968 1537 1016 1545 1016 1545 1015 1538 1015 1538 969 1545 969 1545 968 8 _pl _cp 
0 g _f _s _s 
0 g 1596 968 _m
_sp 1596 968 1596 1016 1588 1016 1588 1015 1594 1015 1594 969 1588 969 1588 968 8 _pl _cp 
0 g _f _s _s 
0 g 911 1022 _m
_sp 911 1022 912 1020 913 1019 915 1020 916 1022 915 1024 913 1025 912 1024 8 _pl _cp 
0 g _f _s _s 
0 g 906 989 _m
_sp 906 989 906 1008 906 1012 908 1013 909 1013 910 1014 898 1014 897 1013 898 1013 900 1012 900 1008 901 981 902 981 922 1008 924 1010 
925 1012 926 1012 927 1013 928 1014 919 1014 919 1013 920 1013 921 1013 921 1012 921 1010 919 1008 26 _pl _cp 
0 g _f _s _s 
0 g 955 976 _m
_sp 955 976 959 988 953 987 953 987 954 987 955 987 955 986 955 985 955 984 950 968 950 967 950 967 950 967 950 966 950 966 
952 965 954 965 956 965 958 966 960 967 962 968 963 970 964 972 965 974 965 976 964 979 961 980 961 980 960 980 959 979 
958 978 956 977 32 _pl _cp 953 967 _m
_sp 953 967 954 966 955 966 957 966 959 968 960 970 961 972 962 974 962 976 961 977 960 978 959 978 957 977 956 975 955 973 
954 971 954 969 953 968 18 _pl _cp 
0 g _f _s _s 
0 g 967 970 _m
_sp 967 970 967 968 968 966 970 965 972 965 974 965 975 966 977 967 978 968 979 970 980 972 981 973 981 975 981 977 980 979 
978 980 976 980 975 980 973 979 972 978 970 977 969 975 968 974 967 972 967 970 967 970 26 _pl _cp 970 969 _m
_sp 970 969 971 967 972 966 974 967 976 969 977 971 977 973 978 974 978 976 977 978 976 979 975 979 973 978 972 977 971 975 
970 974 970 972 970 971 970 969 970 969 20 _pl _cp 
0 g _f _s _s 
0 g 992 969 _m
_sp 992 969 992 968 992 967 992 966 993 965 993 965 994 965 996 965 997 966 999 968 998 969 997 968 996 967 995 967 995 967 
995 967 995 968 995 969 1000 988 995 987 995 987 996 987 997 987 997 986 997 985 997 984 995 979 994 980 993 980 992 980 
990 979 989 978 987 977 985 975 984 973 983 971 983 969 984 966 986 965 989 965 991 967 992 968 42 _pl _cp 986 969 _m
_sp 986 969 987 967 988 966 990 967 992 970 993 971 993 972 994 975 994 977 994 978 993 979 992 979 991 978 989 977 988 976 
987 974 987 973 986 971 986 969 986 969 20 _pl _cp 
0 g _f _s _s 
0 g 999 979 _m
_sp 999 979 1000 979 1000 979 1001 979 1002 978 1003 976 1004 975 1004 973 1005 971 1005 969 1006 967 1006 965 1005 964 1004 963 1003 961 
1002 960 1002 960 1001 961 1001 961 1001 961 1000 961 1000 961 999 961 999 960 999 959 1000 958 1001 959 1002 959 1004 961 1006 963 
1008 966 1009 967 1010 969 1011 971 1012 974 1013 975 1013 977 1013 978 1013 979 1011 980 1011 980 1010 979 1010 978 1011 978 1012 977 
1012 976 1012 976 1012 975 1012 974 1011 973 1010 972 1009 970 1009 970 1009 969 1008 968 1008 968 1008 969 1008 969 1007 971 1007 973 
1007 975 1006 977 1005 979 1004 980 64 _pl _cp 
0 g _f _s _s 
0 g 1108 1011 _m
_sp 1108 1011 1102 987 1101 985 1100 983 1099 982 1098 982 1098 982 1097 981 1107 981 1108 982 1106 982 1105 983 1104 984 1104 985 1104 986 
1105 986 1105 988 1110 1007 1113 981 1114 981 1132 1008 1126 987 1125 985 1124 983 1123 982 1122 982 1122 982 1122 981 1134 981 1134 982 
1133 982 1132 983 1131 985 1131 985 1131 986 1132 988 1137 1008 1138 1010 1138 1012 1139 1013 1140 1013 1141 1013 1141 1014 1133 1014 1117 990 
1114 1014 1105 1014 1105 1013 1105 1013 1107 1012 50 _pl _cp 
0 g _f _s _s 
0 g 1286 1014 _m
_sp 1286 1014 1262 1014 1261 1013 1263 1013 1264 1012 1265 1011 1265 1010 1265 1010 1264 1008 1259 987 1258 985 1257 983 1256 982 1255 982 1254 982 
1254 981 1267 981 1267 982 1265 982 1264 983 1263 984 1263 985 1263 986 1264 987 1264 987 1267 998 1270 998 1272 998 1274 997 1275 996 
1275 994 1275 994 1275 994 1275 993 1275 992 1276 992 1279 1004 1278 1004 1277 1002 1275 1001 1274 1000 1271 1000 1267 1000 1270 1012 1276 1012 
1280 1012 1282 1011 1284 1010 1284 1008 1284 1008 1284 1008 1284 1007 1284 1006 1285 1006 54 _pl _cp 
0 g _f _s _s 
0 g 1317 976 _m
_sp 1317 976 1320 988 1315 987 1315 987 1316 987 1317 987 1317 986 1317 985 1317 984 1312 968 1312 967 1312 967 1312 967 1312 966 1312 966 
1314 965 1316 965 1318 965 1320 966 1321 967 1323 968 1325 970 1326 972 1327 974 1327 976 1326 979 1323 980 1322 980 1321 980 1319 978 
30 _pl _cp 1315 967 _m
_sp 1315 967 1315 966 1317 966 1319 966 1320 968 1322 970 1323 972 1324 974 1324 976 1323 977 1322 978 1321 978 1319 977 1318 975 1316 973 
1315 971 1315 969 1315 968 18 _pl _cp 
0 g _f _s _s 
0 g 1328 970 _m
_sp 1328 970 1328 968 1329 966 1331 965 1333 965 1335 965 1337 966 1338 967 1340 968 1341 970 1342 972 1343 973 1343 975 1343 977 1342 979 
1340 980 1338 980 1336 980 1334 979 1333 978 1331 977 1330 975 1329 974 1328 972 1328 970 1328 970 26 _pl _cp 1331 969 _m
_sp 1331 969 1332 967 1334 966 1336 967 1338 969 1339 971 1339 973 1340 974 1340 976 1339 978 1337 979 1335 978 1333 975 1332 974 1332 972 
1331 971 1331 969 1331 969 18 _pl _cp 
0 g _f _s _s 
0 g 1354 969 _m
_sp 1354 969 1354 968 1354 967 1354 966 1354 965 1355 965 1356 965 1358 965 1359 966 1360 968 1360 969 1359 968 1358 967 1357 967 1357 967 
1357 967 1357 968 1357 969 1362 988 1357 987 1356 987 1358 987 1359 987 1359 986 1359 985 1358 984 1357 979 1356 980 1354 980 1353 980 
1351 979 1350 978 1348 977 1347 975 1345 973 1344 971 1344 969 1345 966 1348 965 1351 965 1353 967 1354 968 42 _pl _cp 1347 969 _m
_sp 1347 969 1348 967 1350 966 1352 967 1354 970 1355 971 1355 972 1356 975 1356 977 1355 978 1354 979 1352 978 1350 976 1349 974 1348 973 
1347 971 1347 969 1347 969 18 _pl _cp 
0 g _f _s _s 
0 g 1361 979 _m
_sp 1361 979 1361 979 1362 979 1363 979 1364 978 1365 976 1366 975 1366 973 1366 971 1367 969 1367 967 1368 965 1367 964 1366 963 1365 961 
1363 960 1363 960 1363 961 1363 961 1362 961 1362 961 1361 961 1361 961 1360 960 1361 959 1362 958 1363 959 1364 959 1366 961 1368 963 
1369 966 1371 967 1372 969 1373 971 1374 974 1374 975 1375 977 1375 978 1374 979 1373 980 1372 980 1372 979 1372 978 1373 978 1374 977 
1374 976 1374 976 1374 975 1373 974 1373 973 1372 972 1371 970 1371 970 1370 969 1370 968 1370 968 1370 969 1370 969 1369 971 1369 973 
1368 975 1368 977 1367 979 1366 980 64 _pl _cp 
0 g _f _s _s 
0 g 1559 989 _m
_sp 1559 989 1559 1008 1559 1010 1559 1012 1560 1013 1562 1013 1563 1013 1563 1014 1551 1014 1551 1013 1551 1013 1552 1013 1553 1012 1554 1010 1554 1008 
1554 981 1555 981 1575 1008 1577 1010 1578 1012 1580 1012 1581 1013 1581 1014 1572 1014 1572 1013 1573 1013 1574 1013 1574 1012 1574 1010 1572 1008 
30 _pl _cp 
0 g _f _s _s 
0 g 1609 976 _m
_sp 1609 976 1612 988 1606 987 1606 987 1607 987 1608 987 1608 986 1608 985 1608 984 1604 968 1603 967 1603 967 1603 967 1603 966 1604 966 
1606 965 1608 965 1610 965 1612 966 1613 967 1615 968 1616 970 1617 972 1618 974 1618 976 1617 979 1615 980 1614 980 1613 980 1611 978 
30 _pl _cp 1606 967 _m
_sp 1606 967 1607 966 1608 966 1610 966 1612 968 1613 970 1614 972 1615 974 1615 976 1615 977 1613 978 1612 978 1610 977 1609 975 1608 973 
1607 971 1607 969 1606 968 18 _pl _cp 
0 g _f _s _s 
0 g 1620 970 _m
_sp 1620 970 1620 968 1621 966 1623 965 1625 965 1627 965 1628 966 1630 967 1631 968 1632 970 1633 972 1634 973 1634 975 1634 977 1633 979 
1631 980 1629 980 1628 980 1626 979 1625 978 1623 977 1622 975 1621 974 1620 972 1620 970 1620 970 26 _pl _cp 1623 969 _m
_sp 1623 969 1624 967 1626 966 1628 967 1629 969 1630 971 1631 973 1631 974 1631 976 1630 978 1629 979 1628 979 1627 978 1625 977 1624 975 
1624 974 1624 972 1623 971 1623 969 1623 969 20 _pl _cp 
0 g _f _s _s 
0 g 1646 969 _m
_sp 1646 969 1645 968 1645 967 1645 966 1646 965 1647 965 1648 965 1649 965 1650 966 1652 968 1651 969 1651 968 1649 967 1649 967 1648 967 
1648 967 1648 968 1648 969 1654 988 1648 987 1648 987 1649 987 1650 987 1650 986 1650 985 1650 984 1648 979 1647 980 1646 980 1645 980 
1643 979 1642 978 1640 977 1638 975 1637 973 1636 971 1636 969 1637 966 1640 965 1642 965 1644 967 1645 968 42 _pl _cp 1639 969 _m
_sp 1639 969 1640 967 1641 966 1643 967 1645 970 1646 971 1646 972 1647 975 1648 977 1647 978 1646 979 1645 979 1644 978 1642 977 1641 976 
1640 974 1640 973 1639 971 1639 969 1639 969 20 _pl _cp 
0 g _f _s _s 
0 g 1653 979 _m
_sp 1653 979 1653 979 1654 979 1654 979 1655 978 1656 976 1657 975 1657 973 1658 971 1658 969 1659 967 1659 965 1658 964 1657 963 1656 961 
1655 960 1655 960 1655 961 1654 961 1654 961 1654 961 1653 961 1652 961 1652 960 1652 959 1653 958 1655 959 1656 959 1658 961 1659 963 
1661 966 1662 967 1663 969 1664 971 1665 974 1666 975 1667 977 1667 978 1666 979 1665 980 1664 980 1663 979 1664 978 1664 978 1665 977 
1665 976 1665 976 1665 975 1665 974 1664 973 1664 972 1663 970 1663 970 1662 969 1662 968 1661 968 1661 969 1661 969 1660 971 1660 973 
1660 975 1659 977 1658 979 1658 980 64 _pl _cp 
0 g _f _s _s 
0 g 1062 1000 _m
_sp 1062 1000 1043 1000 1043 999 1062 999 4 _pl _cp 1062 993 _m
_sp 1062 993 1043 993 1043 991 1062 991 4 _pl _cp 
0 g _f _s _s 
0 g 1179 1011 _m
_sp 1179 1011 1167 1011 1167 1010 1179 1010 4 _pl _cp 
0 g _f _s _s 
0 g 1216 998 _m
_sp 1216 998 1217 996 1219 995 1221 996 1222 998 1221 1000 1219 1001 1217 1000 8 _pl _cp 
0 g _f _s _s 
0 g 1424 997 _m
_sp 1424 997 1405 997 1405 995 1424 995 4 _pl _cp 
0 g _f _s _s 
0 g 1500 1001 _m
_sp 1500 1001 1510 992 1500 982 1502 981 1511 991 1520 981 1521 983 1512 992 1522 1001 1520 1003 1511 993 1502 1002 12 _pl _cp 
0 g _f _s _s 
0 g 1185 1020 _m
_sp 1185 1020 1185 1019 1187 1020 1187 1020 1188 1020 1189 1019 1189 1018 1189 1005 1188 1002 1186 1001 1186 1001 1186 1001 1195 1001 1195 1001 1194 1001 
1192 1002 1192 1005 1192 1023 18 _pl _cp 
0 g _f _s _s 
0 g 1467 994 _m
_sp 1467 994 1467 989 1467 986 1466 985 1465 983 1463 983 1462 984 1460 985 1459 988 1459 992 1459 995 1460 998 1462 1000 1464 1002 1463 1004 
1459 1002 1456 999 1455 996 1454 992 1455 988 1457 984 1460 982 1463 981 1465 981 1466 982 1468 983 1469 984 1470 983 1472 982 1473 981 
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1479 992 1479 988 1478 986 1476 984 1475 983 1473 983 1472 985 1471 986 1471 989 1471 994 55 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8017 3975 _m
/Times-BoldR 600 _ff
(\(6.30\))_S /Times-RomanR 600 _ff
2400 3295 _m
(This)_S 67 _t
(form)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equation)_S 67 _t
(is)_S 67 _t
(very)_S 67 _t
(important)_S 67 _t
(from)_S 67 _t
(a)_S 1500 2946 _m
(time-integration)_S 67 _t
(perspective,)_S 67 _t
(since)_S 67 _t
(all)_S 67 _t
(accelerations)_S 67 _t
(are)_S 67 _t
(grouped)_S 67 _t
(together)_S 67 _t
(on)_S 67 _t
(the)_S 1500 2597 _m
(left-hand)_S 67 _t
(side.)_S 134 _t
(All)_S 67 _t
(terms)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(right-hand)_S 67 _t
(sides)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
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(116)_S _ep
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0 13200 10200 _ornt 
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(or)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(determined)_S 67 _t
(during)_S 67 _t
(vehicle)_S 67 _t
(operation)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(virtual)_S 67 _t
(world.)_S 134 _t
(Thus)_S 67 _t
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(of)_S 67 _t
(the)_S 67 _t
(right-hand)_S 67 _t
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(to)_S 67 _t
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(updated)_S 67 _t
(values)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(left-hand)_S 67 _t
(side.)_S 134 _t
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(Minimizing)_S 67 _t
(errors)_S 67 _t
(during)_S 67 _t
(the)_S 67 _t
(integration)_S 67 _t
(time)_S 67 _t
(step)_S 67 _t
(is)_S 67 _t
(essential)_S 67 _t
(for)_S 67 _t
(accurate)_S 1500 10808 _m
(real-time)_S 67 _t
(simulation)_S 67 _t
(of)_S 67 _t
(hydrodynamics)_S 67 _t
(models.)_S 134 _t
(This)_S 67 _t
(is)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(sensitivity)_S 67 _t
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(the)_S 1500 10459 _m
(hydrodynamics)_S 67 _t
(model)_S 67 _t
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(small)_S 67 _t
(perturbations,)_S 67 _t
(as)_S 67 _t
(well)_S 67 _t
(as)_S 67 _t
(the)_S 67 _t
(high)_S 67 _t
(degree)_S 67 _t
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(cross-coupling)_S 67 _t
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(forces)_S 67 _t
(acting)_S 67 _t
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(the)_S 67 _t
(three)_S 67 _t
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(body)_S 67 _t
(axes)_S 67 _t
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(an)_S 67 _t
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(vehicle.)_S 134 _t
(If)_S 67 _t
(errors)_S 67 _t
(in)_S 67 _t
(determining)_S 67 _t
(body)_S 67 _t
(accelerations)_S 67 _t
(are)_S 67 _t
(minimized,)_S 67 _t
(then)_S 67 _t
(integration)_S 67 _t
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(accelerations)_S 67 _t
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(subsequent)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(transformations)_S 67 _t
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(velocities,)_S 1500 9063 _m
(positions)_S 67 _t
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(orientations)_S 67 _t
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(accumulated)_S 67 _t
(errors)_S 67 _t
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(velocity)_S 67 _t
(and)_S 67 _t
(posture)_S 67 _t
(estimation.)_S 2400 8365 _m
(The)_S 67 _t
(local)_S 67 _t
(forces)_S 67 _t
(acting)_S 67 _t
(on)_S 67 _t
(an)_S 67 _t
(autonomous)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
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(due)_S 67 _t
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(onboard)_S 67 _t
(effectors)_S 67 _t
(such)_S 67 _t
(as)_S 67 _t
(propellers,)_S 67 _t
(thrusters,)_S 67 _t
(planes)_S 67 _t
(and)_S 67 _t
(rudders.)_S 134 _t
(External)_S 67 _t
(ocean)_S 1500 7667 _m
(current)_S 67 _t
(forces)_S 67 _t
(are)_S 67 _t
(assumed)_S 67 _t
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(vary)_S 67 _t
(slowly)_S 67 _t
(with)_S 67 _t
(respect)_S 67 _t
(to)_S 67 _t
(vehicle)_S 67 _t
(time)_S 67 _t
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(vehicle)_S 67 _t
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(having)_S 67 _t
(no)_S 67 _t
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(on)_S 67 _t
(the)_S 67 _t
(interactions)_S 67 _t
(between)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
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(the)_S 67 _t
(immediately)_S 67 _t
(adjacent)_S 67 _t
(water)_S 67 _t
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(Ocean)_S 67 _t
(current)_S 67 _t
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(a)_S 67 _t
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(calculating)_S 67 _t
(the)_S 67 _t
(effects)_S 67 _t
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(accelerations)_S 67 _t
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(velocities,)_S 67 _t
(and)_S 67 _t
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(from)_S 67 _t
(a)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(system)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
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(Thus)_S 67 _t
(all)_S 67 _t
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(completely)_S 67 _t
(determined)_S 67 _t
(or)_S 67 _t
(estimated)_S 67 _t
(in)_S 67 _t
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(time)_S 67 _t
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(vehicle)_S 67 _t
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(constant-ballast)_S 67 _t
(vehicles,)_S 67 _t
(all)_S 67 _t
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(the)_S 67 _t
(body)_S 67 _t
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(matrix)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(M)_S /Times-RomanR 600 _ff
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(corresponding)_S 67 _t
(inverse)_S 67 _t
([)_S /Times-BoldItalicR 600 _ff
(M)_S /Times-RomanR 600 _ff
(])_S /Times-RomanR 360 _ff
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(-1)_S 3767 4954 _m
/Times-RomanR 600 _ff
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67 _t
(can)_S 67 _t
(be)_S 67 _t
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(empirically)_S 67 _t
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(prior)_S 67 _t
(testing)_S 67 _t
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/Times-BoldR 600 _ff
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(and)_S 67 _t
(Postures)_S /Times-RomanR 600 _ff
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(matrices)_S 67 _t
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(described)_S 67 _t
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(estimation)_S 67 _t
(of)_S 67 _t
(time)_S 67 _t
(rates)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
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(velocities.)_S 134 _t
(The)_S 67 _t
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(velocity)_S 67 _t
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(matrix)_S 67 _t
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(velocities,)_S 67 _t
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(integration)_S 67 _t
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(body)_S 67 _t
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/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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(Integration)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(new)_S 67 _t
(body)_S 67 _t
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_sp 798 2940 798 2899 809 2899 809 2900 806 2900 803 2901 803 2904 803 2934 803 2936 803 2938 806 2939 809 2939 809 2940 13 _pl _cp 
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0 g 864 2899 _m
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0 g 1245 2940 _m
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30 _pl _cp 
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0 g 875 2902 _m
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872 2891 874 2891 876 2891 878 2892 879 2893 881 2894 883 2896 884 2898 885 2900 885 2902 884 2905 881 2906 880 2906 879 2906 877 2904 
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_sp 873 2893 873 2892 875 2892 877 2892 878 2894 880 2896 881 2898 882 2900 882 2902 881 2903 880 2904 879 2904 877 2903 876 2901 874 2899 
873 2897 873 2895 873 2894 18 _pl _cp 
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_sp 886 2896 886 2894 887 2892 889 2891 891 2891 893 2891 895 2892 896 2893 898 2894 899 2896 900 2898 901 2899 901 2901 901 2903 900 2905 
898 2906 896 2906 894 2906 892 2905 891 2904 889 2903 888 2901 887 2900 886 2898 886 2896 886 2896 26 _pl _cp 889 2895 _m
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889 2897 889 2895 889 2895 18 _pl _cp 
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909 2905 908 2904 906 2903 905 2901 903 2899 902 2897 902 2895 903 2892 906 2891 909 2891 911 2893 912 2894 42 _pl _cp 905 2895 _m
_sp 905 2895 906 2893 908 2892 910 2893 912 2896 913 2897 913 2898 914 2901 914 2903 913 2904 912 2905 910 2904 908 2902 907 2900 906 2899 
905 2897 905 2895 905 2895 18 _pl _cp 
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1174 2959 1172 2956 1171 2951 1170 2947 1170 2947 20 _pl _cp 1173 2944 _m
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1176 2955 1174 2952 1173 2948 1173 2945 1173 2945 20 _pl _cp 
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_sp 1230 2953 1228 2944 1228 2942 1227 2941 1228 2940 1229 2939 1231 2940 1232 2940 1233 2942 1234 2943 1234 2944 1232 2942 1231 2941 1230 2941 1230 2942 
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1166 2894 1164 2891 1163 2886 1162 2882 1162 2882 20 _pl _cp 1165 2880 _m
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1167 2891 1166 2887 1165 2884 1165 2880 1165 2880 20 _pl _cp 
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30 _pl _cp 
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0 g 1323 2902 _m
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30 _pl _cp 1320 2893 _m
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1321 2897 1321 2895 1320 2894 18 _pl _cp 
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0 g 1334 2896 _m
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1338 2900 1338 2898 1337 2897 1337 2895 1337 2895 20 _pl _cp 
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1377 2062 1379 2062 1398 2089 1400 2091 1401 2093 1403 2094 1404 2094 1404 2096 1395 2096 1395 2094 1396 2094 1397 2094 1398 2093 1397 2092 1395 2089 
30 _pl _cp 
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1445 2060 1446 2059 1447 2059 1447 2058 1447 2057 1446 2057 1445 2055 1444 2053 1442 2051 1442 2050 1440 2061 1440 2062 42 _pl _cp 
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1461 2062 1459 2062 1458 2062 1456 2061 1455 2060 1453 2059 1452 2057 1451 2056 1450 2054 1450 2052 1450 2052 26 _pl _cp 1453 2050 _m
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1453 2055 1453 2054 1453 2052 1453 2051 1453 2051 20 _pl _cp 
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1478 2061 1477 2062 1476 2061 1474 2060 1473 2059 1472 2057 1472 2057 1471 2056 1473 2062 1468 2061 1467 2060 1469 2060 1470 2060 1470 2060 1470 2059 
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1500 2049 1500 2050 1500 2051 1506 2070 1500 2069 1500 2068 1501 2068 1502 2068 1502 2067 1502 2067 1502 2066 1500 2060 1499 2062 1498 2062 1497 2062 
1495 2061 1494 2060 1492 2059 1490 2057 1489 2055 1488 2053 1488 2051 1489 2048 1492 2047 1494 2047 1496 2049 1497 2050 42 _pl _cp 1491 2050 _m
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1492 2056 1492 2054 1491 2053 1491 2051 1491 2051 20 _pl _cp 
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1580 2072 1577 2070 1575 2068 1572 2065 1571 2062 1569 2059 1569 2056 1569 2053 1570 2052 1572 2050 1574 2050 1576 2050 1578 2051 1580 2052 1582 2053 
1583 2055 46 _pl _cp 1573 2056 _m
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1599 2054 1599 2055 1600 2057 1604 2070 1608 2070 1608 2072 1604 2072 1606 2078 1605 2078 1602 2076 1601 2074 1599 2073 1596 2072 1596 2070 29 _pl _cp 
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1246 1941 1247 1941 1247 1942 1249 1951 1252 1951 1253 1953 1250 1953 1251 1956 1250 1956 1249 1955 1247 1954 1246 1953 1244 1952 1244 1951 29 _pl _cp 
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1258 1954 1257 1950 1256 1947 1256 1943 1256 1943 20 _pl _cp 
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1313 1941 1313 1941 1313 1942 1316 1951 1319 1951 1319 1953 1316 1953 1317 1956 1317 1956 1315 1955 1314 1954 1313 1953 1311 1952 1311 1951 29 _pl _cp 
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1248 1893 1246 1890 1245 1886 1244 1881 1244 1881 20 _pl _cp 1247 1878 _m
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1250 1889 1248 1886 1247 1882 1247 1879 1247 1879 20 _pl _cp 
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1396 1910 1400 1914 1402 1918 1404 1922 1405 1927 1404 1931 1403 1934 1400 1937 1396 1938 24 _pl _cp 1392 1937 _m
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1381 1908 1384 1907 1386 1907 1389 1908 1391 1910 1393 1912 1395 1915 1396 1918 1398 1921 1399 1925 1399 1929 1398 1932 1397 1935 1395 1936 29 _pl _cp 
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1422 1926 1422 1926 1421 1926 1421 1925 1421 1924 1421 1924 1421 1922 1423 1921 1424 1922 1425 1924 1425 1926 1424 1927 1422 1928 1420 1928 1417 1928 
1415 1927 1412 1926 1410 1924 1408 1922 1407 1919 1406 1916 1406 1913 1407 1910 1408 1907 1410 1906 1413 1905 1416 1905 1418 1906 1420 1908 1422 1911 
45 _pl _cp 
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1433 1923 1431 1921 1429 1918 1428 1915 1428 1912 1429 1909 1430 1907 1432 1906 1435 1905 1437 1905 1438 1906 1440 1907 1442 1908 1443 1909 1445 1910 
1444 1911 1442 1909 1440 1908 1438 1908 1437 1908 1435 1908 1434 1909 1433 1911 1432 1912 1433 1914 40 _pl _cp 1433 1916 _m
_sp 1433 1916 1436 1917 1438 1918 1440 1919 1442 1921 1443 1923 1443 1925 1443 1926 1442 1927 1440 1926 1438 1925 1437 1923 1436 1921 1434 1919 14 _pl _cp 
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1467 1911 1467 1913 1468 1915 1470 1921 1472 1926 1472 1928 1468 1928 1468 1926 1466 1928 1464 1928 1462 1928 1461 1927 1459 1926 1457 1925 1454 1923 
1452 1920 1450 1917 1449 1914 1449 1911 1449 1909 1450 1907 1452 1906 1454 1905 1457 1906 1459 1907 1462 1909 41 _pl _cp 1454 1912 _m
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1459 1924 1457 1922 1456 1919 1455 1917 1454 1914 20 _pl _cp 
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1492 1923 1492 1922 1491 1921 1489 1912 1489 1910 1488 1908 1489 1906 1491 1905 1493 1905 1494 1907 1496 1908 1498 1911 1497 1912 1494 1909 1493 1908 
1493 1908 1492 1909 1492 1909 1492 1909 1493 1912 1495 1921 1496 1923 1496 1925 1495 1927 1493 1928 1491 1927 1488 1926 1487 1925 1486 1923 1484 1922 
1483 1919 1483 1919 1482 1918 1485 1928 1477 1927 1477 1926 1478 1926 1479 1926 1480 1925 1480 1924 1479 1922 56 _pl _cp 
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1538 1926 1538 1926 1538 1926 1537 1925 1537 1924 1537 1924 1538 1922 1539 1921 1541 1922 1542 1924 1541 1926 1540 1927 1538 1928 1536 1928 1534 1928 
1531 1927 1529 1926 1527 1924 1525 1922 1523 1919 1522 1916 1522 1913 1523 1910 1524 1907 1527 1906 1530 1905 1532 1905 1535 1906 1537 1908 1539 1911 
45 _pl _cp 
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1549 1910 1549 1911 1554 1928 1546 1927 1546 1926 1547 1926 1548 1926 1548 1925 1548 1924 1548 1922 1545 1912 1545 1911 1545 1910 1545 1909 1545 1908 
1546 1906 1547 1905 1549 1905 1550 1906 1552 1907 1553 1908 1554 1909 1555 1911 1556 1913 1558 1916 1557 1912 1557 1910 1557 1908 1558 1906 1560 1905 
1561 1905 1562 1906 1564 1908 1566 1911 1565 1912 1565 1911 1563 1909 1562 1908 1561 1908 1561 1908 1561 1908 1561 1909 1561 1910 1561 1912 1562 1913 
1562 1915 1563 1917 1563 1918 1563 1919 1565 1925 1566 1928 66 _pl _cp 
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1587 1924 1588 1925 1587 1927 1585 1928 1583 1927 1581 1926 1580 1925 1580 1924 1579 1923 1578 1921 1578 1920 1577 1919 1579 1928 1571 1927 1571 1926 
1573 1926 1574 1926 1574 1925 1574 1924 1574 1922 35 _pl _cp 
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1606 1924 1607 1925 1606 1927 1605 1928 1603 1927 1601 1926 1600 1925 1599 1924 1598 1923 1597 1921 1597 1920 1596 1919 1599 1928 1591 1927 1591 1926 
1592 1926 1593 1926 1594 1925 1594 1924 1593 1922 35 _pl _cp 
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1625 1911 1623 1909 1621 1908 1619 1908 1618 1908 1616 1908 1614 1909 1613 1911 1613 1912 1613 1914 40 _pl _cp 1614 1916 _m
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1648 1909 1648 1909 1648 1912 1651 1921 1652 1923 1652 1925 1651 1927 1649 1928 1646 1927 1644 1926 1643 1925 1642 1923 1640 1922 1639 1919 1638 1919 
1638 1918 1641 1928 1632 1927 1632 1926 1634 1926 1635 1926 1635 1925 1635 1924 1635 1922 54 _pl _cp 
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1684 1913 1684 1914 1682 1916 1680 1919 1678 1921 1677 1922 1676 1923 1676 1924 1677 1926 1679 1927 1681 1927 1683 1926 1684 1924 1685 1921 1686 1921 
1687 1928 1687 1928 1686 1928 1685 1927 1684 1928 1682 1928 1681 1928 1679 1928 1676 1928 1674 1927 1673 1925 1672 1923 1672 1921 1673 1920 1675 1918 
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1734 1895 1734 1893 1734 1893 18 _pl _cp 
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1751 1901 31 _pl _cp 
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1774 1898 1773 1897 1772 1895 1772 1893 1772 1893 20 _pl _cp 
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1864 1910 46 _pl _cp 1855 1911 _m
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1391 1815 1388 1815 1378 1815 1378 1813 1379 1813 1381 1813 1381 1811 1381 1810 1381 1808 1375 1788 1374 1786 1373 1784 1372 1783 1371 1783 1371 1783 
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1470 1805 1462 1803 1462 1802 1463 1802 1464 1802 1465 1801 1465 1800 1464 1798 1462 1789 1461 1788 1461 1786 1461 1785 1461 1784 1462 1782 1463 1781 
1465 1781 1466 1782 1468 1783 1469 1784 1470 1785 1471 1787 1473 1789 1475 1792 1474 1788 1473 1786 1473 1784 1474 1782 1476 1781 1477 1781 1479 1783 
1481 1784 1483 1787 1482 1788 1481 1787 1479 1785 1478 1784 1477 1784 1477 1784 1477 1785 1477 1786 1477 1787 1478 1788 1478 1789 1478 1791 1479 1793 
1479 1794 1479 1796 1481 1801 1482 1804 64 _pl _cp 
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1503 1800 1504 1802 1503 1804 1502 1805 1500 1804 1498 1802 1497 1801 1496 1800 1495 1799 1494 1797 1494 1797 1493 1796 1496 1805 1488 1803 1487 1802 
1489 1802 1490 1802 1491 1801 1491 1800 1490 1798 35 _pl _cp 
0 g _f _s _s 
0 g 1510 1791 _m
_sp 1510 1791 1511 1791 1513 1792 1515 1792 1516 1792 1518 1793 1521 1795 1523 1797 1524 1799 1524 1801 1523 1804 1520 1805 1518 1805 1515 1804 1512 1802 
1510 1800 1508 1797 1506 1794 1505 1791 1505 1788 1506 1785 1507 1783 1509 1782 1512 1781 1514 1781 1516 1782 1517 1783 1519 1784 1521 1785 1522 1787 
1522 1787 1520 1785 1518 1784 1516 1784 1515 1784 1513 1784 1511 1785 1510 1787 1510 1788 1510 1790 40 _pl _cp 1511 1793 _m
_sp 1511 1793 1513 1793 1515 1794 1517 1795 1519 1797 1520 1799 1521 1801 1520 1802 1519 1803 1517 1802 1515 1801 1514 1799 1513 1797 1512 1795 14 _pl _cp 
0 g _f _s _s 
0 g 1558 1770 _m
_sp 1558 1770 1558 1772 1558 1773 1558 1775 1558 1776 1557 1779 1557 1781 1552 1780 1552 1779 1553 1779 1554 1779 1555 1778 1556 1775 1556 1772 1556 1769 
1556 1766 1557 1766 1563 1777 1565 1766 1565 1766 1567 1768 1569 1770 1570 1772 1572 1774 1573 1777 1574 1779 1573 1780 1572 1781 1571 1781 1571 1780 
1571 1779 1571 1778 1572 1778 1572 1777 1572 1776 1572 1776 1571 1774 1569 1772 1568 1770 1567 1769 1565 1780 1565 1781 42 _pl _cp 
0 g _f _s _s 
0 g 1575 1770 _m
_sp 1575 1770 1575 1768 1576 1767 1578 1766 1580 1766 1582 1766 1583 1766 1585 1767 1586 1769 1587 1771 1588 1772 1589 1774 1589 1776 1589 1778 1588 1780 
1586 1781 1584 1781 1583 1781 1581 1780 1580 1779 1578 1778 1577 1776 1576 1775 1575 1773 1575 1771 1575 1771 26 _pl _cp 1578 1769 _m
_sp 1578 1769 1579 1767 1581 1766 1583 1767 1584 1770 1585 1772 1586 1773 1586 1775 1586 1776 1585 1779 1584 1780 1583 1780 1582 1779 1580 1778 1579 1776 
1579 1774 1579 1773 1578 1771 1578 1770 1578 1770 20 _pl _cp 
0 g _f _s _s 
0 g 1592 1766 _m
_sp 1592 1766 1594 1766 1595 1769 1596 1771 1596 1772 1598 1774 1599 1776 1600 1778 1601 1778 1601 1778 1601 1778 1602 1777 1602 1777 1603 1778 1604 1779 
1603 1780 1602 1781 1601 1780 1599 1779 1599 1778 1597 1776 1597 1776 1597 1775 1598 1781 1593 1780 1593 1779 1594 1779 1595 1779 1595 1779 1595 1778 
1595 1777 31 _pl _cp 
0 g _f _s _s 
0 g 1613 1789 _m
_sp 1613 1789 1608 1788 1608 1787 1609 1787 1610 1787 1610 1786 1610 1786 1610 1785 1606 1771 1605 1768 1605 1767 1606 1766 1607 1766 1609 1766 1610 1767 
1611 1768 1612 1770 1611 1770 1611 1770 1610 1768 1608 1767 1608 1767 1608 1768 1608 1768 1608 1769 25 _pl _cp 
0 g _f _s _s 
0 g 1623 1769 _m
_sp 1623 1769 1623 1769 1623 1768 1623 1767 1623 1766 1624 1766 1625 1766 1626 1766 1627 1767 1629 1769 1628 1770 1628 1769 1626 1767 1626 1767 1626 1768 
1625 1768 1625 1769 1626 1770 1631 1789 1625 1788 1625 1787 1626 1787 1627 1787 1627 1786 1627 1786 1627 1785 1626 1779 1625 1781 1623 1781 1622 1781 
1620 1780 1619 1779 1617 1778 1616 1776 1614 1774 1613 1772 1613 1770 1614 1767 1617 1766 1619 1766 1622 1768 1622 1769 42 _pl _cp 1616 1769 _m
_sp 1616 1769 1617 1768 1618 1767 1619 1767 1621 1768 1622 1769 1623 1771 1623 1772 1624 1773 1625 1776 1625 1778 1624 1779 1623 1780 1621 1779 1619 1776 
1618 1775 1617 1773 1616 1772 1616 1770 1616 1770 20 _pl _cp 
0 g _f _s _s 
0 g 1656 1779 _m
_sp 1656 1779 1653 1770 1653 1769 1653 1767 1654 1766 1655 1766 1657 1766 1658 1767 1659 1768 1660 1770 1659 1770 1658 1768 1656 1767 1656 1767 1656 1768 
1656 1768 1656 1769 1656 1770 1659 1779 1662 1779 1662 1780 1659 1780 1660 1784 1659 1784 1658 1783 1657 1781 1656 1781 1654 1780 1653 1779 29 _pl _cp 
0 g _f _s _s 
0 g 1662 1772 _m
_sp 1662 1772 1663 1769 1664 1768 1666 1766 1668 1766 1671 1767 1674 1769 1676 1772 1677 1776 1678 1780 1678 1783 1677 1786 1675 1787 1673 1788 1669 1787 
1666 1785 1664 1782 1662 1778 1662 1773 1662 1773 20 _pl _cp 1665 1771 _m
_sp 1665 1771 1666 1768 1668 1767 1670 1768 1672 1770 1673 1773 1674 1776 1675 1779 1675 1782 1675 1784 1674 1786 1673 1787 1672 1787 1671 1786 1669 1784 
1668 1781 1666 1778 1665 1775 1665 1771 1665 1771 20 _pl _cp 
0 g _f _s _s 
0 g 968 2058 _m
_sp 968 2058 968 2058 964 2054 962 2050 961 2046 961 2043 961 2041 961 2039 961 2036 962 2033 964 2029 968 2025 968 2025 964 2028 961 2031 
959 2034 958 2037 958 2041 958 2045 960 2048 962 2052 965 2055 968 2058 23 _pl _cp 
0 g _f _s _s 
0 g 1046 2058 _m
_sp 1046 2058 1046 2058 1049 2054 1051 2050 1052 2046 1053 2043 1053 2041 1053 2039 1053 2036 1051 2033 1049 2029 1046 2025 1046 2025 1050 2028 1052 2031 
1054 2034 1056 2037 1056 2041 1055 2045 1054 2048 1052 2052 1049 2055 1046 2058 23 _pl _cp 
0 g _f _s _s 
0 g 1234 2113 _m
_sp 1234 2113 1234 2113 1235 2111 1236 2109 1235 2108 1234 2106 1232 2107 1231 2108 1232 2110 1234 2111 1233 2112 1232 2113 1230 2113 1229 2111 1227 2108 
1225 2102 1225 2098 1224 2094 1224 2090 1223 2086 1223 2082 1222 2076 1221 2070 1221 2064 1220 2059 1220 2054 1219 2050 1219 2048 1219 2047 1217 2041 
1215 2037 1213 2035 1211 2035 1209 2035 1208 2036 1207 2037 1206 2039 1207 2041 1209 2042 1210 2041 1211 2039 1210 2038 1209 2037 1210 2037 1212 2037 
1213 2038 1215 2041 1216 2044 1216 2047 1216 2052 1217 2057 1217 2061 1217 2065 1217 2069 1218 2072 1218 2077 1218 2083 1219 2088 1220 2092 1220 2095 
1221 2099 1222 2103 1224 2108 1227 2112 1230 2114 65 _pl _cp 
0 g _f _s _s 
0 g 1234 1956 _m
_sp 1234 1956 1234 1956 1235 1954 1236 1952 1235 1950 1234 1949 1232 1950 1231 1951 1232 1953 1234 1954 1233 1955 1232 1955 1230 1955 1229 1954 1227 1951 
1225 1945 1225 1941 1224 1937 1224 1933 1223 1929 1223 1925 1222 1919 1221 1913 1221 1907 1220 1902 1220 1897 1219 1893 1219 1891 1219 1890 1217 1884 
1215 1880 1213 1878 1211 1878 1209 1878 1208 1878 1207 1879 1206 1881 1207 1884 1209 1884 1210 1883 1211 1882 1210 1881 1209 1880 1210 1879 1212 1879 
1213 1881 1215 1884 1216 1887 1216 1890 1216 1895 1217 1900 1217 1904 1217 1908 1217 1911 1218 1915 1218 1920 1218 1926 1219 1931 1220 1935 1220 1938 
1221 1942 1222 1945 1223 1949 1226 1953 1228 1956 1231 1957 66 _pl _cp 
0 g _f _s _s 
0 g 1652 1789 _m
_sp 1652 1789 1652 1789 1648 1785 1646 1781 1644 1778 1644 1775 1644 1773 1644 1771 1644 1768 1646 1764 1648 1760 1652 1756 1651 1756 1648 1759 1645 1762 
1643 1766 1642 1769 1642 1773 1642 1776 1644 1780 1646 1783 1648 1786 1651 1789 23 _pl _cp 
0 g _f _s _s 
0 g 1679 1789 _m
_sp 1679 1789 1679 1789 1683 1785 1685 1781 1686 1778 1687 1775 1687 1773 1687 1771 1686 1768 1685 1764 1683 1760 1679 1756 1680 1756 1683 1759 1686 1762 
1687 1766 1689 1769 1689 1773 1689 1776 1687 1780 1686 1783 1683 1786 1680 1789 23 _pl _cp 
0 g _f _s _s 
0 g 1005 2050 _m
_sp 1005 2050 1005 2045 999 2045 999 2043 1005 2043 1005 2038 1006 2038 1006 2043 1012 2043 1012 2045 1006 2045 1006 2050 12 _pl _cp 
0 g _f _s _s 
0 g 1105 2070 _m
_sp 1105 2070 1086 2070 1086 2068 1105 2068 4 _pl _cp 1105 2062 _m
_sp 1105 2062 1086 2062 1086 2060 1105 2060 4 _pl _cp 
0 g _f _s _s 
0 g 1279 2111 _m
_sp 1279 2111 1279 2106 1274 2106 1274 2104 1279 2104 1279 2099 1280 2099 1280 2104 1286 2104 1286 2106 1280 2106 1280 2111 12 _pl _cp 
0 g _f _s _s 
0 g 1169 1929 _m
_sp 1169 1929 1169 1921 1160 1921 1160 1919 1169 1919 1169 1911 1171 1911 1171 1919 1179 1919 1179 1921 1171 1921 1171 1929 12 _pl _cp 
0 g _f _s _s 
0 g 1279 1954 _m
_sp 1279 1954 1279 1948 1274 1948 1274 1947 1279 1947 1279 1942 1280 1942 1280 1947 1286 1947 1286 1948 1280 1948 1280 1954 12 _pl _cp 
0 g _f _s _s 
0 g 1169 1806 _m
_sp 1169 1806 1169 1797 1160 1797 1160 1796 1169 1796 1169 1787 1171 1787 1171 1796 1179 1796 1179 1797 1171 1797 1171 1806 12 _pl _cp 
0 g _f _s _s 
0 g 1029 2053 _m
_sp 1029 2053 1027 2055 1025 2056 1023 2057 1021 2056 1020 2054 1020 2053 1021 2052 1022 2050 1024 2049 1021 2048 1019 2047 1018 2044 1017 2041 1018 2038 
1019 2036 1021 2035 1024 2034 1027 2035 1029 2036 1030 2039 1031 2042 1031 2044 1030 2045 1029 2047 1026 2049 1024 2051 1022 2052 1022 2053 1022 2054 
1022 2055 1022 2055 1024 2054 1026 2053 1027 2052 35 _pl _cp 1028 2041 _m
_sp 1028 2041 1028 2039 1027 2037 1025 2036 1024 2035 1023 2036 1021 2037 1020 2039 1020 2041 1020 2044 1021 2046 1023 2047 1024 2047 1026 2047 1027 2046 
1028 2044 16 _pl _cp 
0 g _f _s _s 
0 g 1303 2114 _m
_sp 1303 2114 1301 2116 1299 2117 1297 2118 1295 2117 1294 2115 1294 2114 1295 2113 1297 2111 1298 2110 1295 2109 1294 2108 1292 2105 1292 2102 1293 2099 
1294 2097 1296 2096 1298 2095 1301 2096 1303 2097 1304 2100 1305 2103 1305 2105 1305 2106 1304 2107 1303 2108 1302 2109 1300 2110 1298 2112 1297 2113 
1296 2114 1296 2115 1296 2116 1297 2116 1298 2115 1300 2114 1301 2113 37 _pl _cp 1302 2102 _m
_sp 1302 2102 1302 2100 1301 2098 1300 2097 1298 2096 1297 2097 1296 2098 1295 2100 1295 2102 1295 2105 1296 2107 1297 2108 1298 2108 1300 2108 1301 2107 
1302 2105 16 _pl _cp 
0 g _f _s _s 
0 g 1303 1957 _m
_sp 1303 1957 1301 1959 1299 1960 1297 1961 1295 1960 1294 1958 1294 1957 1295 1956 1297 1954 1298 1953 1295 1952 1294 1951 1292 1948 1292 1945 1293 1942 
1294 1940 1296 1939 1298 1938 1301 1939 1303 1940 1304 1942 1305 1945 1305 1947 1305 1948 1304 1949 1303 1951 1302 1952 1300 1953 1298 1955 1297 1956 
1296 1957 1296 1958 1296 1959 1297 1959 1298 1958 1300 1957 1301 1955 37 _pl _cp 1302 1945 _m
_sp 1302 1945 1302 1943 1301 1941 1300 1940 1298 1939 1297 1940 1296 1941 1295 1943 1295 1945 1295 1948 1296 1950 1297 1951 1298 1951 1300 1951 1301 1950 
1302 1948 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 7763 _m
/Times-BoldR 600 _ff
(\(6.33\))_S /Times-RomanR 600 _ff
1980 6426 _m
/Times-BoldR 600 _ff
(6.)_S 2400 6426 _m
(Deriving)_S 67 _t
(Desired)_S 67 _t
(Form)_S 67 _t
(of)_S 67 _t
(Dynamics)_S 67 _t
(Equations)_S 67 _t
(of)_S 67 _t
(Motion)_S /Times-RomanR 600 _ff
2400 6077 _m
(A)_S 67 _t
(full)_S 67 _t
(set)_S 67 _t
(of)_S 67 _t
(hydrodynamic)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(for)_S 67 _t
(a)_S 67 _t
(submerged)_S 67 _t
(vehicle)_S 1500 5728 _m
(are)_S 67 _t
(not)_S 67 _t
(usually)_S 67 _t
(written)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(form)_S 67 _t
(suggested)_S 67 _t
(by)_S 67 _t
(Equations)_S 67 _t
(\(6.30\),)_S 67 _t
(\(6.31\),)_S 67 _t
(\(6.32\))_S 67 _t
(and)_S 1500 5379 _m
(\(6.33\).)_S 134 _t
(Other)_S 67 _t
(derivations)_S 67 _t
(have)_S 67 _t
(been)_S 67 _t
(presented)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(open)_S 67 _t
(literature)_S 67 _t
(\(Gertler)_S 67 _t
(76\))_S 1500 5030 _m
(\(Smith)_S 67 _t
(79\))_S 67 _t
(\(Feldman)_S 67 _t
(79\))_S 67 _t
(\(Papoulias)_S 67 _t
(89\))_S 67 _t
(\(Watkinson)_S 67 _t
(89\))_S 67 _t
(\(Yuh)_S 67 _t
(90\))_S 67 _t
(\(Humphreys)_S 67 _t
(91\))_S 1500 4681 _m
(\(Baiardi)_S 67 _t
(92\))_S 67 _t
(\(Healey)_S 67 _t
(93\))_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 67 _t
(and)_S 67 _t
(a)_S 67 _t
(variety)_S 67 _t
(of)_S 67 _t
(other)_S 67 _t
(sources,)_S 67 _t
(but)_S 67 _t
(are)_S 67 _t
(structured)_S 1500 4332 _m
(in)_S 67 _t
(such)_S 67 _t
(a)_S 67 _t
(way)_S 67 _t
(that)_S 67 _t
(similar)_S 67 _t
(time-dependent)_S 67 _t
(acceleration-related)_S 67 _t
(terms)_S 67 _t
(are)_S 67 _t
(present)_S 67 _t
(on)_S 1500 3983 _m
(both)_S 67 _t
(sides)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion.)_S 134 _t
(Because)_S 67 _t
(related)_S 67 _t
(body)_S 67 _t
(acceleration)_S 1500 3634 _m
(terms)_S 67 _t
(are)_S 67 _t
(not)_S 67 _t
(grouped)_S 67 _t
(together,)_S 67 _t
(direct)_S 67 _t
(time)_S 67 _t
(integration)_S 67 _t
(of)_S 67 _t
(both)_S 67 _t
(sides)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(equations)_S 1500 3285 _m
(of)_S 67 _t
(motion)_S 67 _t
(is)_S 67 _t
(not)_S 67 _t
(mathematically)_S 67 _t
(valid)_S 67 _t
(in)_S 67 _t
(those)_S 67 _t
(representations.)_S 134 _t
(Furthermore)_S 67 _t
(these)_S 1500 2936 _m
(many)_S 67 _t
(references)_S 67 _t
(are)_S 67 _t
(all)_S 67 _t
(handicapped)_S 67 _t
(by)_S 67 _t
(variations)_S 67 _t
(in)_S 67 _t
(nomenclature)_S 67 _t
(and)_S 67 _t
(even)_S 67 _t
(a)_S 1500 2587 _m
(surprising)_S 67 _t
(variety)_S 67 _t
(of)_S 67 _t
(typographical)_S 67 _t
(errors,)_S 67 _t
(mathematical)_S 67 _t
(errors)_S 67 _t
(or)_S 67 _t
(omissions.)_S 134 _t
(None)_S 67 _t
(of)_S 1500 2238 _m
(these)_S 67 _t
(other)_S 67 _t
(models)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(directly)_S 67 _t
(applied)_S 67 _t
(as)_S 67 _t
(a)_S 67 _t
(valid)_S 67 _t
(real-time)_S 67 _t
(underwater)_S 67 _t
(virtual)_S 4950 1288 _m
(118)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11853 _m
(world)_S 67 _t
(component.)_S 134 _t
/Times-ItalicR 600 _ff
(Therefore)_S 67 _t
(the)_S 67 _t
(primary)_S 67 _t
(intended)_S 67 _t
(contributions)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(hydrodynamic)_S 1500 11501 _m
(model)_S 67 _t
(developed)_S 67 _t
(here)_S 67 _t
(are)_S 67 _t
(clarity,)_S 67 _t
(correctness,)_S 67 _t
(generality,)_S 67 _t
(standardized)_S 67 _t
(nomenclature)_S 1500 11152 _m
(and)_S 67 _t
(suitability)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(simulation)_S /Times-RomanR 600 _ff
(.)_S 2400 10802 _m
(Given)_S 67 _t
(this)_S 67 _t
(broad)_S 67 _t
(outline)_S 67 _t
(showing)_S 67 _t
(how)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 1500 10453 _m
(will)_S 67 _t
(be)_S 67 _t
(utilized,)_S 67 _t
(it)_S 67 _t
(is)_S 67 _t
(time)_S 67 _t
(to)_S 67 _t
(derive)_S 67 _t
(the)_S 67 _t
(desired)_S 67 _t
(forms)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(equations.)_S 67 _t
1500 10104 _m
(We)_S 67 _t
(can)_S 67 _t
(reorganize)_S 67 _t
(all)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(original)_S 67 _t
(\(Healey)_S 67 _t
(93\))_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(to)_S 67 _t
(solely)_S 67 _t
(have)_S 1500 9554 _m
(mass-related,)_S 67 _t
(inertia-related)_S 67 _t
(and)_S 67 _t
4172 9506 _m
4745 9554 _m
(-related)_S 67 _t
(terms)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(left-hand)_S 67 _t
(side.)_S 134 _t
(That)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 86 143 1043 2376 _cw 
_s 1050 2391 _m
_sp 1050 2391 1050 2451 1058 2451 1058 2450 1051 2450 1051 2393 1058 2393 1058 2391 8 _pl _cp 
0 g _f _s _s 
0 g 1109 2391 _m
_sp 1109 2391 1109 2451 1101 2451 1101 2450 1107 2450 1107 2393 1101 2393 1101 2391 8 _pl _cp 
0 g _f _s _s 
0 g 1077 2446 _m
_sp 1077 2446 1078 2444 1080 2443 1081 2444 1082 2446 1081 2448 1080 2449 1078 2448 8 _pl _cp 
0 g _f _s _s 
0 g 1072 2413 _m
_sp 1072 2413 1072 2432 1072 2434 1072 2436 1073 2437 1075 2437 1076 2437 1076 2438 1064 2438 1064 2437 1064 2437 1065 2437 1066 2436 1067 2434 1067 2432 
1067 2405 1068 2405 1088 2432 1090 2434 1091 2436 1093 2436 1094 2437 1094 2438 1085 2438 1085 2437 1086 2437 1087 2437 1087 2436 1087 2434 1085 2432 
30 _pl _cp 
0 g _f _s _s 
0 g 1122 2400 _m
_sp 1122 2400 1125 2412 1119 2411 1119 2411 1120 2411 1121 2411 1121 2410 1121 2409 1121 2408 1117 2392 1116 2391 1116 2391 1116 2391 1116 2390 1117 2390 
1119 2389 1121 2389 1123 2389 1125 2390 1126 2391 1128 2392 1129 2394 1130 2396 1131 2398 1131 2400 1130 2403 1128 2404 1127 2404 1126 2404 1124 2402 
30 _pl _cp 1119 2391 _m
_sp 1119 2391 1120 2390 1121 2390 1123 2390 1125 2392 1126 2394 1127 2396 1128 2398 1128 2400 1128 2401 1126 2402 1125 2402 1123 2401 1122 2399 1121 2397 
1120 2395 1120 2393 1119 2392 18 _pl _cp 
0 g _f _s _s 
0 g 1133 2394 _m
_sp 1133 2394 1133 2392 1134 2390 1136 2389 1138 2389 1140 2389 1141 2390 1143 2391 1144 2392 1145 2394 1146 2396 1147 2397 1147 2399 1147 2401 1146 2403 
1144 2404 1142 2404 1141 2404 1139 2403 1138 2402 1136 2401 1135 2399 1134 2398 1133 2396 1133 2394 1133 2394 26 _pl _cp 1136 2393 _m
_sp 1136 2393 1137 2391 1139 2390 1141 2391 1142 2393 1143 2395 1144 2397 1144 2398 1144 2400 1143 2402 1142 2403 1141 2403 1140 2402 1138 2401 1137 2399 
1137 2398 1137 2396 1136 2395 1136 2393 1136 2393 20 _pl _cp 
0 g _f _s _s 
0 g 1159 2393 _m
_sp 1159 2393 1158 2392 1158 2391 1158 2390 1159 2389 1160 2389 1161 2389 1162 2389 1163 2390 1165 2392 1164 2393 1164 2392 1162 2391 1162 2391 1161 2391 
1161 2391 1161 2392 1161 2393 1167 2412 1161 2411 1161 2411 1162 2411 1163 2411 1163 2410 1163 2409 1163 2408 1161 2403 1160 2404 1159 2404 1158 2404 
1156 2403 1155 2402 1153 2401 1151 2399 1150 2397 1149 2395 1149 2393 1150 2390 1153 2389 1155 2389 1157 2391 1158 2392 42 _pl _cp 1152 2393 _m
_sp 1152 2393 1153 2391 1154 2390 1156 2391 1158 2394 1159 2395 1159 2396 1160 2399 1161 2401 1160 2402 1159 2403 1158 2403 1157 2402 1155 2401 1154 2400 
1153 2398 1153 2397 1152 2395 1152 2393 1152 2393 20 _pl _cp 
0 g _f _s _s 
0 g 1166 2403 _m
_sp 1166 2403 1166 2403 1167 2403 1167 2403 1168 2402 1169 2400 1170 2399 1170 2397 1171 2395 1171 2393 1172 2391 1172 2389 1171 2388 1170 2387 1169 2385 
1168 2384 1168 2384 1168 2385 1167 2385 1167 2385 1167 2385 1166 2385 1165 2385 1165 2384 1165 2383 1166 2382 1168 2383 1169 2383 1171 2385 1172 2387 
1174 2390 1175 2391 1176 2393 1177 2395 1178 2398 1179 2399 1180 2401 1180 2402 1179 2403 1178 2404 1177 2404 1176 2403 1177 2402 1177 2402 1178 2401 
1178 2400 1178 2400 1178 2399 1178 2398 1177 2397 1177 2396 1176 2394 1176 2394 1175 2393 1175 2392 1174 2392 1174 2393 1174 2393 1173 2395 1173 2397 
1173 2399 1172 2401 1171 2403 1171 2404 64 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 1500 9104 _m
(rearrangement)_S 67 _t
(leaves)_S 67 _t
(lift)_S 67 _t
(and)_S 67 _t
(drag,)_S 67 _t
(buoyancy,)_S 67 _t
(weight,)_S 67 _t
(propulsion)_S 67 _t
(thrust,)_S 67 _t
(and)_S 67 _t
(other)_S 1500 8754 _m
(forces)_S 67 _t
(and)_S 67 _t
(moments)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(right-hand)_S 67 _t
(side.)_S 134 _t
(At)_S 67 _t
(any)_S 67 _t
(given)_S 67 _t
(instant)_S 67 _t
/Times-BoldItalicR 600 _ff
(t)_S /Times-BoldItalicR 360 _ff
6987 8709 _m
(0)_S 7047 8709 _m
/Times-RomanR 600 _ff
7047 8754 _m
(:)_S gsave 4 4 scale 16 _sr 
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_sp 1607 1592 1607 1589 1608 1587 1609 1585 1610 1585 1611 1585 1612 1585 1613 1586 1613 1588 1613 1590 1613 1592 1613 1595 1612 1598 1611 1599 1610 1600 
1609 1599 1608 1598 1607 1595 18 _pl _cp 
0 g _f _s _s 
0 g 1617 1587 _m
_sp 1617 1587 1619 1589 1621 1591 1622 1593 1623 1594 1623 1596 1623 1598 1623 1600 1623 1602 1622 1603 1621 1605 1619 1607 1617 1609 1617 1608 1618 1607 
1619 1606 1620 1605 1620 1603 1621 1601 1621 1598 1621 1597 1621 1595 1621 1594 1620 1592 1620 1591 1619 1590 1618 1589 1617 1588 28 _pl _cp 
0 g _f _s _s 
0 g 1959 2051 _m
_sp 1959 2051 1960 2050 1960 2050 1959 2048 1958 2046 1956 2044 1954 2043 1954 2042 1957 2043 1960 2045 1961 2047 1962 2050 1962 2052 1961 2054 1959 2055 
1957 2055 1955 2054 1954 2052 1955 2051 1957 2050 1958 2050 21 _pl _cp 
0 g _f _s _s 
0 g 1930 1962 _m
_sp 1930 1962 1931 1961 1931 1961 1930 1959 1929 1957 1927 1955 1925 1954 1925 1954 1928 1955 1931 1956 1932 1958 1933 1961 1933 1963 1932 1965 1930 1966 
1928 1967 1926 1966 1925 1963 1926 1962 1928 1961 1929 1961 21 _pl _cp 
0 g _f _s _s 
0 g 2019 1625 _m
_sp 2019 1625 2017 1624 2016 1623 2014 1621 2013 1620 2012 1618 2012 1615 2011 1613 2011 1610 2011 1608 2012 1606 2012 1603 2013 1601 2014 1600 2016 1599 
2017 1597 2019 1596 2019 1597 2018 1599 2016 1600 2016 1602 2015 1603 2014 1605 2014 1607 2014 1608 2014 1610 2014 1612 2014 1614 2014 1616 2015 1618 
2016 1620 2016 1621 2018 1623 2019 1624 34 _pl _cp 
0 g _f _s _s 
0 g 2030 1600 _m
_sp 2030 1600 2030 1598 2030 1595 2031 1594 2032 1593 2034 1592 2035 1592 2038 1593 2040 1594 2041 1597 2041 1600 2041 1604 2040 1606 2038 1608 2035 1609 
2033 1608 2031 1606 2030 1604 18 _pl _cp 2032 1600 _m
_sp 2032 1600 2032 1597 2033 1595 2034 1593 2035 1593 2036 1593 2037 1593 2038 1594 2038 1596 2038 1598 2038 1600 2038 1603 2037 1606 2036 1607 2035 1608 
2034 1607 2033 1606 2032 1603 18 _pl _cp 
0 g _f _s _s 
0 g 2043 1596 _m
_sp 2043 1596 2044 1597 2046 1599 2047 1600 2048 1601 2049 1603 2050 1606 2051 1608 2051 1610 2051 1613 2050 1615 2049 1618 2048 1620 2047 1621 2046 1623 
2044 1624 2043 1625 2042 1624 2044 1623 2045 1621 2046 1620 2047 1618 2047 1616 2048 1614 2048 1612 2048 1610 2048 1608 2048 1607 2047 1605 2047 1603 
2046 1602 2045 1600 2044 1599 2042 1597 34 _pl _cp 
0 g _f _s _s 
0 g 673 1792 _m
_sp 673 1792 654 1792 654 1790 673 1790 4 _pl _cp 
0 g _f _s _s 
0 g 996 1853 _m
_sp 996 1853 977 1853 977 1852 996 1852 4 _pl _cp 996 1845 _m
_sp 996 1845 977 1845 977 1844 996 1844 4 _pl _cp 
0 g _f _s _s 
0 g 1270 2066 _m
_sp 1270 2066 1251 2066 1251 2064 1270 2064 4 _pl _cp 
0 g _f _s _s 
0 g 883 2086 _m
_sp 883 2086 884 2084 886 2083 888 2084 889 2086 888 2088 886 2089 884 2088 8 _pl _cp 
0 g _f _s _s 
0 g 883 1997 _m
_sp 883 1997 884 1995 886 1994 888 1995 889 1997 888 1999 886 2000 884 1999 8 _pl _cp 
0 g _f _s _s 
0 g 883 1909 _m
_sp 883 1909 884 1907 886 1906 888 1907 889 1908 888 1910 886 1911 884 1910 8 _pl _cp 
0 g _f _s _s 
0 g 883 1820 _m
_sp 883 1820 884 1818 886 1817 888 1818 889 1820 888 1822 886 1823 884 1822 8 _pl _cp 
0 g _f _s _s 
0 g 883 1731 _m
_sp 883 1731 884 1729 886 1728 888 1729 889 1731 888 1733 886 1734 884 1733 8 _pl _cp 
0 g _f _s _s 
0 g 883 1642 _m
_sp 883 1642 884 1640 886 1639 888 1640 889 1642 888 1644 886 1645 884 1644 8 _pl _cp 
0 g _f _s _s 
0 g 1674 1858 _m
_sp 1674 1858 1674 1849 1665 1849 1665 1848 1674 1848 1674 1839 1676 1839 1676 1848 1684 1848 1684 1849 1676 1849 1676 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1674 1858 _m
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0 g _f _s _s 
0 g 1674 1858 _m
_sp 1674 1858 1674 1849 1666 1849 1666 1848 1674 1848 1674 1839 1676 1839 1676 1848 1685 1848 1685 1849 1676 1849 1676 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1675 1858 _m
_sp 1675 1858 1675 1849 1666 1849 1666 1848 1675 1848 1675 1839 1676 1839 1676 1848 1685 1848 1685 1849 1676 1849 1676 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1675 1858 _m
_sp 1675 1858 1675 1849 1666 1849 1666 1848 1675 1848 1675 1839 1677 1839 1677 1848 1685 1848 1685 1849 1677 1849 1677 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1675 1858 _m
_sp 1675 1858 1675 1849 1667 1849 1667 1848 1675 1848 1675 1839 1677 1839 1677 1848 1686 1848 1686 1849 1677 1849 1677 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1675 1858 _m
_sp 1675 1858 1675 1849 1667 1849 1667 1848 1675 1848 1675 1839 1677 1839 1677 1848 1686 1848 1686 1849 1677 1849 1677 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1676 1858 _m
_sp 1676 1858 1676 1849 1667 1849 1667 1848 1676 1848 1676 1839 1677 1839 1677 1848 1686 1848 1686 1849 1677 1849 1677 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1676 1858 _m
_sp 1676 1858 1676 1849 1667 1849 1667 1848 1676 1848 1676 1839 1678 1839 1678 1848 1686 1848 1686 1849 1678 1849 1678 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1676 1858 _m
_sp 1676 1858 1676 1849 1668 1849 1668 1848 1676 1848 1676 1839 1678 1839 1678 1848 1687 1848 1687 1849 1678 1849 1678 1858 12 _pl _cp 
0 g _f _s _s 
0 g 1676 1858 _m
_sp 1676 1858 1676 1849 1668 1849 1668 1848 1676 1848 1676 1839 1678 1839 1678 1848 1687 1848 1687 1849 1678 1849 1678 1858 12 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 7463 _m
/Times-BoldR 600 _ff
(\(6.34\))_S /Times-RomanR 600 _ff
2400 5725 _m
(Calculating)_S 67 _t
(the)_S 67 _t
(inverse)_S 67 _t
(mass)_S 67 _t
(matrix)_S 67 _t
(and)_S 67 _t
(multiplying)_S 67 _t
(it)_S 67 _t
(against)_S 67 _t
(both)_S 67 _t
(sides)_S 67 _t
(of)_S 1500 5376 _m
(Equation)_S 67 _t
(\(6.34\))_S 67 _t
(leaves)_S 67 _t
(only)_S 67 _t
(body)_S 67 _t
(accelerations)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(left-hand)_S 67 _t
(side.)_S 134 _t
(Further)_S 1500 5027 _m
(classification)_S 67 _t
(of)_S 67 _t
(individual)_S 67 _t
(terms)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(right-hand)_S 67 _t
(side)_S 67 _t
(as)_S 67 _t
(corresponding)_S 67 _t
(to)_S 67 _t
(Coriolis,)_S 1500 4678 _m
(centripetal)_S 67 _t
(and)_S 67 _t
(other)_S 67 _t
(forces)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(found)_S 67 _t
(in)_S 67 _t
(\(Greenwood)_S 67 _t
(88\))_S 67 _t
(\(Healey)_S 67 _t
(92c\).)_S 134 _t
(For)_S 67 _t
(the)_S 1500 4329 _m
(purpose)_S 67 _t
(of)_S 67 _t
(this)_S 67 _t
(derivation)_S 67 _t
(it)_S 67 _t
(is)_S 67 _t
(sufficient)_S 67 _t
(to)_S 67 _t
(group)_S 67 _t
(these)_S 67 _t
(accelerations)_S 67 _t
(together)_S 67 _t
(without)_S 1500 3980 _m
(further)_S 67 _t
(discussion.)_S 134 _t
(Such)_S 67 _t
(an)_S 67 _t
(arrangement)_S 67 _t
(prepares)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 1500 3631 _m
(for)_S 67 _t
(temporal)_S 67 _t
(integration)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(body-fixed)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(as)_S 67 _t
(follows:)_S 4950 1288 _m
(119)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr 
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_sp 823 2565 825 2565 825 2502 832 2502 832 2500 823 2500 6 _pl _cp 
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0 g 874 2897 _m
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0 g 876 2798 _m
_sp 876 2798 874 2798 874 2821 876 2821 4 _pl _cp 
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_sp 876 2779 874 2779 874 2801 876 2801 4 _pl _cp 
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0 g 876 2759 _m
_sp 876 2759 874 2759 874 2781 876 2781 4 _pl _cp 
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_sp 876 2680 874 2680 874 2702 876 2702 4 _pl _cp 
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_sp 1036 2852 1034 2852 1034 2874 1036 2874 4 _pl _cp 
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_sp 1036 2832 1034 2832 1034 2854 1036 2854 4 _pl _cp 
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0 g 1036 2792 _m
_sp 1036 2792 1034 2792 1034 2815 1036 2815 4 _pl _cp 
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_sp 1036 2773 1034 2773 1034 2795 1036 2795 4 _pl _cp 
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0 g 1036 2753 _m
_sp 1036 2753 1034 2753 1034 2775 1036 2775 4 _pl _cp 
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_sp 1036 2733 1034 2733 1034 2755 1036 2755 4 _pl _cp 
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_sp 1036 2713 1034 2713 1034 2736 1036 2736 4 _pl _cp 
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_sp 1036 2694 1034 2694 1034 2716 1036 2716 4 _pl _cp 
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0 g 1036 2674 _m
_sp 1036 2674 1034 2674 1034 2696 1036 2696 4 _pl _cp 
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_sp 1036 2654 1034 2654 1034 2676 1036 2676 4 _pl _cp 
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0 g 1036 2634 _m
_sp 1036 2634 1034 2634 1034 2657 1036 2657 4 _pl _cp 
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_sp 1036 2615 1034 2615 1034 2637 1036 2637 4 _pl _cp 
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_sp 1036 2595 1034 2595 1034 2617 1036 2617 4 _pl _cp 
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_sp 1036 2575 1034 2575 1034 2597 1036 2597 4 _pl _cp 
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_sp 1327 2891 1329 2891 1329 2951 1319 2951 1319 2949 1327 2949 6 _pl _cp 
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0 g 1329 2852 _m
_sp 1329 2852 1327 2852 1327 2874 1329 2874 4 _pl _cp 
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_sp 1329 2832 1327 2832 1327 2854 1329 2854 4 _pl _cp 
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_sp 1329 2773 1327 2773 1327 2795 1329 2795 4 _pl _cp 
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0 g 1329 2595 _m
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_sp 1378 2903 1376 2903 1376 2963 1385 2963 1385 2961 1378 2961 6 _pl _cp 
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_sp 1378 2883 1376 2883 1376 2906 1378 2906 4 _pl _cp 
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_sp 1378 2864 1376 2864 1376 2886 1378 2886 4 _pl _cp 
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_sp 1644 2903 1646 2903 1646 2963 1636 2963 1636 2961 1644 2961 6 _pl _cp 
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1525 2606 1523 2604 1521 2601 1520 2598 1520 2595 1521 2592 1522 2590 1524 2589 1527 2588 1529 2588 1530 2589 1532 2590 1534 2591 1535 2592 1537 2593 
1536 2594 1534 2592 1532 2591 1530 2591 1529 2591 1527 2591 1526 2592 1525 2594 1524 2595 1525 2597 40 _pl _cp 1525 2599 _m
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1557 2596 1556 2597 1554 2599 1552 2602 1551 2604 1550 2605 1549 2606 1549 2607 1550 2609 1552 2610 1554 2610 1556 2609 1557 2607 1558 2604 1559 2604 
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1677 2506 1677 2507 1677 2508 1680 2517 1683 2517 1683 2518 1680 2518 1681 2522 1681 2522 1679 2521 1678 2519 1677 2519 1675 2518 1675 2517 29 _pl _cp 
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899 2515 900 2517 901 2518 903 2519 34 _pl _cp 
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917 2503 915 2502 914 2499 18 _pl _cp 916 2496 _m
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928 2519 926 2520 926 2519 928 2518 929 2517 930 2515 931 2513 931 2511 932 2510 932 2508 932 2506 932 2504 932 2502 931 2501 931 2499 
930 2497 929 2495 928 2494 926 2493 34 _pl _cp 
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1217 2848 1216 2851 1216 2869 18 _pl _cp 
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1670 2499 1672 2498 1673 2499 1671 2500 1670 2501 1669 2503 1668 2505 1667 2507 1667 2508 1667 2510 1667 2512 1667 2514 1667 2516 1667 2517 1668 2519 
1669 2521 1670 2523 1671 2524 1673 2525 34 _pl _cp 
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1686 2509 1685 2508 1683 2505 18 _pl _cp 1685 2502 _m
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1687 2509 1686 2507 1685 2505 18 _pl _cp 
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1699 2503 1698 2501 1697 2500 1695 2499 34 _pl _cp 
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_sp 963 2735 944 2735 944 2733 963 2733 4 _pl _cp 963 2727 _m
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_sp 1520 2685 1501 2685 1501 2683 1520 2683 4 _pl _cp 
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(\(6.35\))_S /Times-RomanR 600 _ff
2400 9408 _m
(The)_S 67 _t
(body)_S 67 _t
(frame)_S 67 _t
(velocity)_S 67 _t
(matrix)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-BoldR 600 _ff
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5346 9363 _m
(body)_S 5579 9363 _m
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67 _t
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(now)_S 67 _t
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(example,)_S 67 _t
(Euler)_S 67 _t
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(\(Hamming)_S 67 _t
(86\))_S 67 _t
(\(Green)_S 67 _t
(91\))_S 67 _t
(\(Press)_S 67 _t
(92\))_S 1500 8709 _m
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1156 2468 1153 2473 1151 2478 1149 2481 1148 2484 1147 2488 1146 2491 1146 2495 1145 2499 1145 2504 1145 2508 1145 2512 1145 2516 28 _pl _cp 
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_sp 837 2480 839 2481 840 2483 841 2484 842 2485 843 2487 844 2489 845 2491 845 2494 845 2497 844 2499 843 2501 842 2503 841 2505 840 2506 
839 2507 837 2508 837 2507 839 2506 840 2505 841 2503 841 2501 842 2499 842 2498 842 2496 842 2494 842 2492 842 2490 842 2489 841 2487 
841 2485 840 2483 839 2482 837 2481 34 _pl _cp 
0 g _f _s _s 
0 g 1060 2760 _m
_sp 1060 2760 1060 2759 1061 2760 1062 2760 1063 2760 1064 2759 1064 2758 1064 2737 1064 2735 1064 2733 1063 2732 1061 2732 1060 2732 1060 2731 1074 2731 
1074 2732 1073 2732 1071 2732 1070 2733 1069 2735 1069 2737 1069 2765 22 _pl _cp 
0 g _f _s _s 
0 g 1060 2668 _m
_sp 1060 2668 1062 2670 1066 2674 1067 2675 1068 2676 1069 2678 1070 2679 1072 2682 1073 2684 1074 2686 1074 2688 1073 2692 1072 2695 1069 2696 1065 2697 
1063 2697 1061 2696 1060 2696 1058 2695 1057 2693 1056 2692 1055 2690 1055 2687 1056 2687 1057 2689 1058 2691 1060 2692 1063 2693 1066 2692 1068 2691 
1069 2689 1070 2686 1070 2683 1068 2680 1066 2677 1063 2673 1059 2669 1054 2664 1054 2664 1074 2664 1077 2670 1076 2671 1075 2670 1074 2669 1074 2668 
1072 2668 1070 2668 47 _pl _cp 
0 g _f _s _s 
0 g 1260 2508 _m
_sp 1260 2508 1258 2507 1257 2506 1255 2505 1254 2503 1253 2501 1252 2499 1251 2497 1251 2494 1251 2491 1252 2489 1253 2487 1254 2485 1255 2484 1257 2483 
1258 2481 1260 2480 1260 2481 1258 2482 1257 2483 1256 2485 1255 2487 1255 2489 1255 2490 1254 2492 1254 2494 1254 2496 1255 2498 1255 2499 1255 2501 
1256 2503 1257 2505 1258 2506 1260 2507 34 _pl _cp 
0 g _f _s _s 
0 g 1270 2483 _m
_sp 1270 2483 1271 2481 1271 2479 1272 2478 1273 2476 1275 2475 1276 2475 1278 2476 1280 2477 1281 2480 1282 2484 1281 2487 1280 2490 1278 2491 1276 2492 
1274 2491 1272 2490 1271 2487 18 _pl _cp 1273 2484 _m
_sp 1273 2484 1273 2481 1274 2478 1275 2477 1276 2476 1277 2476 1278 2477 1279 2478 1279 2479 1279 2481 1279 2484 1279 2487 1278 2489 1277 2491 1276 2491 
1275 2491 1274 2489 1273 2487 18 _pl _cp 
0 g _f _s _s 
0 g 1348 2480 _m
_sp 1348 2480 1349 2481 1351 2483 1352 2484 1353 2485 1354 2487 1355 2489 1356 2491 1356 2494 1356 2497 1355 2499 1354 2501 1353 2503 1352 2505 1351 2506 
1349 2507 1348 2508 1347 2507 1349 2506 1350 2505 1351 2503 1352 2501 1352 2499 1353 2498 1353 2496 1353 2494 1353 2492 1353 2490 1352 2489 1352 2487 
1351 2485 1350 2483 1349 2482 1347 2481 34 _pl _cp 
0 g _f _s _s 
0 g 1557 2508 _m
_sp 1557 2508 1555 2507 1554 2506 1552 2505 1551 2503 1550 2501 1550 2499 1549 2497 1549 2494 1549 2491 1550 2489 1550 2487 1551 2485 1552 2484 1554 2483 
1555 2481 1557 2480 1557 2481 1556 2482 1554 2483 1554 2485 1553 2487 1552 2489 1552 2490 1552 2492 1552 2494 1552 2496 1552 2498 1552 2499 1553 2501 
1554 2503 1554 2505 1556 2506 1557 2507 34 _pl _cp 
0 g _f _s _s 
0 g 1568 2483 _m
_sp 1568 2483 1568 2481 1568 2479 1569 2478 1570 2476 1572 2475 1573 2475 1576 2476 1578 2477 1579 2480 1579 2484 1579 2487 1578 2490 1576 2491 1573 2492 
1571 2491 1569 2490 1568 2487 18 _pl _cp 1570 2484 _m
_sp 1570 2484 1570 2481 1571 2478 1572 2477 1573 2476 1574 2476 1575 2477 1576 2478 1576 2479 1576 2481 1576 2484 1576 2487 1575 2489 1574 2491 1573 2491 
1572 2491 1571 2489 1570 2487 18 _pl _cp 
0 g _f _s _s 
0 g 1581 2480 _m
_sp 1581 2480 1582 2481 1584 2483 1585 2484 1586 2485 1587 2487 1588 2489 1589 2491 1589 2494 1589 2497 1588 2499 1587 2501 1586 2503 1585 2505 1584 2506 
1582 2507 1581 2508 1580 2507 1582 2506 1583 2505 1584 2503 1585 2501 1585 2499 1586 2498 1586 2496 1586 2494 1586 2492 1586 2490 1585 2489 1585 2487 
1584 2485 1583 2483 1582 2482 1580 2481 34 _pl _cp 
0 g _f _s _s 
0 g 1852 2508 _m
_sp 1852 2508 1850 2507 1849 2506 1847 2505 1846 2503 1845 2501 1845 2499 1844 2497 1844 2494 1844 2491 1845 2489 1845 2487 1846 2485 1847 2484 1849 2483 
1850 2481 1852 2480 1852 2481 1851 2482 1849 2483 1849 2485 1848 2487 1847 2489 1847 2490 1847 2492 1847 2494 1847 2496 1847 2498 1847 2499 1848 2501 
1849 2503 1849 2505 1851 2506 1852 2507 34 _pl _cp 
0 g _f _s _s 
0 g 1863 2483 _m
_sp 1863 2483 1863 2481 1863 2479 1864 2478 1865 2476 1867 2475 1868 2475 1871 2476 1873 2477 1874 2480 1874 2484 1874 2487 1873 2490 1871 2491 1868 2492 
1866 2491 1864 2490 1863 2487 18 _pl _cp 1865 2484 _m
_sp 1865 2484 1865 2481 1866 2478 1867 2477 1868 2476 1869 2476 1870 2477 1871 2478 1871 2479 1871 2481 1871 2484 1871 2487 1870 2489 1869 2491 1868 2491 
1867 2491 1866 2489 1865 2487 18 _pl _cp 
0 g _f _s _s 
0 g 1876 2480 _m
_sp 1876 2480 1877 2481 1879 2483 1880 2484 1881 2485 1882 2487 1883 2489 1884 2491 1884 2494 1884 2497 1883 2499 1882 2501 1881 2503 1880 2505 1879 2506 
1877 2507 1876 2508 1875 2507 1877 2506 1878 2505 1879 2503 1880 2501 1880 2499 1881 2498 1881 2496 1881 2494 1881 2492 1881 2490 1880 2489 1880 2487 
1879 2485 1878 2483 1877 2482 1875 2481 34 _pl _cp 
0 g _f _s _s 
0 g 790 2502 _m
_sp 790 2502 790 2496 784 2496 784 2495 790 2495 790 2489 791 2489 791 2495 797 2495 797 2496 791 2496 791 2502 12 _pl _cp 
0 g _f _s _s 
0 g 874 2723 _m
_sp 874 2723 855 2723 855 2721 874 2721 4 _pl _cp 874 2715 _m
_sp 874 2715 855 2715 855 2713 874 2713 4 _pl _cp 
0 g _f _s _s 
0 g 1017 2720 _m
_sp 1017 2720 1018 2718 1020 2717 1022 2718 1023 2720 1022 2723 1020 2724 1018 2723 8 _pl _cp 
0 g _f _s _s 
0 g 1113 2720 _m
_sp 1113 2720 1114 2718 1116 2717 1118 2718 1119 2720 1118 2723 1116 2724 1114 2723 8 _pl _cp 
0 g _f _s _s 
0 g 1300 2502 _m
_sp 1300 2502 1300 2496 1295 2496 1295 2495 1300 2495 1300 2489 1301 2489 1301 2495 1307 2495 1307 2496 1301 2496 1301 2502 12 _pl _cp 
0 g _f _s _s 
0 g 1396 2727 _m
_sp 1396 2727 1396 2719 1387 2719 1387 2717 1396 2717 1396 2709 1397 2709 1397 2717 1406 2717 1406 2719 1397 2719 1397 2727 12 _pl _cp 
0 g _f _s _s 
0 g 1691 2727 _m
_sp 1691 2727 1691 2719 1682 2719 1682 2717 1691 2717 1691 2709 1692 2709 1692 2717 1701 2717 1701 2719 1692 2719 1692 2727 12 _pl _cp 
0 g _f _s _s 
0 g 821 2505 _m
_sp 821 2505 819 2506 817 2508 815 2509 813 2508 812 2505 812 2504 813 2503 814 2501 816 2500 813 2499 811 2498 810 2496 809 2493 810 2490 
811 2488 813 2487 816 2486 819 2487 821 2488 822 2490 823 2493 823 2495 822 2496 822 2497 821 2499 820 2500 818 2501 816 2503 814 2504 
814 2505 814 2505 814 2506 814 2506 816 2506 818 2504 819 2503 37 _pl _cp 820 2493 _m
_sp 820 2493 820 2490 819 2489 817 2487 816 2487 815 2487 813 2489 812 2490 812 2493 812 2496 813 2498 815 2499 816 2499 818 2499 819 2498 
820 2496 16 _pl _cp 
0 g _f _s _s 
0 g 965 2732 _m
_sp 965 2732 962 2734 961 2736 959 2737 958 2737 956 2737 954 2737 952 2736 951 2734 951 2733 952 2731 953 2729 955 2727 958 2725 954 2724 
951 2722 949 2719 948 2714 949 2710 951 2706 954 2704 958 2703 962 2704 965 2706 967 2710 968 2714 968 2717 967 2719 966 2721 965 2722 
963 2724 961 2726 959 2727 957 2729 956 2730 955 2731 954 2732 954 2733 955 2734 955 2734 956 2734 957 2733 959 2732 960 2731 962 2729 
45 _pl _cp 964 2714 _m
_sp 964 2714 963 2710 962 2708 960 2706 958 2705 955 2706 954 2708 952 2710 952 2714 952 2718 954 2721 955 2722 958 2723 961 2722 963 2721 
964 2718 16 _pl _cp 
0 g _f _s _s 
0 g 1331 2505 _m
_sp 1331 2505 1330 2506 1329 2507 1328 2508 1326 2509 1325 2509 1323 2508 1322 2505 1322 2504 1323 2503 1325 2501 1327 2500 1324 2499 1322 2498 1320 2496 
1320 2493 1321 2490 1322 2488 1324 2487 1326 2486 1329 2487 1331 2488 1332 2490 1333 2493 1333 2495 1333 2496 1332 2497 1331 2499 1330 2500 1329 2501 
1326 2503 1325 2504 1324 2505 1324 2505 1324 2506 1325 2506 1326 2506 1328 2504 1330 2503 39 _pl _cp 1330 2493 _m
_sp 1330 2493 1330 2490 1329 2489 1328 2487 1327 2487 1325 2487 1324 2489 1323 2490 1323 2493 1323 2496 1324 2498 1325 2499 1327 2499 1328 2499 1329 2498 
1330 2496 16 _pl _cp 
0 g _f _s _s 
0 g 1207 2936 _m
_sp 1207 2936 1208 2934 1210 2933 1212 2934 1213 2935 1212 2937 1210 2938 1208 2937 8 _pl _cp 
0 g _f _s _s 
0 g 1207 2855 _m
_sp 1207 2855 1208 2853 1210 2852 1212 2853 1213 2855 1212 2857 1210 2858 1208 2857 8 _pl _cp 
0 g _f _s _s 
0 g 1207 2774 _m
_sp 1207 2774 1208 2772 1210 2771 1212 2772 1213 2774 1212 2776 1210 2777 1208 2776 8 _pl _cp 
0 g _f _s _s 
0 g 1207 2693 _m
_sp 1207 2693 1208 2691 1210 2690 1212 2691 1213 2693 1212 2695 1210 2696 1208 2695 8 _pl _cp 
0 g _f _s _s 
0 g 1207 2613 _m
_sp 1207 2613 1208 2611 1210 2610 1212 2611 1213 2612 1212 2614 1210 2615 1208 2614 8 _pl _cp 
0 g _f _s _s 
0 g 1207 2532 _m
_sp 1207 2532 1208 2530 1210 2529 1212 2530 1213 2532 1212 2534 1210 2535 1208 2534 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2936 _m
_sp 1504 2936 1505 2934 1507 2933 1509 2934 1510 2935 1509 2937 1507 2938 1505 2937 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2855 _m
_sp 1504 2855 1505 2853 1507 2852 1509 2853 1510 2855 1509 2857 1507 2858 1505 2857 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2774 _m
_sp 1504 2774 1505 2772 1507 2771 1509 2772 1510 2774 1509 2776 1507 2777 1505 2776 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2693 _m
_sp 1504 2693 1505 2691 1507 2690 1509 2691 1510 2693 1509 2695 1507 2696 1505 2695 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2613 _m
_sp 1504 2613 1505 2611 1507 2610 1509 2611 1510 2612 1509 2614 1507 2615 1505 2614 8 _pl _cp 
0 g _f _s _s 
0 g 1504 2532 _m
_sp 1504 2532 1505 2530 1507 2529 1509 2530 1510 2532 1509 2534 1507 2535 1505 2534 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 10871 _m
/Times-BoldR 600 _ff
(\(6.37\))_S /Times-RomanR 600 _ff
1500 8959 _m
(where)_S 67 _t
2056 8899 _m
3615 8959 _m
67 _t
(in)_S 67 _t
(Equation)_S 67 _t
(\(6.37\))_S 67 _t
(is)_S 67 _t
(itself)_S 67 _t
(an)_S 67 _t
(estimate)_S 67 _t
(obtained)_S 67 _t
(by)_S 67 _t
(Euler)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 91 389 514 2224 _cw 
_s 521 2240 _m
_sp 521 2240 521 2288 529 2288 529 2287 522 2287 522 2241 529 2241 529 2240 8 _pl _cp 
0 g _f _s _s 
0 g 804 2240 _m
_sp 804 2240 804 2288 796 2288 796 2287 802 2287 802 2241 796 2241 796 2240 8 _pl _cp 
0 g _f _s _s 
0 g 543 2283 _m
_sp 543 2283 544 2281 546 2280 547 2281 548 2283 547 2285 546 2286 544 2285 8 _pl _cp 
0 g _f _s _s 
0 g 588 2283 _m
_sp 588 2283 589 2281 591 2280 593 2281 594 2283 593 2285 591 2286 589 2285 8 _pl _cp 
0 g _f _s _s 
0 g 638 2283 _m
_sp 638 2283 639 2281 641 2280 643 2281 644 2283 643 2285 641 2286 639 2285 8 _pl _cp 
0 g _f _s _s 
0 g 689 2283 _m
_sp 689 2283 690 2281 692 2280 694 2281 695 2283 694 2285 692 2286 690 2285 8 _pl _cp 
0 g _f _s _s 
0 g 736 2283 _m
_sp 736 2283 737 2281 739 2280 741 2281 742 2283 741 2285 739 2286 737 2285 8 _pl _cp 
0 g _f _s _s 
0 g 781 2283 _m
_sp 781 2283 782 2281 783 2280 785 2281 786 2283 785 2285 783 2286 782 2285 8 _pl _cp 
0 g _f _s _s 
0 g 548 2275 _m
_sp 548 2275 547 2273 546 2270 545 2268 544 2266 543 2264 542 2262 540 2259 538 2257 537 2256 535 2255 535 2256 535 2256 535 2258 535 2259 
540 2276 532 2275 532 2274 533 2274 534 2273 534 2272 534 2271 534 2270 531 2260 531 2259 531 2258 531 2257 531 2255 532 2254 533 2253 
535 2253 536 2254 538 2255 539 2256 540 2257 541 2259 542 2261 544 2264 543 2259 543 2257 543 2255 544 2253 546 2253 547 2253 548 2254 
550 2256 552 2259 551 2259 551 2258 549 2257 548 2255 547 2255 547 2255 547 2256 547 2257 547 2258 547 2259 548 2261 548 2263 549 2264 
549 2266 549 2267 551 2272 552 2275 64 _pl _cp 
0 g _f _s _s 
0 g 577 2274 _m
_sp 577 2274 576 2274 577 2274 577 2274 579 2273 581 2271 581 2270 582 2268 582 2267 582 2265 583 2263 583 2260 583 2257 583 2253 584 2253 
585 2254 586 2254 588 2256 589 2257 591 2259 592 2261 593 2263 595 2264 596 2266 597 2267 598 2269 598 2270 599 2272 599 2273 598 2275 
596 2276 594 2275 593 2274 594 2273 595 2272 596 2271 596 2270 595 2268 594 2266 593 2265 592 2263 591 2261 590 2260 588 2259 587 2258 
587 2260 587 2263 587 2266 586 2268 586 2270 585 2272 585 2274 584 2275 584 2276 54 _pl _cp 
0 g _f _s _s 
0 g 630 2260 _m
_sp 630 2260 630 2263 630 2265 630 2267 629 2269 629 2272 629 2273 628 2275 628 2276 621 2274 621 2273 623 2273 624 2273 625 2271 626 2268 
626 2264 627 2261 627 2257 627 2253 628 2253 638 2269 640 2253 641 2253 643 2256 646 2259 648 2262 650 2265 652 2268 653 2270 653 2271 
653 2273 652 2275 651 2276 649 2275 649 2274 649 2273 650 2272 651 2271 651 2270 651 2269 650 2268 649 2267 649 2265 648 2264 646 2262 
644 2259 643 2258 641 2275 640 2276 49 _pl _cp 
0 g _f _s _s 
0 g 685 2271 _m
_sp 685 2271 687 2276 678 2275 678 2274 680 2274 681 2273 682 2272 682 2271 681 2270 675 2248 674 2245 672 2244 672 2244 671 2243 682 2243 
682 2244 680 2244 679 2245 679 2246 679 2246 679 2247 679 2248 681 2253 683 2253 684 2253 686 2253 689 2254 692 2255 694 2257 696 2260 
698 2263 699 2266 699 2269 699 2272 698 2274 696 2275 694 2276 691 2276 689 2275 687 2273 40 _pl _cp 682 2257 _m
_sp 682 2257 682 2257 681 2256 682 2255 684 2254 685 2254 686 2255 688 2256 689 2257 691 2260 693 2263 694 2266 695 2270 694 2272 692 2273 
690 2273 687 2271 686 2270 685 2268 684 2266 683 2263 21 _pl _cp 
0 g _f _s _s 
0 g 742 2273 _m
_sp 742 2273 740 2275 738 2276 736 2276 734 2275 731 2273 729 2271 726 2268 725 2265 723 2262 723 2259 724 2256 725 2255 727 2253 729 2253 
731 2253 732 2253 733 2254 735 2255 736 2257 738 2259 735 2248 734 2245 732 2244 730 2244 730 2243 742 2243 742 2244 740 2244 739 2245 
738 2246 739 2247 739 2248 746 2275 742 2275 35 _pl _cp 728 2259 _m
_sp 728 2259 729 2256 731 2255 733 2255 734 2257 736 2258 737 2261 739 2264 740 2267 741 2269 741 2271 740 2273 738 2274 736 2273 733 2272 
731 2269 729 2266 728 2263 728 2260 728 2260 20 _pl _cp 
0 g _f _s _s 
0 g 771 2253 _m
_sp 771 2253 775 2253 776 2258 777 2261 778 2263 779 2265 780 2266 780 2268 781 2269 783 2271 784 2272 785 2272 785 2271 786 2271 787 2270 
788 2271 789 2273 788 2275 787 2276 785 2275 783 2273 781 2272 779 2269 779 2268 778 2267 781 2276 773 2275 773 2274 774 2274 775 2273 
776 2272 776 2271 775 2270 33 _pl _cp 
0 g _f _s _s 
0 g 820 2296 _m
_sp 820 2296 821 2298 822 2299 824 2300 826 2300 828 2300 823 2284 822 2281 821 2280 820 2280 819 2280 829 2280 829 2280 828 2280 827 2281 
827 2282 827 2282 827 2283 827 2284 831 2300 833 2300 836 2299 837 2297 837 2297 837 2297 836 2297 836 2296 837 2296 838 2301 821 2301 
819 2296 31 _pl _cp 
0 g _f _s _s 
0 g 832 2254 _m
_sp 832 2254 829 2244 829 2243 829 2242 829 2241 830 2240 832 2240 833 2241 834 2242 835 2244 835 2244 833 2242 832 2242 832 2242 831 2242 
831 2243 832 2243 832 2245 834 2254 837 2254 838 2255 835 2255 836 2259 835 2259 834 2257 832 2256 831 2255 829 2255 829 2254 29 _pl _cp 
0 g _f _s _s 
0 g 881 2254 _m
_sp 881 2254 879 2244 879 2243 878 2242 879 2241 880 2240 882 2240 883 2241 884 2242 885 2244 885 2244 883 2242 882 2242 881 2242 881 2242 
881 2243 881 2243 882 2245 884 2254 887 2254 887 2255 884 2255 885 2259 885 2259 883 2257 882 2256 881 2255 879 2255 879 2254 29 _pl _cp 
0 g _f _s _s 
0 g 827 2263 _m
_sp 827 2263 825 2262 824 2261 822 2259 821 2258 820 2256 819 2253 818 2251 818 2248 818 2246 819 2244 820 2241 821 2239 822 2238 824 2237 
825 2235 827 2234 827 2235 825 2237 824 2238 823 2240 822 2241 822 2243 822 2245 821 2246 821 2248 821 2250 822 2252 822 2254 822 2256 
823 2258 824 2259 825 2261 827 2262 34 _pl _cp 
0 g _f _s _s 
0 g 888 2234 _m
_sp 888 2234 889 2235 891 2237 892 2238 893 2239 894 2241 895 2244 896 2246 896 2248 896 2251 895 2253 894 2256 893 2258 892 2259 891 2261 
889 2262 888 2263 887 2262 889 2261 890 2259 891 2258 892 2256 892 2254 893 2252 893 2250 893 2248 893 2246 893 2245 892 2243 892 2241 
891 2240 890 2238 889 2237 887 2235 34 _pl _cp 
0 g _f _s _s 
0 g 847 2256 _m
_sp 847 2256 847 2251 842 2251 842 2249 847 2249 847 2244 849 2244 849 2249 854 2249 854 2251 849 2251 849 2256 12 _pl _cp 
0 g _f _s _s 
0 g 871 2259 _m
_sp 871 2259 870 2261 868 2262 865 2263 863 2262 862 2260 862 2259 863 2258 865 2256 867 2255 864 2254 862 2253 860 2250 860 2247 861 2244 
862 2242 864 2241 866 2240 869 2241 871 2242 872 2245 873 2248 873 2250 873 2251 871 2253 869 2255 866 2257 865 2258 864 2259 864 2260 
864 2261 865 2261 866 2260 868 2259 870 2258 35 _pl _cp 870 2247 _m
_sp 870 2247 870 2245 869 2243 868 2242 867 2241 865 2242 864 2243 863 2245 863 2247 863 2250 864 2252 865 2253 867 2253 868 2253 869 2252 
870 2250 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 1500 8284 _m
(integration)_S 67 _t
(of)_S 67 _t
2667 8224 _m
4027 8284 _m
(.)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 90 340 666 2056 _cw 
_s 673 2072 _m
_sp 673 2072 673 2120 681 2120 681 2119 674 2119 674 2073 681 2073 681 2072 8 _pl _cp 
0 g _f _s _s 
0 g 956 2072 _m
_sp 956 2072 956 2120 948 2120 948 2119 954 2119 954 2073 948 2073 948 2072 8 _pl _cp 
0 g _f _s _s 
0 g 695 2115 _m
_sp 695 2115 696 2113 698 2112 699 2113 700 2115 699 2117 698 2118 696 2117 8 _pl _cp 
0 g _f _s _s 
0 g 740 2115 _m
_sp 740 2115 741 2113 743 2112 745 2113 746 2115 745 2117 743 2118 741 2117 8 _pl _cp 
0 g _f _s _s 
0 g 790 2115 _m
_sp 790 2115 791 2113 793 2112 795 2113 796 2115 795 2117 793 2118 791 2117 8 _pl _cp 
0 g _f _s _s 
0 g 841 2115 _m
_sp 841 2115 842 2113 844 2112 846 2113 847 2115 846 2117 844 2118 842 2117 8 _pl _cp 
0 g _f _s _s 
0 g 888 2115 _m
_sp 888 2115 889 2113 891 2112 893 2113 894 2115 893 2117 891 2118 889 2117 8 _pl _cp 
0 g _f _s _s 
0 g 933 2115 _m
_sp 933 2115 934 2113 935 2112 937 2113 938 2115 937 2117 935 2118 934 2117 8 _pl _cp 
0 g _f _s _s 
0 g 700 2107 _m
_sp 700 2107 699 2105 698 2102 697 2100 696 2098 695 2096 694 2094 692 2091 690 2089 689 2088 687 2087 687 2088 687 2088 687 2090 687 2091 
692 2108 684 2107 684 2106 685 2106 686 2105 686 2104 686 2103 686 2102 683 2092 683 2091 683 2090 683 2089 683 2087 684 2086 685 2085 
687 2085 688 2086 690 2087 691 2088 692 2089 693 2091 694 2093 696 2096 695 2091 695 2089 695 2087 696 2085 698 2085 699 2085 700 2086 
702 2088 704 2091 703 2091 703 2090 701 2089 700 2087 699 2087 699 2087 699 2088 699 2089 699 2090 699 2091 700 2093 700 2095 701 2096 
701 2098 701 2099 703 2104 704 2107 64 _pl _cp 
0 g _f _s _s 
0 g 729 2106 _m
_sp 729 2106 728 2106 729 2106 729 2106 731 2105 733 2103 733 2102 734 2100 734 2099 734 2097 735 2095 735 2092 735 2089 735 2085 736 2085 
737 2086 738 2086 740 2088 741 2089 743 2091 744 2093 745 2095 747 2096 748 2098 749 2099 750 2101 750 2102 751 2104 751 2105 750 2107 
748 2108 746 2107 745 2106 746 2105 747 2104 748 2103 748 2102 747 2100 746 2098 745 2097 744 2095 743 2093 742 2092 740 2091 739 2090 
739 2092 739 2095 739 2098 738 2100 738 2102 737 2104 737 2106 736 2107 736 2108 54 _pl _cp 
0 g _f _s _s 
0 g 782 2092 _m
_sp 782 2092 782 2095 782 2097 782 2099 781 2101 781 2104 781 2105 780 2107 780 2108 773 2106 773 2105 775 2105 776 2105 777 2103 778 2100 
778 2096 779 2093 779 2089 779 2085 780 2085 790 2101 792 2085 793 2085 795 2088 798 2091 800 2094 802 2097 804 2100 805 2102 805 2103 
805 2105 804 2107 803 2108 801 2107 801 2106 801 2105 802 2104 803 2103 803 2102 803 2101 802 2100 801 2099 801 2097 800 2096 798 2094 
796 2091 795 2090 793 2107 792 2108 49 _pl _cp 
0 g _f _s _s 
0 g 837 2103 _m
_sp 837 2103 839 2108 830 2107 830 2106 832 2106 833 2105 834 2104 834 2103 833 2102 827 2080 826 2077 824 2076 824 2076 823 2075 834 2075 
834 2076 832 2076 831 2077 831 2078 831 2078 831 2079 831 2080 833 2085 835 2085 836 2085 838 2085 841 2086 844 2087 846 2089 848 2092 
850 2095 851 2098 851 2101 851 2104 850 2106 848 2107 846 2108 843 2108 841 2107 839 2105 40 _pl _cp 834 2089 _m
_sp 834 2089 834 2089 833 2088 834 2087 836 2086 837 2086 838 2087 840 2088 841 2089 843 2092 845 2095 846 2098 847 2102 846 2104 844 2105 
842 2105 839 2103 838 2102 837 2100 836 2098 835 2095 21 _pl _cp 
0 g _f _s _s 
0 g 894 2105 _m
_sp 894 2105 892 2107 890 2108 888 2108 886 2107 883 2105 881 2103 878 2100 877 2097 875 2094 875 2091 876 2088 877 2087 879 2085 881 2085 
883 2085 884 2085 885 2086 887 2087 888 2089 890 2091 887 2080 886 2077 884 2076 882 2076 882 2075 894 2075 894 2076 892 2076 891 2077 
890 2078 891 2079 891 2080 898 2107 894 2107 35 _pl _cp 880 2091 _m
_sp 880 2091 881 2088 883 2087 885 2087 886 2089 888 2090 889 2093 891 2096 892 2099 893 2101 893 2103 892 2105 890 2106 888 2105 885 2104 
883 2101 881 2098 880 2095 880 2092 880 2092 20 _pl _cp 
0 g _f _s _s 
0 g 923 2085 _m
_sp 923 2085 927 2085 928 2090 929 2093 930 2095 931 2097 932 2098 932 2100 933 2101 935 2103 936 2104 937 2104 937 2103 938 2103 939 2102 
940 2103 941 2105 940 2107 939 2108 937 2107 935 2105 933 2104 931 2101 931 2100 930 2099 933 2108 925 2107 925 2106 926 2106 927 2105 
928 2104 928 2103 927 2102 33 _pl _cp 
0 g _f _s _s 
0 g 972 2128 _m
_sp 972 2128 973 2130 974 2131 976 2132 978 2132 980 2132 975 2116 974 2113 973 2112 972 2112 971 2112 981 2112 981 2112 980 2112 979 2113 
979 2114 979 2114 979 2115 979 2116 983 2132 985 2132 988 2131 989 2129 989 2129 989 2129 988 2129 988 2128 989 2128 990 2133 973 2133 
971 2128 31 _pl _cp 
0 g _f _s _s 
0 g 984 2086 _m
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983 2075 984 2075 984 2077 986 2086 989 2086 990 2087 987 2087 988 2091 987 2091 986 2089 984 2088 983 2087 981 2087 981 2086 29 _pl _cp 
0 g _f _s _s 
0 g 979 2095 _m
_sp 979 2095 977 2094 976 2093 974 2091 973 2090 972 2088 971 2085 970 2083 970 2080 970 2078 971 2076 972 2073 973 2071 974 2070 976 2069 
977 2067 979 2066 979 2067 977 2069 976 2070 975 2072 974 2073 974 2075 974 2077 973 2078 973 2080 973 2082 974 2084 974 2086 974 2088 
975 2090 976 2091 977 2093 979 2094 34 _pl _cp 
0 g _f _s _s 
0 g 990 2066 _m
_sp 990 2066 992 2067 993 2069 994 2070 995 2071 996 2073 997 2076 998 2078 998 2080 998 2083 997 2085 996 2088 995 2090 994 2091 993 2093 
992 2094 990 2095 989 2094 991 2093 992 2091 993 2090 994 2088 995 2086 995 2084 995 2082 995 2080 995 2078 995 2077 995 2075 994 2073 
993 2072 992 2070 991 2069 989 2067 34 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 2400 7826 _m
(Conversion)_S 67 _t
(of)_S 67 _t
(these)_S 67 _t
(body)_S 67 _t
(velocities)_S 67 _t
(to)_S 67 _t
(world)_S 67 _t
(velocities)_S 67 _t
(is)_S 67 _t
(performed)_S 67 _t
(using)_S 1500 7477 _m
(the)_S 67 _t
(transformation)_S 67 _t
(of)_S 67 _t
(Equation)_S 67 _t
(\(6.22\).)_S 134 _t
(Subsequent)_S 67 _t
(integration)_S 67 _t
(of)_S 67 _t
(world)_S 67 _t
(velocities)_S 67 _t
(into)_S 1500 7128 _m
(world)_S 67 _t
(posture)_S 67 _t
(is)_S 67 _t
(performed)_S 67 _t
(by)_S 67 _t
(Euler)_S 67 _t
(integration)_S 67 _t
(as)_S 67 _t
(follows:)_S gsave 4 4 scale 16 _sr 
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0 g 955 1394 _m
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0 g 955 1375 _m
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0 g _f _s _s 
0 g 955 1335 _m
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0 g _f _s _s 
0 g 955 1315 _m
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0 g _f _s _s 
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_sp 955 1296 953 1296 953 1318 955 1318 4 _pl _cp 
0 g _f _s _s 
0 g 955 1276 _m
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0 g _f _s _s 
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_sp 955 1262 953 1262 953 1199 945 1199 945 1197 955 1197 6 _pl _cp 
0 g _f _s _s 
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_sp 1280 1610 1278 1610 1278 1670 1287 1670 1287 1668 1280 1668 6 _pl _cp 
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0 g _f _s _s 
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_sp 1280 1570 1278 1570 1278 1592 1280 1592 4 _pl _cp 
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0 g _f _s _s 
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0 g _f _s _s 
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0 g _f _s _s 
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0 g 1280 1254 _m
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0 g _f _s _s 
0 g 1280 1234 _m
_sp 1280 1234 1278 1234 1278 1257 1280 1257 4 _pl _cp 
0 g _f _s _s 
0 g 1278 1238 _m
_sp 1278 1238 1280 1238 1280 1175 1287 1175 1287 1173 1278 1173 6 _pl _cp 
0 g _f _s _s 
0 g 1333 1610 _m
_sp 1333 1610 1334 1610 1334 1670 1325 1670 1325 1668 1333 1668 6 _pl _cp 
0 g _f _s _s 
0 g 1334 1590 _m
_sp 1334 1590 1333 1590 1333 1612 1334 1612 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1570 _m
_sp 1334 1570 1333 1570 1333 1592 1334 1592 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1550 _m
_sp 1334 1550 1333 1550 1333 1573 1334 1573 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1531 _m
_sp 1334 1531 1333 1531 1333 1553 1334 1553 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1511 _m
_sp 1334 1511 1333 1511 1333 1533 1334 1533 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1491 _m
_sp 1334 1491 1333 1491 1333 1513 1334 1513 4 _pl _cp 
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0 g 1334 1471 _m
_sp 1334 1471 1333 1471 1333 1494 1334 1494 4 _pl _cp 
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0 g 1334 1452 _m
_sp 1334 1452 1333 1452 1333 1474 1334 1474 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1432 _m
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0 g _f _s _s 
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_sp 1334 1373 1333 1373 1333 1395 1334 1395 4 _pl _cp 
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0 g 1334 1333 _m
_sp 1334 1333 1333 1333 1333 1355 1334 1355 4 _pl _cp 
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_sp 1334 1313 1333 1313 1333 1336 1334 1336 4 _pl _cp 
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_sp 1334 1274 1333 1274 1333 1296 1334 1296 4 _pl _cp 
0 g _f _s _s 
0 g 1334 1254 _m
_sp 1334 1254 1333 1254 1333 1276 1334 1276 4 _pl _cp 
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0 g 1334 1234 _m
_sp 1334 1234 1333 1234 1333 1257 1334 1257 4 _pl _cp 
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_sp 1334 1241 1333 1241 1333 1177 1325 1177 1325 1175 1334 1175 6 _pl _cp 
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0 g 1538 1592 _m
_sp 1538 1592 1536 1592 1536 1652 1545 1652 1545 1650 1538 1650 6 _pl _cp 
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_sp 1538 1473 1536 1473 1536 1496 1538 1496 4 _pl _cp 
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_sp 924 1623 923 1622 920 1618 919 1616 918 1615 917 1615 916 1615 916 1616 915 1616 914 1615 913 1614 914 1613 915 1612 917 1612 918 1613 
919 1614 920 1615 921 1616 922 1617 923 1619 924 1621 924 1621 925 1620 925 1617 926 1615 927 1613 928 1612 929 1612 930 1612 932 1613 
933 1615 935 1617 935 1618 934 1618 932 1616 931 1615 930 1615 930 1616 929 1618 928 1622 927 1626 928 1626 930 1629 931 1631 931 1632 
932 1632 933 1632 934 1631 935 1631 935 1631 936 1632 937 1633 936 1634 934 1635 933 1635 931 1634 930 1632 928 1629 927 1628 927 1630 
926 1632 926 1634 925 1635 924 1635 922 1635 920 1634 917 1633 918 1632 919 1633 920 1633 920 1633 921 1633 922 1631 923 1629 924 1626 
75 _pl _cp 
0 g _f _s _s 
0 g 915 1553 _m
_sp 915 1553 915 1552 916 1552 917 1552 919 1551 921 1548 921 1546 922 1543 923 1541 924 1538 924 1536 924 1535 924 1533 925 1531 923 1529 
922 1528 920 1525 918 1525 918 1525 918 1525 918 1525 917 1525 916 1526 915 1526 914 1525 913 1524 914 1522 916 1521 918 1522 919 1523 
920 1524 922 1525 923 1527 925 1529 927 1532 929 1535 930 1537 932 1541 934 1544 935 1547 936 1549 936 1551 935 1553 933 1554 932 1553 
931 1552 931 1551 932 1550 933 1549 934 1548 934 1548 933 1547 933 1546 932 1544 931 1542 930 1539 930 1538 929 1537 928 1537 928 1536 
928 1537 927 1537 927 1541 926 1544 926 1547 925 1550 923 1553 922 1554 68 _pl _cp 
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(adaptively)_S 67 _t
(if)_S 67 _t
(necessary.)_S 134 _t
(Further)_S 67 _t
(numerical)_S 67 _t
(analysis)_S 67 _t
(considerations)_S 67 _t
(and)_S 1500 2704 _m
(recommendations)_S 67 _t
(appear)_S 67 _t
(in)_S 67 _t
(\(Press)_S 67 _t
(92\))_S 67 _t
(\(Green)_S 67 _t
(91\))_S 67 _t
(and)_S 67 _t
(\(Hamming)_S 67 _t
(86\).)_S 134 _t
(In)_S 67 _t
(practice,)_S 67 _t
(a)_S 1500 2355 _m
(fixed)_S 67 _t
(time)_S 67 _t
(step)_S 67 _t
(of)_S 67 _t
(0.1)_S 67 _t
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(has)_S 67 _t
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(well)_S 67 _t
(for)_S 67 _t
(model)_S 67 _t
(resolution,)_S 67 _t
(real-time)_S 67 _t
(robot)_S 1500 2006 _m
(hardware)_S 67 _t
(control)_S 67 _t
(response,)_S 67 _t
(network)_S 67 _t
(latency,)_S 67 _t
(remote)_S 67 _t
(interaction,)_S 67 _t
(computer)_S 67 _t
(graphics)_S 4950 1288 _m
(121)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
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1500 11855 _m
(rendering)_S 67 _t
(update)_S 67 _t
(rate,)_S 67 _t
(and)_S 67 _t
(human)_S 67 _t
(observation.)_S 134 _t
(Care)_S 67 _t
(must)_S 67 _t
(be)_S 67 _t
(taken)_S 67 _t
(if)_S 67 _t
(higher-order)_S 1500 11506 _m
(integration)_S 67 _t
(methods)_S 67 _t
(are)_S 67 _t
(employed)_S 67 _t
(to)_S 67 _t
(ensure)_S 67 _t
(that)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(responsiveness)_S 1500 11157 _m
(does)_S 67 _t
(not)_S 67 _t
(degrade)_S 67 _t
(past)_S 67 _t
(the)_S 67 _t
(real-time)_S 67 _t
(requirements)_S 67 _t
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(the)_S 67 _t
(robot)_S 67 _t
(operating)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(virtual)_S 1500 10808 _m
(world.)_S 2400 10459 _m
(To)_S 67 _t
(summarize:)_S 134 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(not)_S 67 _t
(mathematically)_S 1500 10110 _m
(rewritten)_S 67 _t
(in)_S 67 _t
(world)_S 67 _t
(coordinates,)_S 67 _t
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(are)_S 67 _t
(kept)_S 67 _t
(in)_S 67 _t
(body)_S 67 _t
(coordinates.)_S 134 _t
(Integrating)_S 67 _t
(the)_S 1500 9761 _m
(dynamics)_S 67 _t
(equations)_S 67 _t
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(motion)_S 67 _t
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(body)_S 67 _t
(velocity)_S 67 _t
(values)_S 67 _t
(at)_S 67 _t
(the)_S 67 _t
(next)_S 67 _t
(time)_S 67 _t
(step.)_S 67 _t
1500 9412 _m
(These)_S 67 _t
(new)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(velocities)_S 67 _t
(are)_S 67 _t
(combined)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(kinematics)_S 1500 9063 _m
(equations)_S 67 _t
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(motion)_S 67 _t
(to)_S 67 _t
(produce)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(velocities.)_S 134 _t
(World)_S 67 _t
(velocities)_S 1500 8714 _m
(are)_S 67 _t
(then)_S 67 _t
(integrated)_S 67 _t
(and)_S 67 _t
(added)_S 67 _t
(to)_S 67 _t
(ocean)_S 67 _t
(current)_S 67 _t
(effects)_S 67 _t
(to)_S 67 _t
(produce)_S 67 _t
(updated)_S 67 _t
(world)_S 1500 8365 _m
(postures.)_S 134 _t
(Algorithmic)_S 67 _t
(complexity)_S 67 _t
(is)_S 67 _t
(sufficiently)_S 67 _t
(low)_S 67 _t
(to)_S 67 _t
(permit)_S 67 _t
(rapid)_S 67 _t
(model)_S 67 _t
(response)_S 1500 8016 _m
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(the)_S 67 _t
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(the)_S 67 _t
(robot)_S 67 _t
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(query)_S 67 _t
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/Times-BoldR 600 _ff
(7.)_S 2400 7594 _m
(Nomenclature)_S 67 _t
(Tables)_S 67 _t
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(Variables)_S 67 _t
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(Coefficients)_S /Times-RomanR 600 _ff
2400 7245 _m
(The)_S 67 _t
(many)_S 67 _t
(details)_S 67 _t
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(still)_S 67 _t
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(be)_S 67 _t
(filled)_S 67 _t
(in)_S 67 _t
(using)_S 67 _t
(a)_S 1500 6896 _m
(complete)_S 67 _t
(six-degree-of-freedom)_S 67 _t
(set)_S 67 _t
(of)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
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(motion.)_S 134 _t
(First,)_S 67 _t
(however,)_S 1500 6547 _m
(it)_S 67 _t
(must)_S 67 _t
(be)_S 67 _t
(noted)_S 67 _t
(that)_S 67 _t
(small)_S 67 _t
(yet)_S 67 _t
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(nomenclature)_S 67 _t
(inconsistencies)_S 67 _t
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(encountered)_S 67 _t
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(all)_S 67 _t
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(the)_S 67 _t
(dozens)_S 67 _t
(of)_S 67 _t
(hydrodynamics)_S 67 _t
(references)_S 67 _t
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(This)_S 67 _t
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(serious)_S 67 _t
(problem)_S 67 _t
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(newcomers)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(literature,)_S 67 _t
(since)_S 67 _t
(both)_S 67 _t
(names)_S 67 _t
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(definitions)_S 67 _t
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(key)_S 67 _t
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(may)_S 67 _t
(vary.)_S 134 _t
(This)_S 67 _t
(lack)_S 67 _t
(of)_S 67 _t
(standardization)_S 67 _t
(results)_S 67 _t
(in)_S 67 _t
(troubling)_S 1500 5151 _m
(mathematical)_S 67 _t
(incompatibilities)_S 67 _t
(throughout)_S 67 _t
(an)_S 67 _t
(entire)_S 67 _t
(body)_S 67 _t
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(literature.)_S 67 _t
1500 4802 _m
(Clearly)_S 67 _t
(an)_S 67 _t
(important)_S 67 _t
(prerequisite)_S 67 _t
(for)_S 67 _t
(describing)_S 67 _t
(any)_S 67 _t
(general)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
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(use)_S 67 _t
(well-defined)_S 67 _t
(\(and)_S 67 _t
(hopefully)_S 67 _t
(standardized\))_S 67 _t
(nomenclature.)_S 134 _t
(Of)_S 67 _t
(all)_S 67 _t
(the)_S 1500 4104 _m
(hydrodynamics)_S 67 _t
(models)_S 67 _t
(studied)_S 67 _t
(in)_S 67 _t
(this)_S 67 _t
(work,)_S 67 _t
(\(Healey)_S 67 _t
(93\))_S 67 _t
(and)_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 67 _t
(appear)_S 67 _t
(to)_S 67 _t
(be)_S 1500 3755 _m
(the)_S 67 _t
(most)_S 67 _t
(general)_S 67 _t
(and)_S 67 _t
(most)_S 67 _t
(applicable)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(of)_S 67 _t
(autonomous)_S 1500 3406 _m
(underwater)_S 67 _t
(vehicle)_S 67 _t
(response.)_S 134 _t
(The)_S 67 _t
(nomenclature)_S 67 _t
(of)_S 67 _t
(\(Healey)_S 67 _t
(93\))_S 67 _t
(closely)_S 67 _t
(follows)_S 67 _t
(that)_S 67 _t
(of)_S 1500 3057 _m
(the)_S 67 _t
(standard)_S 67 _t
(reference)_S 67 _t
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(ship)_S 67 _t
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(\(Lewis)_S 67 _t
(88\).)_S 134 _t
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1500 11855 _m
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(defining)_S 67 _t
(all)_S 67 _t
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(coefficients,)_S 67 _t
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(mathematically)_S 67 _t
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(Coefficient)_S 67 _t
(subscripts)_S 67 _t
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(previous)_S 67 _t
(models)_S 67 _t
(have)_S 67 _t
(been)_S 67 _t
(corrected)_S 67 _t
(when)_S 1500 11157 _m
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(explicitly)_S 67 _t
(indicate)_S 67 _t
(accompanying)_S 67 _t
(variable)_S 67 _t
(factors.)_S 134 _t
(Such)_S 67 _t
(an)_S 67 _t
(approach)_S 1500 10808 _m
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(comparison)_S 67 _t
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(this)_S 67 _t
(hydrodynamics)_S 67 _t
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(coefficient)_S 1500 9412 _m
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(\(for)_S 67 _t
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(NPS)_S 67 _t
(AUV\))_S 67 _t
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(software)_S 67 _t
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(\(Brutzman)_S 67 _t
(94e\))_S 67 _t
(match)_S 67 _t
(exactly)_S 67 _t
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(encourage)_S 67 _t
(clarity)_S 67 _t
(and)_S 67 _t
(correctness.)_S 2400 8365 _m
(Close)_S 67 _t
(examination)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
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(equations)_S 67 _t
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(reveals)_S 67 _t
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(body)_S 67 _t
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(presented)_S 67 _t
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(\(Brutzman)_S 67 _t
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(complexities)_S 67 _t
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(hydrodynamics)_S 67 _t
(testing)_S 1500 5920 _m
(and)_S 67 _t
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(this)_S 67 _t
(model)_S 67 _t
(preclude)_S 67 _t
(complete)_S 67 _t
(validation,)_S 67 _t
(verification)_S 67 _t
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(accreditation.)_S 134 _t
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(dynamics)_S 67 _t
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(\(Humphreys)_S 67 _t
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(90\))_S 67 _t
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(vehicles)_S 67 _t
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1500 11855 _m
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_sp 498 2909 498 2912 495 2912 3 _pl _pf _np _s _s 495 2721 _m
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 480 _ff
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/Times-BoldR 480 _ff
(Name)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 2713 1661 2716 749 2716 3 _pl _pf _np _s _s 749 2909 _m
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 11078 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2713 1929 2716 1661 2716 3 _pl _pf _np _s _s 1661 2909 _m
_sp 1929 2909 1929 2912 1661 2912 3 _pl _pf _np _s _s 1661 2721 _m
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_sp 1664 2909 1664 2912 1661 2912 3 _pl _pf _np _s _s 1661 2721 _m
_sp 1929 2721 1929 2724 1661 2724 3 _pl _pf _np _s _s 1661 2901 _m
_sp 1929 2901 1929 2904 1661 2904 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 6799 11367 _m
(Coordinate)_S 6955 11078 _m
(system)_S gsave 4 4 scale 16 _sr _s 
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_sp 2242 2713 2242 2716 1928 2716 3 _pl _pf _np _s _s 2247 2713 _m
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_sp 1931 2721 1931 2904 1928 2904 3 _pl _pf _np _s _s 1928 2909 _m
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_sp 2242 2721 2242 2724 1928 2724 3 _pl _pf _np _s _s 2239 2721 _m
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_s 0 g 0 0 0 0 _cw 
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(Units)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 496 2711 496 2714 308 2714 3 _pl _pf _np _s _s 300 2592 _m
_sp 303 2592 303 2714 300 2714 3 _pl _pf _np _s _s 308 2592 _m
_sp 311 2592 311 2714 308 2714 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1587 10575 _m
/Times-BoldItalicR 600 _ff
(t)_S gsave 4 4 scale 16 _sr _s 
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_sp 749 2711 749 2714 495 2714 3 _pl _pf _np _s _s 495 2592 _m
_sp 498 2592 498 2714 495 2714 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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/Times-RomanR 600 _ff
(time)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 2711 1661 2714 749 2714 3 _pl _pf _np _s _s 749 2592 _m
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10576 _m
(Clock)_S 67 _t
(time)_S 67 _t
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(simulated\))_S gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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_sp 2250 2592 2250 2714 2247 2714 3 _pl _pf _np _s _s 1928 2711 _m
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_s 0 g 0 0 0 0 _cw 
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(seconds)_S gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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(t)_S gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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/Times-RomanR 600 _ff
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(step)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 2589 1661 2592 749 2592 3 _pl _pf _np _s _s 749 2470 _m
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10091 _m
(Loop)_S 67 _t
(interval)_S 67 _t
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(model\))_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2589 1929 2592 1661 2592 3 _pl _pf _np _s _s 1661 2470 _m
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_s 0 g 0 0 0 0 _cw 
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(-)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 2470 2250 2592 2247 2592 3 _pl _pf _np _s _s 1928 2589 _m
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_s 0 g 0 0 0 0 _cw 
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(seconds)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 2468 496 2471 308 2471 3 _pl _pf _np _s _s 300 2262 _m
_sp 303 2262 303 2471 300 2471 3 _pl _pf _np _s _s 308 2262 _m
_sp 311 2262 311 2471 308 2471 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1565 9605 _m
/Times-BoldItalicR 600 _ff
(x)_S gsave 4 4 scale 16 _sr _s 
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_sp 749 2468 749 2471 495 2471 3 _pl _pf _np _s _s 495 2262 _m
_sp 498 2262 498 2471 495 2471 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 2447 9606 _m
/Times-RomanR 600 _ff
(x)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 2468 1661 2471 749 2471 3 _pl _pf _np _s _s 749 2262 _m
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_s 0 g 0 0 0 0 _cw 
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(Position)_S 67 _t
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(positive.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2468 1929 2471 1661 2471 3 _pl _pf _np _s _s 1661 2262 _m
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_s 0 g 0 0 0 0 _cw 
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(world)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 2262 2250 2471 2247 2471 3 _pl _pf _np _s _s 1928 2468 _m
_sp 2242 2468 2242 2471 1928 2471 3 _pl _pf _np _s _s 1928 2262 _m
_sp 1931 2262 1931 2471 1928 2471 3 _pl _pf _np _s _s 2239 2262 _m
_sp 2242 2262 2242 2471 2239 2471 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(feet)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 2260 496 2263 308 2263 3 _pl _pf _np _s _s 300 2053 _m
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_s 0 g 0 0 0 0 _cw 
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/Times-BoldItalicR 600 _ff
(y)_S gsave 4 4 scale 16 _sr _s 
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_sp 749 2260 749 2263 495 2263 3 _pl _pf _np _s _s 495 2053 _m
_sp 498 2053 498 2263 495 2263 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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/Times-RomanR 600 _ff
(y)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 2260 1661 2263 749 2263 3 _pl _pf _np _s _s 749 2053 _m
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_s 0 g 0 0 0 0 _cw 
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(Position)_S 67 _t
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(East-West)_S 67 _t
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(positive.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2260 1929 2263 1661 2263 3 _pl _pf _np _s _s 1661 2053 _m
_sp 1664 2053 1664 2263 1661 2263 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 6953 8772 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2053 _m
_sp 2250 2053 2250 2263 2247 2263 3 _pl _pf _np _s _s 1928 2260 _m
_sp 2242 2260 2242 2263 1928 2263 3 _pl _pf _np _s _s 1928 2053 _m
_sp 1931 2053 1931 2263 1928 2263 3 _pl _pf _np _s _s 2239 2053 _m
_sp 2242 2053 2242 2263 2239 2263 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(feet)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 2051 496 2054 308 2054 3 _pl _pf _np _s _s 300 1932 _m
_sp 303 1932 303 2054 300 2054 3 _pl _pf _np _s _s 308 1932 _m
_sp 311 1932 311 2054 308 2054 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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/Times-BoldItalicR 600 _ff
(z)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2051 _m
_sp 749 2051 749 2054 495 2054 3 _pl _pf _np _s _s 495 1932 _m
_sp 498 1932 498 2054 495 2054 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 2453 7938 _m
/Times-RomanR 600 _ff
(z)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 2051 1661 2054 749 2054 3 _pl _pf _np _s _s 749 1932 _m
_sp 752 1932 752 2054 749 2054 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(Depth,)_S 67 _t
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(positive.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2051 1929 2054 1661 2054 3 _pl _pf _np _s _s 1661 1932 _m
_sp 1664 1932 1664 2054 1661 2054 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(world)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1932 2250 2054 2247 2054 3 _pl _pf _np _s _s 1928 2051 _m
_sp 2242 2051 2242 2054 1928 2054 3 _pl _pf _np _s _s 1928 1932 _m
_sp 1931 1932 1931 2054 1928 2054 3 _pl _pf _np _s _s 2239 1932 _m
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_s 0 g 0 0 0 0 _cw 
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(feet)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 1930 496 1933 308 1933 3 _pl _pf _np _s _s 300 1549 _m
_sp 303 1549 303 1933 300 1933 3 _pl _pf _np _s _s 308 1549 _m
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_s 0 g 0 0 0 0 _cw 
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/Symbol 600 _ff
(f)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1930 _m
_sp 749 1930 749 1933 495 1933 3 _pl _pf _np _s _s 495 1549 _m
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_s 0 g 0 0 0 0 _cw 
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/Times-RomanR 600 _ff
(roll)_S 67 _t
(Euler)_S 2280 7104 _m
(angle)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1930 _m
_sp 1661 1930 1661 1933 749 1933 3 _pl _pf _np _s _s 749 1549 _m
_sp 752 1549 752 1933 749 1933 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 7453 _m
(Roll)_S 67 _t
(Euler)_S 67 _t
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(vehicle.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 1930 1929 1933 1661 1933 3 _pl _pf _np _s _s 1661 1549 _m
_sp 1664 1549 1664 1933 1661 1933 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(world)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1549 2250 1933 2247 1933 3 _pl _pf _np _s _s 1928 1930 _m
_sp 2242 1930 2242 1933 1928 1933 3 _pl _pf _np _s _s 1928 1549 _m
_sp 1931 1549 1931 1933 1928 1933 3 _pl _pf _np _s _s 2239 1549 _m
_sp 2242 1549 2242 1933 2239 1933 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(radians)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 1547 496 1550 308 1550 3 _pl _pf _np _s _s 300 1079 _m
_sp 303 1079 303 1550 300 1550 3 _pl _pf _np _s _s 308 1079 _m
_sp 311 1079 311 1550 308 1550 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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/Symbol 600 _ff
(q)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 749 1547 749 1550 495 1550 3 _pl _pf _np _s _s 495 1079 _m
_sp 498 1079 498 1550 495 1550 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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/Times-RomanR 600 _ff
(pitch)_S 2280 5572 _m
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(angle)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 1547 1661 1550 749 1550 3 _pl _pf _np _s _s 749 1079 _m
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_s 0 g 0 0 0 0 _cw 
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(Pitch)_S 67 _t
(Euler)_S 67 _t
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(yaw.)_S 67 _t
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(Positive)_S 67 _t
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(vehicle.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 1547 1929 1550 1661 1550 3 _pl _pf _np _s _s 1661 1079 _m
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_s 0 g 0 0 0 0 _cw 
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(world)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1079 2250 1550 2247 1550 3 _pl _pf _np _s _s 1928 1547 _m
_sp 2242 1547 2242 1550 1928 1550 3 _pl _pf _np _s _s 1928 1079 _m
_sp 1931 1079 1931 1550 1928 1550 3 _pl _pf _np _s _s 2239 1079 _m
_sp 2242 1079 2242 1550 2239 1550 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(radians)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 1077 496 1080 308 1080 3 _pl _pf _np _s _s 300 696 _m
_sp 303 696 303 1080 300 1080 3 _pl _pf _np _s _s 308 696 _m
_sp 311 696 311 1080 308 1080 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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/Symbol 600 _ff
(y)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 749 1077 749 1080 495 1080 3 _pl _pf _np _s _s 495 696 _m
_sp 498 696 498 1080 495 1080 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 2330 4040 _m
/Times-RomanR 600 _ff
(yaw)_S 2280 3691 _m
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(angle)_S gsave 4 4 scale 16 _sr _s 
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_sp 1661 1077 1661 1080 749 1080 3 _pl _pf _np _s _s 749 696 _m
_sp 752 696 752 1080 749 1080 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 4040 _m
(Yaw)_S 67 _t
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(rotation)_S 67 _t
(about)_S 67 _t
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(\(depth\))_S 67 _t
(axis,)_S 67 _t
(following)_S 67 _t
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(sense)_S 67 _t
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(clockwise)_S 67 _t
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(above.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 1077 1929 1080 1661 1080 3 _pl _pf _np _s _s 1661 696 _m
_sp 1664 696 1664 1080 1661 1080 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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(world)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 696 2250 1080 2247 1080 3 _pl _pf _np _s _s 1928 1077 _m
_sp 2242 1077 2242 1080 1928 1080 3 _pl _pf _np _s _s 1928 696 _m
_sp 1931 696 1931 1080 1928 1080 3 _pl _pf _np _s _s 2239 696 _m
_sp 2242 696 2242 1080 2239 1080 3 _pl _pf _np 
_s 0 g 380 306 1932 696 _cw 

_s 0 g 0 0 0 0 _cw 
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(radians)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 692 _m
_sp 496 692 496 695 300 695 3 _pl _pf _np _s _s 300 692 _m
_sp 303 692 303 697 300 697 3 _pl _pf _np _s _s 308 692 _m
_sp 311 692 311 697 308 697 3 _pl _pf _np 
_s 0 g 1 184 312 696 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 692 _m
_sp 749 692 749 695 495 695 3 _pl _pf _np _s _s 495 692 _m
_sp 498 692 498 697 495 697 3 _pl _pf _np 
_s 0 g 1 250 499 696 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 692 _m
_sp 1661 692 1661 695 749 695 3 _pl _pf _np _s _s 749 692 _m
_sp 752 692 752 697 749 697 3 _pl _pf _np 
_s 0 g 1 908 753 696 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 692 _m
_sp 1929 692 1929 695 1661 695 3 _pl _pf _np _s _s 1661 692 _m
_sp 1664 692 1664 697 1661 697 3 _pl _pf _np 
_s 0 g 1 264 1665 696 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 692 _m
_sp 2250 692 2250 695 1928 695 3 _pl _pf _np _s _s 2247 692 _m
_sp 2250 692 2250 697 2247 697 3 _pl _pf _np _s _s 1928 692 _m
_sp 1931 692 1931 697 1928 697 3 _pl _pf _np _s _s 2239 692 _m
_sp 2242 692 2242 697 2239 697 3 _pl _pf _np 
_s 0 g 1 306 1932 696 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(125)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 496 2800 496 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 496 2996 496 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 496 2808 496 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 496 2988 496 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 184 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1615 11716 _m
/Times-BoldR 480 _ff
1357 11427 _m
(Symbol)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2800 _m
_sp 749 2800 749 2803 495 2803 3 _pl _pf _np _s _s 495 2996 _m
_sp 749 2996 749 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 498 2808 498 2991 495 2991 3 _pl _pf _np _s _s 495 2996 _m
_sp 498 2996 498 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 749 2808 749 2811 495 2811 3 _pl _pf _np _s _s 495 2988 _m
_sp 749 2988 749 2991 495 2991 3 _pl _pf _np 
_s 0 g 175 250 499 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 480 _ff
2297 11427 _m
/Times-BoldR 480 _ff
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2800 _m
_sp 1661 2800 1661 2803 749 2803 3 _pl _pf _np _s _s 749 2996 _m
_sp 1661 2996 1661 2999 749 2999 3 _pl _pf _np _s _s 749 2808 _m
_sp 752 2808 752 2991 749 2991 3 _pl _pf _np _s _s 749 2996 _m
_sp 752 2996 752 2999 749 2999 3 _pl _pf _np _s _s 749 2808 _m
_sp 1661 2808 1661 2811 749 2811 3 _pl _pf _np _s _s 749 2988 _m
_sp 1661 2988 1661 2991 749 2991 3 _pl _pf _np 
_s 0 g 175 908 753 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2800 _m
_sp 1929 2800 1929 2803 1661 2803 3 _pl _pf _np _s _s 1661 2996 _m
_sp 1929 2996 1929 2999 1661 2999 3 _pl _pf _np _s _s 1661 2808 _m
_sp 1664 2808 1664 2991 1661 2991 3 _pl _pf _np _s _s 1661 2996 _m
_sp 1664 2996 1664 2999 1661 2999 3 _pl _pf _np _s _s 1661 2808 _m
_sp 1929 2808 1929 2811 1661 2811 3 _pl _pf _np _s _s 1661 2988 _m
_sp 1929 2988 1929 2991 1661 2991 3 _pl _pf _np 
_s 0 g 175 264 1665 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6799 11716 _m
(Coordinate)_S 6955 11427 _m
(system)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 2800 _m
_sp 2242 2800 2242 2803 1928 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1928 2996 _m
_sp 2250 2996 2250 2999 1928 2999 3 _pl _pf _np _s _s 1928 2808 _m
_sp 1931 2808 1931 2991 1928 2991 3 _pl _pf _np _s _s 1928 2996 _m
_sp 1931 2996 1931 2999 1928 2999 3 _pl _pf _np _s _s 1928 2808 _m
_sp 2242 2808 2242 2811 1928 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1928 2988 _m
_sp 2242 2988 2242 2991 1928 2991 3 _pl _pf _np 
_s 0 g 175 306 1932 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8158 11427 _m
(Units)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 496 2798 496 2801 308 2801 3 _pl _pf _np _s _s 300 2671 _m
_sp 303 2671 303 2801 300 2801 3 _pl _pf _np _s _s 308 2671 _m
_sp 311 2671 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 126 184 312 2671 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1545 10816 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 35 386 2704 _cw 
_s 404 2751 _m
_sp 404 2751 405 2749 407 2748 408 2749 409 2751 408 2753 407 2754 405 2753 8 _pl _cp 
0 g _f _s _s 
0 g 401 2732 _m
_sp 401 2732 400 2730 397 2726 396 2725 395 2724 394 2724 393 2724 393 2725 392 2725 391 2724 390 2723 391 2721 392 2721 394 2721 395 2722 
396 2723 397 2723 398 2725 399 2726 400 2728 401 2729 401 2730 402 2729 402 2726 403 2724 404 2722 405 2721 406 2721 407 2721 409 2722 
410 2724 412 2726 412 2726 411 2727 409 2724 408 2724 407 2724 407 2725 406 2727 405 2730 404 2734 405 2735 407 2738 408 2740 408 2741 
409 2741 410 2741 411 2740 412 2740 412 2740 413 2741 414 2742 413 2743 411 2744 410 2744 408 2743 407 2741 405 2738 404 2737 404 2739 
403 2741 403 2743 402 2744 401 2744 399 2744 397 2743 394 2742 395 2741 396 2741 397 2742 397 2742 398 2742 399 2740 400 2738 401 2734 
75 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2798 _m
_sp 749 2798 749 2801 495 2801 3 _pl _pf _np _s _s 495 2671 _m
_sp 498 2671 498 2801 495 2801 3 _pl _pf _np 
_s 0 g 126 250 499 2671 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2286 10925 _m
/Times-RomanR 600 _ff
(x)_S 67 _t
(dot)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2798 _m
_sp 1661 2798 1661 2801 749 2801 3 _pl _pf _np _s _s 749 2671 _m
_sp 752 2671 752 2801 749 2801 3 _pl _pf _np 
_s 0 g 126 908 753 2671 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10925 _m
(Linear)_S 67 _t
(velocity)_S 67 _t
(along)_S 67 _t
(North-South)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2798 _m
_sp 1929 2798 1929 2801 1661 2801 3 _pl _pf _np _s _s 1661 2671 _m
_sp 1664 2671 1664 2801 1661 2801 3 _pl _pf _np 
_s 0 g 126 264 1665 2671 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6953 10925 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2671 _m
_sp 2250 2671 2250 2801 2247 2801 3 _pl _pf _np _s _s 1928 2798 _m
_sp 2242 2798 2242 2801 1928 2801 3 _pl _pf _np _s _s 1928 2671 _m
_sp 1931 2671 1931 2801 1928 2801 3 _pl _pf _np _s _s 2239 2671 _m
_sp 2242 2671 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 126 306 1932 2671 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8123 10925 _m
(ft/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2669 _m
_sp 496 2669 496 2672 308 2672 3 _pl _pf _np _s _s 300 2542 _m
_sp 303 2542 303 2672 300 2672 3 _pl _pf _np _s _s 308 2542 _m
_sp 311 2542 311 2672 308 2672 3 _pl _pf _np 
_s 0 g 126 184 312 2542 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1545 10299 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 64 35 386 2574 _cw 
_s 404 2621 _m
_sp 404 2621 405 2619 407 2618 408 2619 409 2621 408 2623 407 2624 405 2623 8 _pl _cp 
0 g _f _s _s 
0 g 392 2612 _m
_sp 392 2612 392 2611 393 2612 394 2612 396 2611 398 2608 398 2606 399 2603 400 2600 401 2597 401 2596 401 2594 401 2593 402 2591 400 2589 
399 2587 397 2585 395 2584 395 2584 395 2584 395 2584 394 2585 393 2585 392 2585 391 2584 390 2583 391 2582 393 2581 395 2581 396 2582 
397 2583 399 2585 400 2587 402 2589 404 2592 406 2595 407 2597 409 2601 411 2604 412 2607 413 2608 413 2610 412 2613 410 2614 409 2613 
408 2612 408 2611 409 2610 410 2609 411 2608 411 2607 410 2607 410 2606 409 2604 408 2601 407 2599 407 2598 406 2597 405 2596 405 2595 
405 2596 404 2597 404 2601 403 2604 403 2607 402 2609 401 2611 400 2612 400 2613 399 2614 70 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2669 _m
_sp 749 2669 749 2672 495 2672 3 _pl _pf _np _s _s 495 2542 _m
_sp 498 2542 498 2672 495 2672 3 _pl _pf _np 
_s 0 g 126 250 499 2542 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2286 10408 _m
/Times-RomanR 600 _ff
(y)_S 67 _t
(dot)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2669 _m
_sp 1661 2669 1661 2672 749 2672 3 _pl _pf _np _s _s 749 2542 _m
_sp 752 2542 752 2672 749 2672 3 _pl _pf _np 
_s 0 g 126 908 753 2542 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10408 _m
(Linear)_S 67 _t
(velocity)_S 67 _t
(along)_S 67 _t
(East-West)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2669 _m
_sp 1929 2669 1929 2672 1661 2672 3 _pl _pf _np _s _s 1661 2542 _m
_sp 1664 2542 1664 2672 1661 2672 3 _pl _pf _np 
_s 0 g 126 264 1665 2542 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6953 10408 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2542 _m
_sp 2250 2542 2250 2672 2247 2672 3 _pl _pf _np _s _s 1928 2669 _m
_sp 2242 2669 2242 2672 1928 2672 3 _pl _pf _np _s _s 1928 2542 _m
_sp 1931 2542 1931 2672 1928 2672 3 _pl _pf _np _s _s 2239 2542 _m
_sp 2242 2542 2242 2672 2239 2672 3 _pl _pf _np 
_s 0 g 126 306 1932 2542 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8123 10408 _m
(ft/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2539 _m
_sp 496 2539 496 2542 308 2542 3 _pl _pf _np _s _s 300 2412 _m
_sp 303 2412 303 2542 300 2542 3 _pl _pf _np _s _s 308 2412 _m
_sp 311 2412 311 2542 308 2542 3 _pl _pf _np 
_s 0 g 126 184 312 2412 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1545 9782 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 35 386 2445 _cw 
_s 403 2492 _m
_sp 403 2492 404 2490 405 2489 407 2490 408 2492 407 2494 405 2495 404 2494 8 _pl _cp 
0 g _f _s _s 
0 g 391 2463 _m
_sp 391 2463 392 2462 393 2463 394 2463 396 2463 398 2462 402 2460 404 2459 405 2459 407 2459 409 2460 410 2461 410 2462 409 2463 408 2464 
407 2464 406 2463 406 2462 406 2462 407 2461 407 2461 407 2461 406 2460 404 2461 402 2463 401 2465 399 2466 398 2466 396 2467 410 2483 
409 2484 396 2484 394 2478 395 2478 396 2480 397 2481 398 2481 401 2481 406 2481 394 2467 393 2465 41 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2539 _m
_sp 749 2539 749 2542 495 2542 3 _pl _pf _np _s _s 495 2412 _m
_sp 498 2412 498 2542 495 2542 3 _pl _pf _np 
_s 0 g 126 250 499 2412 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2291 9891 _m
/Times-RomanR 600 _ff
(z)_S 67 _t
(dot)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2539 _m
_sp 1661 2539 1661 2542 749 2542 3 _pl _pf _np _s _s 749 2412 _m
_sp 752 2412 752 2542 749 2542 3 _pl _pf _np 
_s 0 g 126 908 753 2412 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 9891 _m
(Linear)_S 67 _t
(velocity)_S 67 _t
(along)_S 67 _t
(Depth)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2539 _m
_sp 1929 2539 1929 2542 1661 2542 3 _pl _pf _np _s _s 1661 2412 _m
_sp 1664 2412 1664 2542 1661 2542 3 _pl _pf _np 
_s 0 g 126 264 1665 2412 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6953 9891 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2412 _m
_sp 2250 2412 2250 2542 2247 2542 3 _pl _pf _np _s _s 1928 2539 _m
_sp 2242 2539 2242 2542 1928 2542 3 _pl _pf _np _s _s 1928 2412 _m
_sp 1931 2412 1931 2542 1928 2542 3 _pl _pf _np _s _s 2239 2412 _m
_sp 2242 2412 2242 2542 2239 2542 3 _pl _pf _np 
_s 0 g 126 306 1932 2412 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8123 9891 _m
(ft/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2410 _m
_sp 496 2410 496 2413 308 2413 3 _pl _pf _np _s _s 300 2203 _m
_sp 303 2203 303 2413 300 2413 3 _pl _pf _np _s _s 308 2203 _m
_sp 311 2203 311 2413 308 2413 3 _pl _pf _np 
_s 0 g 206 184 312 2203 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1530 9221 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 74 43 382 2305 _cw 
_s 400 2363 _m
_sp 400 2363 401 2361 403 2360 405 2361 406 2363 405 2365 403 2366 401 2365 8 _pl _cp 
0 g _f _s _s 
0 g 405 2346 _m
_sp 405 2346 405 2349 405 2351 406 2352 406 2353 406 2353 405 2355 403 2356 401 2355 400 2354 400 2353 400 2352 401 2351 401 2349 401 2347 
401 2346 398 2345 396 2344 395 2343 393 2342 392 2340 390 2338 389 2336 389 2333 390 2329 391 2326 394 2324 397 2322 401 2322 401 2313 
405 2313 405 2322 409 2322 412 2324 414 2327 416 2330 416 2334 416 2338 414 2341 412 2343 409 2345 41 _pl _cp 401 2344 _m
_sp 401 2344 401 2323 398 2324 396 2327 395 2329 394 2333 394 2337 396 2340 398 2343 9 _pl _cp 405 2344 _m
_sp 405 2344 408 2343 410 2341 411 2338 412 2334 412 2330 410 2327 408 2324 405 2323 9 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2410 _m
_sp 749 2410 749 2413 495 2413 3 _pl _pf _np _s _s 495 2203 _m
_sp 498 2203 498 2413 495 2413 3 _pl _pf _np 
_s 0 g 206 250 499 2203 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2208 9374 _m
/Times-RomanR 600 _ff
(phi)_S 67 _t
(dot)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2410 _m
_sp 1661 2410 1661 2413 749 2413 3 _pl _pf _np _s _s 749 2203 _m
_sp 752 2203 752 2413 749 2413 3 _pl _pf _np 
_s 0 g 206 908 753 2203 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 9374 _m
(Roll)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rate)_S 67 _t
(component,)_S 67 _t
(about)_S 3112 9024 _m
(North-South)_S 67 _t
(axis.)_S 134 _t
_U (Not)_S _u 67 _t
(equivalent)_S 67 _t
(to)_S 67 _t
/Times-BoldItalicR 600 _ff
(p)_S /Times-RomanR 600 _ff
(.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2410 _m
_sp 1929 2410 1929 2413 1661 2413 3 _pl _pf _np _s _s 1661 2203 _m
_sp 1664 2203 1664 2413 1661 2413 3 _pl _pf _np 
_s 0 g 206 264 1665 2203 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6953 9374 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2203 _m
_sp 2250 2203 2250 2413 2247 2413 3 _pl _pf _np _s _s 1928 2410 _m
_sp 2242 2410 2242 2413 1928 2413 3 _pl _pf _np _s _s 1928 2203 _m
_sp 1931 2203 1931 2413 1928 2413 3 _pl _pf _np _s _s 2239 2203 _m
_sp 2242 2203 2242 2413 2239 2413 3 _pl _pf _np 
_s 0 g 206 306 1932 2203 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7896 9374 _m
(radians/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2201 _m
_sp 496 2201 496 2204 308 2204 3 _pl _pf _np _s _s 300 1994 _m
_sp 303 1994 303 2204 300 2204 3 _pl _pf _np _s _s 308 1994 _m
_sp 311 1994 311 2204 308 2204 3 _pl _pf _np 
_s 0 g 206 184 312 1994 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1538 8385 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 74 38 384 2096 _cw 
_s 400 2154 _m
_sp 400 2154 401 2152 403 2151 405 2152 406 2154 405 2156 403 2157 401 2156 8 _pl _cp 
0 g _f _s _s 
0 g 413 2132 _m
_sp 413 2132 413 2137 411 2142 409 2144 406 2146 403 2147 400 2147 398 2146 396 2144 394 2141 393 2139 393 2136 392 2133 392 2129 392 2123 
394 2119 396 2115 399 2114 402 2113 405 2113 407 2114 409 2116 411 2118 412 2120 413 2123 413 2126 413 2130 413 2131 28 _pl _cp 397 2133 _m
_sp 397 2133 397 2136 397 2138 398 2141 399 2143 401 2144 402 2145 405 2144 407 2142 408 2138 409 2133 11 _pl _cp 409 2131 _m
_sp 409 2131 409 2129 409 2127 409 2125 409 2124 408 2120 407 2117 405 2115 403 2114 401 2115 399 2117 398 2120 397 2124 397 2130 397 2130 
397 2131 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2201 _m
_sp 749 2201 749 2204 495 2204 3 _pl _pf _np _s _s 495 1994 _m
_sp 498 1994 498 2204 495 2204 3 _pl _pf _np 
_s 0 g 206 250 499 1994 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2141 8538 _m
/Times-RomanR 600 _ff
(theta)_S 67 _t
(dot)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2201 _m
_sp 1661 2201 1661 2204 749 2204 3 _pl _pf _np _s _s 749 1994 _m
_sp 752 1994 752 2204 749 2204 3 _pl _pf _np 
_s 0 g 206 908 753 1994 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 8538 _m
(Pitch)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rate)_S 67 _t
(component,)_S 67 _t
(about)_S 3112 8188 _m
(East-West)_S 67 _t
(axis.)_S 134 _t
_U (Not)_S _u 67 _t
(equivalent)_S 67 _t
(to)_S 67 _t
/Times-BoldItalicR 600 _ff
(q)_S /Times-RomanR 600 _ff
(.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2201 _m
_sp 1929 2201 1929 2204 1661 2204 3 _pl _pf _np _s _s 1661 1994 _m
_sp 1664 1994 1664 2204 1661 2204 3 _pl _pf _np 
_s 0 g 206 264 1665 1994 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6953 8538 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1994 _m
_sp 2250 1994 2250 2204 2247 2204 3 _pl _pf _np _s _s 1928 2201 _m
_sp 2242 2201 2242 2204 1928 2204 3 _pl _pf _np _s _s 1928 1994 _m
_sp 1931 1994 1931 2204 1928 2204 3 _pl _pf _np _s _s 2239 1994 _m
_sp 2242 1994 2242 2204 2239 2204 3 _pl _pf _np 
_s 0 g 206 306 1932 1994 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7896 8538 _m
(radians/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1992 _m
_sp 496 1992 496 1995 308 1995 3 _pl _pf _np _s _s 300 1785 _m
_sp 303 1785 303 1995 300 1995 3 _pl _pf _np _s _s 308 1785 _m
_sp 311 1785 311 1995 308 1995 3 _pl _pf _np 
_s 0 g 206 184 312 1785 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1519 7506 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 85 48 379 1876 _cw 
_s 400 1932 _m
_sp 400 1932 401 1930 404 1929 406 1930 407 1932 406 1934 404 1935 401 1934 8 _pl _cp 
0 g _f _s _s 
0 g 401 1923 _m
_sp 401 1923 401 1895 399 1895 397 1897 396 1899 396 1903 396 1915 393 1915 391 1915 390 1915 388 1915 388 1913 389 1913 389 1913 391 1912 
392 1910 392 1909 392 1903 392 1901 392 1899 392 1897 393 1896 395 1895 396 1894 398 1893 401 1893 401 1883 405 1883 405 1893 409 1894 
411 1895 413 1898 413 1903 413 1909 414 1912 416 1913 416 1913 416 1913 417 1913 417 1913 417 1915 415 1915 413 1915 412 1915 410 1915 
410 1903 410 1900 409 1897 407 1896 405 1895 405 1923 51 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1992 _m
_sp 749 1992 749 1995 495 1995 3 _pl _pf _np _s _s 495 1785 _m
_sp 498 1785 498 1995 495 1995 3 _pl _pf _np 
_s 0 g 206 250 499 1785 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2219 7702 _m
/Times-RomanR 600 _ff
(psi)_S 67 _t
(dot)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1992 _m
_sp 1661 1992 1661 1995 749 1995 3 _pl _pf _np _s _s 749 1785 _m
_sp 752 1785 752 1995 749 1995 3 _pl _pf _np 
_s 0 g 206 908 753 1785 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 7702 _m
(Yaw)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rate)_S 67 _t
(component,)_S 67 _t
(about)_S 3112 7352 _m
(vertical)_S 67 _t
(\(depth\))_S 67 _t
(axis.)_S 67 _t
_U (Not)_S _u 67 _t
(equivalent)_S 67 _t
(to)_S 67 _t
/Times-BoldItalicR 600 _ff
(r)_S /Times-RomanR 600 _ff
(.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1992 _m
_sp 1929 1992 1929 1995 1661 1995 3 _pl _pf _np _s _s 1661 1785 _m
_sp 1664 1785 1664 1995 1661 1995 3 _pl _pf _np 
_s 0 g 206 264 1665 1785 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6953 7702 _m
(world)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1785 _m
_sp 2250 1785 2250 1995 2247 1995 3 _pl _pf _np _s _s 1928 1992 _m
_sp 2242 1992 2242 1995 1928 1995 3 _pl _pf _np _s _s 1928 1785 _m
_sp 1931 1785 1931 1995 1928 1995 3 _pl _pf _np _s _s 2239 1785 _m
_sp 2242 1785 2242 1995 2239 1995 3 _pl _pf _np 
_s 0 g 206 306 1932 1785 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7896 7702 _m
(radians/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1783 _m
_sp 496 1783 496 1786 308 1786 3 _pl _pf _np _s _s 300 1664 _m
_sp 303 1664 303 1786 300 1786 3 _pl _pf _np _s _s 308 1664 _m
_sp 311 1664 311 1786 308 1786 3 _pl _pf _np 
_s 0 g 118 184 312 1664 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1559 6865 _m
/Times-BoldItalicR 600 _ff
(u)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1783 _m
_sp 749 1783 749 1786 495 1786 3 _pl _pf _np _s _s 495 1664 _m
_sp 498 1664 498 1786 495 1786 3 _pl _pf _np 
_s 0 g 118 250 499 1664 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2280 6866 _m
/Times-RomanR 600 _ff
(surge)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1783 _m
_sp 1661 1783 1661 1786 749 1786 3 _pl _pf _np _s _s 749 1664 _m
_sp 752 1664 752 1786 749 1786 3 _pl _pf _np 
_s 0 g 118 908 753 1664 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 6866 _m
(Linear)_S 67 _t
(velocity)_S 67 _t
(along)_S 67 _t
(longitudinal)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1783 _m
_sp 1929 1783 1929 1786 1661 1786 3 _pl _pf _np _s _s 1661 1664 _m
_sp 1664 1664 1664 1786 1661 1786 3 _pl _pf _np 
_s 0 g 118 264 1665 1664 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 6866 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1664 _m
_sp 2250 1664 2250 1786 2247 1786 3 _pl _pf _np _s _s 1928 1783 _m
_sp 2242 1783 2242 1786 1928 1786 3 _pl _pf _np _s _s 1928 1664 _m
_sp 1931 1664 1931 1786 1928 1786 3 _pl _pf _np _s _s 2239 1664 _m
_sp 2242 1664 2242 1786 2239 1786 3 _pl _pf _np 
_s 0 g 118 306 1932 1664 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8123 6866 _m
(ft/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1662 _m
_sp 496 1662 496 1665 308 1665 3 _pl _pf _np _s _s 300 1456 _m
_sp 303 1456 303 1665 300 1665 3 _pl _pf _np _s _s 308 1456 _m
_sp 311 1456 311 1665 308 1665 3 _pl _pf _np 
_s 0 g 205 184 312 1456 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1571 6380 _m
/Times-BoldItalicR 600 _ff
(v)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1662 _m
_sp 749 1662 749 1665 495 1665 3 _pl _pf _np _s _s 495 1456 _m
_sp 498 1456 498 1665 495 1665 3 _pl _pf _np 
_s 0 g 205 250 499 1456 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2292 6381 _m
/Times-RomanR 600 _ff
(sway)_S 2125 6032 _m
(\(sideslip\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1662 _m
_sp 1661 1662 1661 1665 749 1665 3 _pl _pf _np _s _s 749 1456 _m
_sp 752 1456 752 1665 749 1665 3 _pl _pf _np 
_s 0 g 205 908 753 1456 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 6381 _m
(Linear)_S 67 _t
(velocity)_S 67 _t
(along)_S 67 _t
(lateral)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1662 _m
_sp 1929 1662 1929 1665 1661 1665 3 _pl _pf _np _s _s 1661 1456 _m
_sp 1664 1456 1664 1665 1661 1665 3 _pl _pf _np 
_s 0 g 205 264 1665 1456 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 6381 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1456 _m
_sp 2250 1456 2250 1665 2247 1665 3 _pl _pf _np _s _s 1928 1662 _m
_sp 2242 1662 2242 1665 1928 1665 3 _pl _pf _np _s _s 1928 1456 _m
_sp 1931 1456 1931 1665 1928 1665 3 _pl _pf _np _s _s 2239 1456 _m
_sp 2242 1456 2242 1665 2239 1665 3 _pl _pf _np 
_s 0 g 205 306 1932 1456 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8123 6381 _m
(ft/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1453 _m
_sp 496 1453 496 1456 308 1456 3 _pl _pf _np _s _s 300 1334 _m
_sp 303 1334 303 1456 300 1456 3 _pl _pf _np _s _s 308 1334 _m
_sp 311 1334 311 1456 308 1456 3 _pl _pf _np 
_s 0 g 118 184 312 1334 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1548 5546 _m
/Times-BoldItalicR 600 _ff
(w)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1453 _m
_sp 749 1453 749 1456 495 1456 3 _pl _pf _np _s _s 495 1334 _m
_sp 498 1334 498 1456 495 1456 3 _pl _pf _np 
_s 0 g 118 250 499 1334 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2264 5547 _m
/Times-RomanR 600 _ff
(heave)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1453 _m
_sp 1661 1453 1661 1456 749 1456 3 _pl _pf _np _s _s 749 1334 _m
_sp 752 1334 752 1456 749 1456 3 _pl _pf _np 
_s 0 g 118 908 753 1334 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 5547 _m
(Linear)_S 67 _t
(velocity)_S 67 _t
(along)_S 67 _t
(vertical)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1453 _m
_sp 1929 1453 1929 1456 1661 1456 3 _pl _pf _np _s _s 1661 1334 _m
_sp 1664 1334 1664 1456 1661 1456 3 _pl _pf _np 
_s 0 g 118 264 1665 1334 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 5547 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1334 _m
_sp 2250 1334 2250 1456 2247 1456 3 _pl _pf _np _s _s 1928 1453 _m
_sp 2242 1453 2242 1456 1928 1456 3 _pl _pf _np _s _s 1928 1334 _m
_sp 1931 1334 1931 1456 1928 1456 3 _pl _pf _np _s _s 2239 1334 _m
_sp 2242 1334 2242 1456 2239 1456 3 _pl _pf _np 
_s 0 g 118 306 1932 1334 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8123 5547 _m
(ft/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1332 _m
_sp 496 1332 496 1335 308 1335 3 _pl _pf _np _s _s 300 1068 _m
_sp 303 1068 303 1335 300 1335 3 _pl _pf _np _s _s 308 1068 _m
_sp 311 1068 311 1335 308 1335 3 _pl _pf _np 
_s 0 g 263 184 312 1068 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1565 5061 _m
/Times-BoldItalicR 600 _ff
(p)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1332 _m
_sp 749 1332 749 1335 495 1335 3 _pl _pf _np _s _s 495 1068 _m
_sp 498 1068 498 1335 495 1335 3 _pl _pf _np 
_s 0 g 263 250 499 1068 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2175 5062 _m
/Times-RomanR 600 _ff
(roll)_S 67 _t
(rate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1332 _m
_sp 1661 1332 1661 1335 749 1335 3 _pl _pf _np _s _s 749 1068 _m
_sp 752 1068 752 1335 749 1335 3 _pl _pf _np 
_s 0 g 263 908 753 1068 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 5062 _m
(Angular)_S 67 _t
(velocity)_S 67 _t
(component)_S 67 _t
(about)_S 3112 4560 _m
(longitudinal)_S 67 _t
(axis.)_S 134 _t
_U (Not)_S _u 67 _t
(equivalent)_S 67 _t
(to)_S 67 _t
6142 4500 _m
6313 4560 _m
(.)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 74 43 1535 1125 _cw 
_s 1553 1183 _m
_sp 1553 1183 1554 1181 1556 1180 1558 1181 1559 1183 1558 1185 1556 1186 1554 1185 8 _pl _cp 
0 g _f _s _s 
0 g 1558 1166 _m
_sp 1558 1166 1558 1169 1558 1171 1559 1172 1559 1173 1559 1173 1558 1175 1556 1176 1554 1175 1553 1174 1553 1173 1553 1172 1554 1171 1554 1169 1554 1167 
1554 1166 1551 1165 1549 1164 1548 1163 1546 1162 1545 1160 1543 1158 1542 1156 1542 1153 1543 1149 1544 1146 1547 1144 1550 1142 1554 1142 1554 1133 
1558 1133 1558 1142 1562 1143 1565 1144 1567 1147 1568 1150 1569 1154 1568 1158 1567 1161 1565 1163 1562 1165 41 _pl _cp 1554 1164 _m
_sp 1554 1164 1554 1143 1551 1144 1549 1147 1548 1149 1547 1153 1547 1157 1549 1160 1551 1163 9 _pl _cp 1558 1164 _m
_sp 1558 1164 1561 1163 1563 1161 1564 1158 1565 1154 1565 1150 1563 1147 1561 1144 1558 1143 9 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1332 _m
_sp 1929 1332 1929 1335 1661 1335 3 _pl _pf _np _s _s 1661 1068 _m
_sp 1664 1068 1664 1335 1661 1335 3 _pl _pf _np 
_s 0 g 263 264 1665 1068 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 5062 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1068 _m
_sp 2250 1068 2250 1335 2247 1335 3 _pl _pf _np _s _s 1928 1332 _m
_sp 2242 1332 2242 1335 1928 1335 3 _pl _pf _np _s _s 1928 1068 _m
_sp 1931 1068 1931 1335 1928 1335 3 _pl _pf _np _s _s 2239 1068 _m
_sp 2242 1068 2242 1335 2239 1335 3 _pl _pf _np 
_s 0 g 263 306 1932 1068 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7896 5062 _m
(radians/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1066 _m
_sp 496 1066 496 1069 308 1069 3 _pl _pf _np _s _s 300 802 _m
_sp 303 802 303 1069 300 1069 3 _pl _pf _np _s _s 308 802 _m
_sp 311 802 311 1069 308 1069 3 _pl _pf _np 
_s 0 g 263 184 312 802 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1565 3997 _m
/Times-BoldItalicR 600 _ff
(q)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1066 _m
_sp 749 1066 749 1069 495 1069 3 _pl _pf _np _s _s 495 802 _m
_sp 498 802 498 1069 495 1069 3 _pl _pf _np 
_s 0 g 263 250 499 802 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2114 3998 _m
/Times-RomanR 600 _ff
(pitch)_S 67 _t
(rate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1066 _m
_sp 1661 1066 1661 1069 749 1069 3 _pl _pf _np _s _s 749 802 _m
_sp 752 802 752 1069 749 1069 3 _pl _pf _np 
_s 0 g 263 908 753 802 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 3998 _m
(Angular)_S 67 _t
(velocity)_S 67 _t
(component)_S 67 _t
(about)_S 3112 3496 _m
(lateral)_S 67 _t
(axis.)_S 134 _t
_U (Not)_S _u 67 _t
(equivalent)_S 67 _t
(to)_S 67 _t
5675 3424 _m
5829 3496 _m
(.)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 74 39 1418 856 _cw 
_s 1434 914 _m
_sp 1434 914 1435 912 1437 911 1439 912 1440 914 1439 916 1437 917 1435 916 8 _pl _cp 
0 g _f _s _s 
0 g 1447 892 _m
_sp 1447 892 1446 897 1445 902 1443 905 1440 906 1437 907 1434 907 1432 906 1430 904 1428 901 1427 899 1427 896 1426 893 1426 889 1426 883 
1428 879 1430 875 1433 874 1436 873 1439 873 1441 874 1443 876 1445 878 1446 880 1447 883 1447 886 1447 890 1447 891 28 _pl _cp 1431 893 _m
_sp 1431 893 1431 896 1431 898 1432 901 1433 903 1435 904 1436 905 1439 904 1441 902 1442 898 1443 893 11 _pl _cp 1443 891 _m
_sp 1443 891 1443 889 1443 887 1443 885 1443 884 1442 880 1441 877 1439 875 1437 874 1435 875 1433 877 1432 880 1431 884 1431 890 1431 890 
1431 891 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1066 _m
_sp 1929 1066 1929 1069 1661 1069 3 _pl _pf _np _s _s 1661 802 _m
_sp 1664 802 1664 1069 1661 1069 3 _pl _pf _np 
_s 0 g 263 264 1665 802 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 3998 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 802 _m
_sp 2250 802 2250 1069 2247 1069 3 _pl _pf _np _s _s 1928 1066 _m
_sp 2242 1066 2242 1069 1928 1069 3 _pl _pf _np _s _s 1928 802 _m
_sp 1931 802 1931 1069 1928 1069 3 _pl _pf _np _s _s 2239 802 _m
_sp 2242 802 2242 1069 2239 1069 3 _pl _pf _np 
_s 0 g 263 306 1932 802 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7896 3998 _m
(radians/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 800 _m
_sp 496 800 496 803 308 803 3 _pl _pf _np _s _s 300 520 _m
_sp 303 520 303 803 300 803 3 _pl _pf _np _s _s 308 520 _m
_sp 311 520 311 803 308 803 3 _pl _pf _np 
_s 0 g 279 184 312 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1576 2933 _m
/Times-BoldItalicR 600 _ff
(r)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 800 _m
_sp 749 800 749 803 495 803 3 _pl _pf _np _s _s 495 520 _m
_sp 498 520 498 803 495 803 3 _pl _pf _np 
_s 0 g 279 250 499 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2147 2934 _m
/Times-RomanR 600 _ff
(yaw)_S 67 _t
(rate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 800 _m
_sp 1661 800 1661 803 749 803 3 _pl _pf _np _s _s 749 520 _m
_sp 752 520 752 803 749 803 3 _pl _pf _np 
_s 0 g 279 908 753 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 2934 _m
(Angular)_S 67 _t
(velocity)_S 67 _t
(component)_S 67 _t
(about)_S 3112 2389 _m
(vertical)_S 67 _t
(axis.)_S 134 _t
_U (Not)_S _u 67 _t
(equivalent)_S 67 _t
(to)_S 67 _t
5775 2329 _m
5967 2389 _m
(.)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 85 48 1443 582 _cw 
_s 1464 638 _m
_sp 1464 638 1465 636 1468 635 1470 636 1471 638 1470 640 1468 641 1465 640 8 _pl _cp 
0 g _f _s _s 
0 g 1465 629 _m
_sp 1465 629 1465 601 1463 601 1461 603 1460 605 1460 609 1460 621 1457 621 1455 621 1454 621 1452 621 1452 619 1453 619 1453 619 1455 618 
1456 616 1456 615 1456 609 1456 607 1456 605 1456 603 1457 602 1459 601 1460 600 1462 599 1465 599 1465 589 1469 589 1469 599 1473 600 
1475 601 1477 604 1477 609 1477 615 1478 618 1480 619 1480 619 1480 619 1481 619 1481 619 1481 621 1479 621 1477 621 1476 621 1474 621 
1474 609 1474 606 1473 603 1471 602 1469 601 1469 629 51 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 800 _m
_sp 1929 800 1929 803 1661 803 3 _pl _pf _np _s _s 1661 520 _m
_sp 1664 520 1664 803 1661 803 3 _pl _pf _np 
_s 0 g 279 264 1665 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 2934 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 520 _m
_sp 2250 520 2250 803 2247 803 3 _pl _pf _np _s _s 1928 800 _m
_sp 2242 800 2242 803 1928 803 3 _pl _pf _np _s _s 1928 520 _m
_sp 1931 520 1931 803 1928 803 3 _pl _pf _np _s _s 2239 520 _m
_sp 2242 520 2242 803 2239 803 3 _pl _pf _np 
_s 0 g 279 306 1932 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7896 2934 _m
(radians/sec)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 516 _m
_sp 496 516 496 519 300 519 3 _pl _pf _np _s _s 300 516 _m
_sp 303 516 303 521 300 521 3 _pl _pf _np _s _s 308 516 _m
_sp 311 516 311 521 308 521 3 _pl _pf _np 
_s 0 g 1 184 312 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 516 _m
_sp 749 516 749 519 495 519 3 _pl _pf _np _s _s 495 516 _m
_sp 498 516 498 521 495 521 3 _pl _pf _np 
_s 0 g 1 250 499 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 516 _m
_sp 1661 516 1661 519 749 519 3 _pl _pf _np _s _s 749 516 _m
_sp 752 516 752 521 749 521 3 _pl _pf _np 
_s 0 g 1 908 753 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 516 _m
_sp 1929 516 1929 519 1661 519 3 _pl _pf _np _s _s 1661 516 _m
_sp 1664 516 1664 521 1661 521 3 _pl _pf _np 
_s 0 g 1 264 1665 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 516 _m
_sp 2250 516 2250 519 1928 519 3 _pl _pf _np _s _s 2247 516 _m
_sp 2250 516 2250 521 2247 521 3 _pl _pf _np _s _s 1928 516 _m
_sp 1931 516 1931 521 1928 521 3 _pl _pf _np _s _s 2239 516 _m
_sp 2242 516 2242 521 2239 521 3 _pl _pf _np 
_s 0 g 1 306 1932 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(126)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 496 2800 496 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 496 2996 496 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 496 2808 496 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 496 2988 496 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 184 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1615 11716 _m
/Times-BoldR 480 _ff
1357 11427 _m
(Symbol)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2800 _m
_sp 749 2800 749 2803 495 2803 3 _pl _pf _np _s _s 495 2996 _m
_sp 749 2996 749 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 498 2808 498 2991 495 2991 3 _pl _pf _np _s _s 495 2996 _m
_sp 498 2996 498 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
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gsave 4 4 scale 16 _sr 
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(radians/sec)_S /Times-RomanR 360 _ff
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gsave 4 4 scale 16 _sr _s 
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gsave 4 4 scale 16 _sr 
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399 1887 400 1887 401 1888 403 1889 404 1891 406 1893 403 1882 402 1879 400 1878 398 1878 398 1877 410 1877 410 1878 408 1878 407 1879 
406 1880 407 1881 407 1882 414 1909 410 1909 35 _pl _cp 396 1893 _m
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399 1903 397 1900 396 1897 396 1894 396 1894 20 _pl _cp 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1471 5764 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 72 367 1441 _cw 
_s 394 1499 _m
_sp 394 1499 392 1501 390 1502 388 1503 387 1504 385 1504 382 1503 381 1500 381 1498 383 1496 384 1494 387 1492 383 1491 380 1489 378 1485 
377 1480 378 1476 380 1473 383 1471 387 1470 391 1471 394 1473 396 1477 397 1481 397 1484 396 1486 395 1488 394 1489 392 1491 390 1493 
388 1494 387 1495 385 1496 384 1497 384 1499 383 1500 384 1501 385 1501 386 1501 387 1500 388 1499 390 1498 392 1496 43 _pl _cp 393 1481 _m
_sp 393 1481 392 1477 391 1474 389 1473 387 1472 384 1473 383 1474 381 1477 381 1481 381 1485 383 1487 384 1489 387 1490 390 1489 392 1488 
393 1485 16 _pl _cp 
0 g _f _s _s 
0 g 404 1454 _m
_sp 404 1454 407 1454 408 1457 408 1459 409 1460 410 1463 411 1465 412 1466 413 1467 413 1467 414 1466 414 1466 415 1465 416 1466 416 1467 
416 1468 415 1469 414 1469 412 1468 411 1466 410 1464 410 1464 409 1463 411 1469 405 1468 405 1468 406 1468 407 1468 407 1467 407 1466 
407 1465 31 _pl _cp 
0 g _f _s _s 
0 g 423 1465 _m
_sp 423 1465 426 1477 420 1476 420 1476 421 1476 422 1476 422 1475 422 1474 422 1473 418 1457 417 1456 417 1456 417 1456 417 1455 418 1455 
420 1454 422 1454 424 1454 426 1455 427 1456 429 1457 430 1459 431 1461 432 1463 432 1465 431 1468 429 1469 428 1469 427 1469 425 1467 
30 _pl _cp 420 1456 _m
_sp 420 1456 421 1455 422 1455 424 1455 426 1457 427 1459 428 1461 429 1463 429 1465 429 1466 427 1467 426 1467 424 1466 423 1464 422 1462 
421 1460 421 1458 420 1457 18 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 1547 _m
_sp 749 1547 749 1550 495 1550 3 _pl _pf _np _s _s 495 991 _m
_sp 498 991 498 1550 495 1550 3 _pl _pf _np 
_s 0 g 555 250 499 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2325 5921 _m
/Times-RomanR 600 _ff
(bow)_S 2197 5572 _m
(rudders)_S 2280 5223 _m
(angle)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1547 _m
_sp 1661 1547 1661 1550 749 1550 3 _pl _pf _np _s _s 749 991 _m
_sp 752 991 752 1550 749 1550 3 _pl _pf _np 
_s 0 g 555 908 753 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 5921 _m
(Bow)_S 67 _t
(rudder)_S 67 _t
(deflection)_S 67 _t
(angle.)_S 134 _t
(Usually)_S 3112 5572 _m
(bow)_S 67 _t
(and)_S 67 _t
(stern)_S 67 _t
(rudders)_S 67 _t
(orders)_S 67 _t
(go)_S 67 _t
(to)_S 3112 5223 _m
(exactly)_S 67 _t
(opposite)_S 67 _t
(positions.)_S 134 _t
(Positive)_S 3112 4874 _m
(sense)_S 67 _t
(is)_S 67 _t
(clockwise)_S 67 _t
(as)_S 67 _t
(seen)_S 67 _t
(from)_S 67 _t
(above.)_S 67 _t
3112 4525 _m
(Positive)_S 67 _t
(bow)_S 67 _t
(rudders)_S 67 _t
(angle)_S 67 _t
(with)_S 67 _t
(positive)_S 3112 4175 _m
(surge)_S 67 _t
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
67 _t
(produces)_S 67 _t
(positive)_S 67 _t
(change)_S 67 _t
(in)_S 67 _t
(yaw.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1547 _m
_sp 1929 1547 1929 1550 1661 1550 3 _pl _pf _np _s _s 1661 991 _m
_sp 1664 991 1664 1550 1661 1550 3 _pl _pf _np 
_s 0 g 555 264 1665 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 5921 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 991 _m
_sp 2250 991 2250 1550 2247 1550 3 _pl _pf _np _s _s 1928 1547 _m
_sp 2242 1547 2242 1550 1928 1550 3 _pl _pf _np _s _s 1928 991 _m
_sp 1931 991 1931 1550 1928 1550 3 _pl _pf _np _s _s 2239 991 _m
_sp 2242 991 2242 1550 2239 1550 3 _pl _pf _np 
_s 0 g 555 306 1932 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8051 5921 _m
(radians)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 987 _m
_sp 496 987 496 990 300 990 3 _pl _pf _np _s _s 300 987 _m
_sp 303 987 303 992 300 992 3 _pl _pf _np _s _s 308 987 _m
_sp 311 987 311 992 308 992 3 _pl _pf _np 
_s 0 g 1 184 312 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 987 _m
_sp 749 987 749 990 495 990 3 _pl _pf _np _s _s 495 987 _m
_sp 498 987 498 992 495 992 3 _pl _pf _np 
_s 0 g 1 250 499 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 987 _m
_sp 1661 987 1661 990 749 990 3 _pl _pf _np _s _s 749 987 _m
_sp 752 987 752 992 749 992 3 _pl _pf _np 
_s 0 g 1 908 753 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 987 _m
_sp 1929 987 1929 990 1661 990 3 _pl _pf _np _s _s 1661 987 _m
_sp 1664 987 1664 992 1661 992 3 _pl _pf _np 
_s 0 g 1 264 1665 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 987 _m
_sp 2250 987 2250 990 1928 990 3 _pl _pf _np _s _s 2247 987 _m
_sp 2250 987 2250 992 2247 992 3 _pl _pf _np _s _s 1928 987 _m
_sp 1931 987 1931 992 1928 992 3 _pl _pf _np _s _s 2239 987 _m
_sp 2242 987 2242 992 2239 992 3 _pl _pf _np 
_s 0 g 1 306 1932 991 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(127)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 496 2800 496 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 496 2996 496 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 496 2808 496 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 496 2988 496 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 184 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1615 11716 _m
/Times-BoldR 480 _ff
1357 11427 _m
(Symbol)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2800 _m
_sp 749 2800 749 2803 495 2803 3 _pl _pf _np _s _s 495 2996 _m
_sp 749 2996 749 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 498 2808 498 2991 495 2991 3 _pl _pf _np _s _s 495 2996 _m
_sp 498 2996 498 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 749 2808 749 2811 495 2811 3 _pl _pf _np _s _s 495 2988 _m
_sp 749 2988 749 2991 495 2991 3 _pl _pf _np 
_s 0 g 175 250 499 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 480 _ff
2297 11427 _m
/Times-BoldR 480 _ff
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2800 _m
_sp 1661 2800 1661 2803 749 2803 3 _pl _pf _np _s _s 749 2996 _m
_sp 1661 2996 1661 2999 749 2999 3 _pl _pf _np _s _s 749 2808 _m
_sp 752 2808 752 2991 749 2991 3 _pl _pf _np _s _s 749 2996 _m
_sp 752 2996 752 2999 749 2999 3 _pl _pf _np _s _s 749 2808 _m
_sp 1661 2808 1661 2811 749 2811 3 _pl _pf _np _s _s 749 2988 _m
_sp 1661 2988 1661 2991 749 2991 3 _pl _pf _np 
_s 0 g 175 908 753 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2800 _m
_sp 1929 2800 1929 2803 1661 2803 3 _pl _pf _np _s _s 1661 2996 _m
_sp 1929 2996 1929 2999 1661 2999 3 _pl _pf _np _s _s 1661 2808 _m
_sp 1664 2808 1664 2991 1661 2991 3 _pl _pf _np _s _s 1661 2996 _m
_sp 1664 2996 1664 2999 1661 2999 3 _pl _pf _np _s _s 1661 2808 _m
_sp 1929 2808 1929 2811 1661 2811 3 _pl _pf _np _s _s 1661 2988 _m
_sp 1929 2988 1929 2991 1661 2991 3 _pl _pf _np 
_s 0 g 175 264 1665 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6799 11716 _m
(Coordinate)_S 6955 11427 _m
(system)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 2800 _m
_sp 2242 2800 2242 2803 1928 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1928 2996 _m
_sp 2250 2996 2250 2999 1928 2999 3 _pl _pf _np _s _s 1928 2808 _m
_sp 1931 2808 1931 2991 1928 2991 3 _pl _pf _np _s _s 1928 2996 _m
_sp 1931 2996 1931 2999 1928 2999 3 _pl _pf _np _s _s 1928 2808 _m
_sp 2242 2808 2242 2811 1928 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1928 2988 _m
_sp 2242 2988 2242 2991 1928 2991 3 _pl _pf _np 
_s 0 g 175 306 1932 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8158 11427 _m
(Units)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 496 2798 496 2801 308 2801 3 _pl _pf _np _s _s 300 2242 _m
_sp 303 2242 303 2801 300 2801 3 _pl _pf _np _s _s 308 2242 _m
_sp 311 2242 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 555 184 312 2242 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1479 10768 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 68 369 2692 _cw 
_s 396 2750 _m
_sp 396 2750 394 2752 392 2753 390 2754 389 2755 387 2755 384 2754 383 2751 383 2749 385 2747 386 2745 389 2743 385 2742 382 2740 380 2736 
379 2731 380 2727 382 2724 385 2722 389 2721 393 2722 396 2724 398 2728 399 2732 399 2735 398 2737 397 2739 396 2740 394 2742 392 2744 
390 2745 389 2746 387 2747 386 2748 386 2750 385 2751 386 2752 387 2752 388 2752 389 2751 390 2750 392 2749 394 2747 43 _pl _cp 395 2732 _m
_sp 395 2732 394 2728 393 2725 391 2724 389 2723 386 2724 385 2725 383 2728 383 2732 383 2736 385 2738 386 2740 389 2741 392 2740 394 2739 
395 2736 16 _pl _cp 
0 g _f _s _s 
0 g 406 2705 _m
_sp 406 2705 409 2705 410 2708 410 2710 411 2711 412 2714 413 2716 414 2717 415 2718 415 2718 416 2717 416 2717 417 2716 418 2717 418 2718 
418 2719 417 2720 416 2720 414 2719 413 2717 412 2715 412 2715 411 2714 413 2720 407 2719 407 2719 408 2719 409 2719 409 2718 409 2717 
409 2716 31 _pl _cp 
0 g _f _s _s 
0 g 418 2710 _m
_sp 418 2710 418 2705 418 2705 419 2705 419 2705 419 2705 419 2705 420 2705 421 2705 422 2705 423 2705 426 2705 428 2706 429 2707 429 2709 
429 2710 428 2711 427 2712 426 2714 424 2716 423 2718 424 2719 425 2719 428 2718 429 2715 430 2715 431 2720 430 2720 430 2720 429 2720 
428 2720 427 2720 426 2720 425 2720 422 2719 421 2717 421 2716 422 2714 423 2713 424 2711 426 2710 426 2708 425 2707 424 2706 422 2706 
421 2707 420 2708 419 2710 48 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2798 _m
_sp 749 2798 749 2801 495 2801 3 _pl _pf _np _s _s 495 2242 _m
_sp 498 2242 498 2801 495 2801 3 _pl _pf _np 
_s 0 g 555 250 499 2242 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2303 10925 _m
/Times-RomanR 600 _ff
(stern)_S 2197 10576 _m
(rudders)_S 2280 10227 _m
(angle)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2798 _m
_sp 1661 2798 1661 2801 749 2801 3 _pl _pf _np _s _s 749 2242 _m
_sp 752 2242 752 2801 749 2801 3 _pl _pf _np 
_s 0 g 555 908 753 2242 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10925 _m
(Stern)_S 67 _t
(rudder)_S 67 _t
(deflection)_S 67 _t
(angle.)_S 134 _t
(Usually)_S 3112 10576 _m
(bow)_S 67 _t
(and)_S 67 _t
(stern)_S 67 _t
(rudders)_S 67 _t
(go)_S 67 _t
(to)_S 67 _t
(exactly)_S 3112 10227 _m
(opposite)_S 67 _t
(positions\).)_S 134 _t
(Positive)_S 67 _t
(sense)_S 67 _t
(is)_S 3112 9878 _m
(clockwise)_S 67 _t
(as)_S 67 _t
(seen)_S 67 _t
(from)_S 67 _t
(above.)_S 134 _t
(Positive)_S 3112 9528 _m
(stern)_S 67 _t
(rudders)_S 67 _t
(angle)_S 67 _t
(with)_S 67 _t
(positive)_S 67 _t
(surge)_S 67 _t
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
3112 9178 _m
(produces)_S 67 _t
(negative)_S 67 _t
(change)_S 67 _t
(in)_S 67 _t
(yaw.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2798 _m
_sp 1929 2798 1929 2801 1661 2801 3 _pl _pf _np _s _s 1661 2242 _m
_sp 1664 2242 1664 2801 1661 2801 3 _pl _pf _np 
_s 0 g 555 264 1665 2242 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 10925 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2242 _m
_sp 2250 2242 2250 2801 2247 2801 3 _pl _pf _np _s _s 1928 2798 _m
_sp 2242 2798 2242 2801 1928 2801 3 _pl _pf _np _s _s 1928 2242 _m
_sp 1931 2242 1931 2801 1928 2801 3 _pl _pf _np _s _s 2239 2242 _m
_sp 2242 2242 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 555 306 1932 2242 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8051 10925 _m
(radians)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2240 _m
_sp 496 2240 496 2243 308 2243 3 _pl _pf _np _s _s 300 1597 _m
_sp 303 1597 303 2243 300 2243 3 _pl _pf _np _s _s 308 1597 _m
_sp 311 1597 311 2243 308 2243 3 _pl _pf _np 
_s 0 g 642 184 312 1597 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1464 8536 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 75 366 2134 _cw 
_s 393 2192 _m
_sp 393 2192 391 2194 389 2195 387 2196 386 2197 384 2197 381 2196 380 2193 380 2191 382 2189 383 2187 386 2185 382 2184 379 2182 377 2178 
376 2173 377 2169 379 2166 382 2164 386 2163 390 2164 393 2166 395 2170 396 2174 396 2177 395 2179 394 2181 393 2182 391 2184 389 2186 
387 2187 386 2188 384 2189 383 2190 383 2192 382 2193 383 2194 384 2194 385 2194 386 2193 387 2192 389 2191 391 2189 43 _pl _cp 392 2174 _m
_sp 392 2174 391 2170 390 2167 388 2166 386 2165 383 2166 382 2167 380 2170 380 2174 380 2178 382 2180 383 2182 386 2183 389 2182 391 2181 
392 2178 16 _pl _cp 
0 g _f _s _s 
0 g 409 2159 _m
_sp 409 2159 410 2162 404 2161 404 2161 405 2161 406 2161 406 2160 406 2159 406 2158 402 2144 401 2142 400 2141 400 2141 400 2141 406 2141 
406 2141 405 2141 405 2142 404 2142 404 2143 404 2143 405 2144 406 2147 407 2147 408 2147 410 2147 411 2148 413 2149 414 2150 415 2152 
417 2154 418 2156 418 2158 417 2161 414 2162 413 2162 411 2161 410 2160 38 _pl _cp 406 2150 _m
_sp 406 2150 406 2149 406 2149 407 2148 408 2148 410 2148 411 2149 412 2151 414 2154 415 2156 415 2158 414 2160 413 2161 412 2160 410 2159 
409 2158 409 2157 408 2155 407 2153 19 _pl _cp 
0 g _f _s _s 
0 g 425 2158 _m
_sp 425 2158 429 2170 423 2169 423 2169 424 2169 425 2169 425 2168 425 2167 425 2166 420 2150 420 2149 420 2149 420 2149 420 2148 420 2148 
422 2147 424 2147 426 2147 428 2148 430 2149 432 2150 433 2152 434 2154 435 2156 435 2158 434 2161 431 2162 431 2162 430 2162 429 2161 
428 2160 426 2159 32 _pl _cp 423 2149 _m
_sp 423 2149 424 2148 425 2148 427 2148 429 2150 430 2152 431 2154 432 2156 432 2158 431 2159 430 2160 429 2160 427 2159 426 2157 425 2155 
424 2153 424 2151 423 2150 18 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2240 _m
_sp 749 2240 749 2243 495 2243 3 _pl _pf _np _s _s 495 1597 _m
_sp 498 1597 498 2243 495 2243 3 _pl _pf _np 
_s 0 g 642 250 499 1597 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2325 8693 _m
/Times-RomanR 600 _ff
(bow)_S 2242 8344 _m
(planes)_S 2280 7995 _m
(angle)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2240 _m
_sp 1661 2240 1661 2243 749 2243 3 _pl _pf _np _s _s 749 1597 _m
_sp 752 1597 752 2243 749 2243 3 _pl _pf _np 
_s 0 g 642 908 753 1597 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 8693 _m
(Bow)_S 67 _t
(planes)_S 67 _t
(deflection)_S 67 _t
(angle.)_S 134 _t
(Usually)_S 3112 8344 _m
(bow)_S 67 _t
(and)_S 67 _t
(stern)_S 67 _t
(planes)_S 67 _t
(go)_S 67 _t
(to)_S 67 _t
(exactly)_S 3112 7995 _m
(opposite)_S 67 _t
(positions\).)_S 134 _t
(Positive)_S 67 _t
(sense)_S 67 _t
(is)_S 3112 7646 _m
(clockwise)_S 67 _t
(as)_S 67 _t
(seen)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(port)_S 67 _t
(side)_S 67 _t
(of)_S 3112 7297 _m
(the)_S 67 _t
(vehicle.)_S 134 _t
(Positive)_S 67 _t
(bow)_S 67 _t
(planes)_S 67 _t
(angle)_S 3112 6947 _m
(with)_S 67 _t
(positive)_S 67 _t
(surge)_S 67 _t
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
67 _t
(produces)_S 67 _t
(positive)_S 3112 6597 _m
(change)_S 67 _t
(in)_S 67 _t
(pitch.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2240 _m
_sp 1929 2240 1929 2243 1661 2243 3 _pl _pf _np _s _s 1661 1597 _m
_sp 1664 1597 1664 2243 1661 2243 3 _pl _pf _np 
_s 0 g 642 264 1665 1597 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 8693 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1597 _m
_sp 2250 1597 2250 2243 2247 2243 3 _pl _pf _np _s _s 1928 2240 _m
_sp 2242 2240 2242 2243 1928 2243 3 _pl _pf _np _s _s 1928 1597 _m
_sp 1931 1597 1931 2243 1928 2243 3 _pl _pf _np _s _s 2239 1597 _m
_sp 2242 1597 2242 2243 2239 2243 3 _pl _pf _np 
_s 0 g 642 306 1932 1597 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8051 8693 _m
(radians)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1595 _m
_sp 496 1595 496 1598 308 1598 3 _pl _pf _np _s _s 300 952 _m
_sp 303 952 303 1598 300 1598 3 _pl _pf _np _s _s 308 952 _m
_sp 311 952 311 1598 308 1598 3 _pl _pf _np 
_s 0 g 642 184 312 952 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1471 5955 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 76 72 367 1488 _cw 
_s 394 1546 _m
_sp 394 1546 392 1548 390 1549 388 1550 387 1551 385 1551 382 1550 381 1547 381 1545 383 1543 384 1541 387 1539 383 1538 380 1536 378 1532 
377 1527 378 1523 380 1520 383 1518 387 1517 391 1518 394 1520 396 1524 397 1528 397 1531 396 1533 395 1535 394 1536 392 1538 390 1540 
388 1541 387 1542 385 1543 384 1544 384 1546 383 1547 384 1548 385 1548 386 1548 387 1547 388 1546 390 1545 392 1543 43 _pl _cp 393 1528 _m
_sp 393 1528 392 1524 391 1521 389 1520 387 1519 384 1520 383 1521 381 1524 381 1528 381 1532 383 1534 384 1536 387 1537 390 1536 392 1535 
393 1532 16 _pl _cp 
0 g _f _s _s 
0 g 410 1513 _m
_sp 410 1513 411 1516 405 1515 405 1515 406 1515 407 1515 407 1514 407 1513 407 1512 403 1498 402 1496 401 1495 401 1495 401 1495 407 1495 
407 1495 406 1495 406 1496 405 1496 405 1497 405 1497 406 1498 407 1501 408 1501 409 1501 411 1501 412 1502 414 1503 415 1504 416 1506 
418 1508 419 1510 419 1512 418 1515 415 1516 414 1516 412 1515 411 1514 38 _pl _cp 407 1504 _m
_sp 407 1504 407 1503 407 1503 408 1502 409 1502 411 1502 412 1503 413 1505 415 1508 416 1510 416 1512 415 1514 414 1515 413 1514 411 1513 
410 1512 410 1511 409 1509 408 1507 19 _pl _cp 
0 g _f _s _s 
0 g 420 1506 _m
_sp 420 1506 420 1501 420 1501 421 1501 421 1501 421 1501 421 1501 422 1501 423 1501 424 1501 425 1501 427 1501 429 1502 430 1503 431 1505 
431 1506 430 1507 429 1508 428 1510 426 1512 425 1514 426 1515 427 1515 430 1514 431 1511 432 1511 433 1516 432 1516 432 1516 431 1516 
430 1516 429 1516 428 1516 427 1516 424 1515 423 1513 423 1512 423 1510 424 1509 426 1507 428 1506 428 1504 427 1503 425 1502 422 1503 
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_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 749 1595 749 1598 495 1598 3 _pl _pf _np _s _s 495 952 _m
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_s 0 g 0 0 0 0 _cw 
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/Times-RomanR 600 _ff
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_sp 1661 1595 1661 1598 749 1598 3 _pl _pf _np _s _s 749 952 _m
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_s 0 g 0 0 0 0 _cw 
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(angle.)_S 134 _t
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/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
67 _t
(produces)_S 67 _t
(negative)_S 3112 4016 _m
(change)_S 67 _t
(in)_S 67 _t
(pitch.)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 1595 1929 1598 1661 1598 3 _pl _pf _np _s _s 1661 952 _m
_sp 1664 952 1664 1598 1661 1598 3 _pl _pf _np 
_s 0 g 642 264 1665 952 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 6112 _m
(body)_S gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
_s grestore 8051 6112 _m
(radians)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 949 496 952 308 952 3 _pl _pf _np _s _s 300 830 _m
_sp 303 830 303 952 300 952 3 _pl _pf _np _s _s 308 830 _m
_sp 311 830 311 952 308 952 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1439 3530 _m
/Times-BoldItalicR 600 _ff
(n)_S /Times-BoldItalicR 360 _ff
1551 3485 _m
(porT)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 949 _m
_sp 749 949 749 952 495 952 3 _pl _pf _np _s _s 495 830 _m
_sp 498 830 498 952 495 952 3 _pl _pf _np 
_s 0 g 118 250 499 830 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2136 3531 _m
/Times-RomanR 600 _ff
(Port)_S 67 _t
(rpm)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 949 _m
_sp 1661 949 1661 952 749 952 3 _pl _pf _np _s _s 749 830 _m
_sp 752 830 752 952 749 952 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 3531 _m
(Port)_S 67 _t
(propeller)_S 67 _t
(ordered)_S 67 _t
(turns)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 949 _m
_sp 1929 949 1929 952 1661 952 3 _pl _pf _np _s _s 1661 830 _m
_sp 1664 830 1664 952 1661 952 3 _pl _pf _np 
_s 0 g 118 264 1665 830 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 3531 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 830 _m
_sp 2250 830 2250 952 2247 952 3 _pl _pf _np _s _s 1928 949 _m
_sp 2242 949 2242 952 1928 952 3 _pl _pf _np _s _s 1928 830 _m
_sp 1931 830 1931 952 1928 952 3 _pl _pf _np _s _s 2239 830 _m
_sp 2242 830 2242 952 2239 952 3 _pl _pf _np 
_s 0 g 118 306 1932 830 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8179 3531 _m
(rpm)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 828 496 831 308 831 3 _pl _pf _np _s _s 300 709 _m
_sp 303 709 303 831 300 831 3 _pl _pf _np _s _s 308 709 _m
_sp 311 709 311 831 308 831 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1459 3045 _m
/Times-BoldItalicR 600 _ff
(n)_S /Times-BoldItalicR 360 _ff
1571 3000 _m
(stbd)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 828 _m
_sp 749 828 749 831 495 831 3 _pl _pf _np _s _s 495 709 _m
_sp 498 709 498 831 495 831 3 _pl _pf _np 
_s 0 g 118 250 499 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2119 3046 _m
/Times-RomanR 600 _ff
(Stbd)_S 67 _t
(rpm)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 828 _m
_sp 1661 828 1661 831 749 831 3 _pl _pf _np _s _s 749 709 _m
_sp 752 709 752 831 749 831 3 _pl _pf _np 
_s 0 g 118 908 753 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 3046 _m
(Starboard)_S 67 _t
(propeller)_S 67 _t
(ordered)_S 67 _t
(turns)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 828 _m
_sp 1929 828 1929 831 1661 831 3 _pl _pf _np _s _s 1661 709 _m
_sp 1664 709 1664 831 1661 831 3 _pl _pf _np 
_s 0 g 118 264 1665 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 3046 _m
(body)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 709 2250 831 2247 831 3 _pl _pf _np _s _s 1928 828 _m
_sp 2242 828 2242 831 1928 831 3 _pl _pf _np _s _s 1928 709 _m
_sp 1931 709 1931 831 1928 831 3 _pl _pf _np _s _s 2239 709 _m
_sp 2242 709 2242 831 2239 831 3 _pl _pf _np 
_s 0 g 118 306 1932 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8179 3046 _m
(rpm)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 705 _m
_sp 496 705 496 708 300 708 3 _pl _pf _np _s _s 300 705 _m
_sp 303 705 303 710 300 710 3 _pl _pf _np _s _s 308 705 _m
_sp 311 705 311 710 308 710 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 749 705 749 708 495 708 3 _pl _pf _np _s _s 495 705 _m
_sp 498 705 498 710 495 710 3 _pl _pf _np 
_s 0 g 1 250 499 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 1661 705 1661 708 749 708 3 _pl _pf _np _s _s 749 705 _m
_sp 752 705 752 710 749 710 3 _pl _pf _np 
_s 0 g 1 908 753 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 705 _m
_sp 1929 705 1929 708 1661 708 3 _pl _pf _np _s _s 1661 705 _m
_sp 1664 705 1664 710 1661 710 3 _pl _pf _np 
_s 0 g 1 264 1665 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 705 _m
_sp 2250 705 2250 708 1928 708 3 _pl _pf _np _s _s 2247 705 _m
_sp 2250 705 2250 710 2247 710 3 _pl _pf _np _s _s 1928 705 _m
_sp 1931 705 1931 710 1928 710 3 _pl _pf _np _s _s 2239 705 _m
_sp 2242 705 2242 710 2239 710 3 _pl _pf _np 
_s 0 g 1 306 1932 709 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(128)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 496 2800 496 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 496 2996 496 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 496 2808 496 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 496 2988 496 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1615 11716 _m
/Times-BoldR 480 _ff
1357 11427 _m
(Symbol)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2800 _m
_sp 749 2800 749 2803 495 2803 3 _pl _pf _np _s _s 495 2996 _m
_sp 749 2996 749 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 498 2808 498 2991 495 2991 3 _pl _pf _np _s _s 495 2996 _m
_sp 498 2996 498 2999 495 2999 3 _pl _pf _np _s _s 495 2808 _m
_sp 749 2808 749 2811 495 2811 3 _pl _pf _np _s _s 495 2988 _m
_sp 749 2988 749 2991 495 2991 3 _pl _pf _np 
_s 0 g 175 250 499 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 480 _ff
2297 11427 _m
/Times-BoldR 480 _ff
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2800 _m
_sp 1661 2800 1661 2803 749 2803 3 _pl _pf _np _s _s 749 2996 _m
_sp 1661 2996 1661 2999 749 2999 3 _pl _pf _np _s _s 749 2808 _m
_sp 752 2808 752 2991 749 2991 3 _pl _pf _np _s _s 749 2996 _m
_sp 752 2996 752 2999 749 2999 3 _pl _pf _np _s _s 749 2808 _m
_sp 1661 2808 1661 2811 749 2811 3 _pl _pf _np _s _s 749 2988 _m
_sp 1661 2988 1661 2991 749 2991 3 _pl _pf _np 
_s 0 g 175 908 753 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2800 1929 2803 1661 2803 3 _pl _pf _np _s _s 1661 2996 _m
_sp 1929 2996 1929 2999 1661 2999 3 _pl _pf _np _s _s 1661 2808 _m
_sp 1664 2808 1664 2991 1661 2991 3 _pl _pf _np _s _s 1661 2996 _m
_sp 1664 2996 1664 2999 1661 2999 3 _pl _pf _np _s _s 1661 2808 _m
_sp 1929 2808 1929 2811 1661 2811 3 _pl _pf _np _s _s 1661 2988 _m
_sp 1929 2988 1929 2991 1661 2991 3 _pl _pf _np 
_s 0 g 175 264 1665 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6799 11716 _m
(Coordinate)_S 6955 11427 _m
(system)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1928 2800 _m
_sp 2242 2800 2242 2803 1928 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1928 2996 _m
_sp 2250 2996 2250 2999 1928 2999 3 _pl _pf _np _s _s 1928 2808 _m
_sp 1931 2808 1931 2991 1928 2991 3 _pl _pf _np _s _s 1928 2996 _m
_sp 1931 2996 1931 2999 1928 2999 3 _pl _pf _np _s _s 1928 2808 _m
_sp 2242 2808 2242 2811 1928 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1928 2988 _m
_sp 2242 2988 2242 2991 1928 2991 3 _pl _pf _np 
_s 0 g 175 306 1932 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8158 11427 _m
(Units)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 496 2798 496 2801 308 2801 3 _pl _pf _np _s _s 300 2592 _m
_sp 303 2592 303 2801 300 2801 3 _pl _pf _np _s _s 308 2592 _m
_sp 311 2592 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 205 184 312 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2798 _m
_sp 749 2798 749 2801 495 2801 3 _pl _pf _np 
_s 0 g 205 254 495 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1752 10924 _m
/Times-BoldItalicR 600 _ff
(V)_S /Times-BoldItalicR 360 _ff
1885 10879 _m
(bow-vertical)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2798 _m
_sp 1661 2798 1661 2801 749 2801 3 _pl _pf _np _s _s 749 2592 _m
_sp 752 2592 752 2801 749 2801 3 _pl _pf _np 
_s 0 g 205 908 753 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10925 _m
/Times-RomanR 600 _ff
(Volts,)_S 67 _t
(bow)_S 67 _t
(vertical)_S 67 _t
(cross-body)_S 67 _t
(thruster)_S 3112 10576 _m
(\(\01524)_S 67 _t
(V)_S 67 _t
(corresponds)_S 67 _t
(to)_S 67 _t
(\0152.0)_S 67 _t
(lb\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2798 _m
_sp 1929 2798 1929 2801 1661 2801 3 _pl _pf _np _s _s 1661 2592 _m
_sp 1664 2592 1664 2801 1661 2801 3 _pl _pf _np 
_s 0 g 205 264 1665 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 10925 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2592 _m
_sp 2250 2592 2250 2801 2247 2801 3 _pl _pf _np _s _s 1928 2798 _m
_sp 2242 2798 2242 2801 1928 2801 3 _pl _pf _np _s _s 1928 2592 _m
_sp 1931 2592 1931 2801 1928 2801 3 _pl _pf _np _s _s 2239 2592 _m
_sp 2242 2592 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 205 306 1932 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8146 10925 _m
(volts)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 2589 496 2592 308 2592 3 _pl _pf _np _s _s 300 2383 _m
_sp 303 2383 303 2592 300 2592 3 _pl _pf _np _s _s 308 2383 _m
_sp 311 2383 311 2592 308 2592 3 _pl _pf _np 
_s 0 g 205 184 312 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 495 2589 _m
_sp 749 2589 749 2592 495 2592 3 _pl _pf _np 
_s 0 g 205 254 495 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1729 10090 _m
/Times-BoldItalicR 600 _ff
(V)_S /Times-BoldItalicR 360 _ff
1862 10045 _m
(stern-vertical)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2589 _m
_sp 1661 2589 1661 2592 749 2592 3 _pl _pf _np _s _s 749 2383 _m
_sp 752 2383 752 2592 749 2592 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 10091 _m
/Times-RomanR 600 _ff
(Volts,)_S 67 _t
(stern)_S 67 _t
(vertical)_S 67 _t
(cross-body)_S 67 _t
(thruster)_S 3112 9742 _m
(\(\01524)_S 67 _t
(V)_S 67 _t
(corresponds)_S 67 _t
(to)_S 67 _t
(\0152.0)_S 67 _t
(lb\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 2589 _m
_sp 1929 2589 1929 2592 1661 2592 3 _pl _pf _np _s _s 1661 2383 _m
_sp 1664 2383 1664 2592 1661 2592 3 _pl _pf _np 
_s 0 g 205 264 1665 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 10091 _m
(body)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2383 _m
_sp 2250 2383 2250 2592 2247 2592 3 _pl _pf _np _s _s 1928 2589 _m
_sp 2242 2589 2242 2592 1928 2592 3 _pl _pf _np _s _s 1928 2383 _m
_sp 1931 2383 1931 2592 1928 2592 3 _pl _pf _np _s _s 2239 2383 _m
_sp 2242 2383 2242 2592 2239 2592 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 8146 10091 _m
(volts)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2381 _m
_sp 496 2381 496 2384 308 2384 3 _pl _pf _np _s _s 300 2175 _m
_sp 303 2175 303 2384 300 2384 3 _pl _pf _np _s _s 308 2175 _m
_sp 311 2175 311 2384 308 2384 3 _pl _pf _np 
_s 0 g 205 184 312 2175 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 749 2381 749 2384 495 2384 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1775 9256 _m
/Times-BoldItalicR 600 _ff
(V)_S /Times-BoldItalicR 360 _ff
1909 9211 _m
(bow-lateral)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 2381 _m
_sp 1661 2381 1661 2384 749 2384 3 _pl _pf _np _s _s 749 2175 _m
_sp 752 2175 752 2384 749 2384 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3112 9257 _m
/Times-RomanR 600 _ff
(Volts,)_S 67 _t
(bow)_S 67 _t
(lateral)_S 67 _t
(cross-body)_S 67 _t
(thruster)_S 3112 8908 _m
(\(\01524)_S 67 _t
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(to)_S 67 _t
(\0152.0)_S 67 _t
(lb\))_S gsave 4 4 scale 16 _sr _s 
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_sp 1929 2381 1929 2384 1661 2384 3 _pl _pf _np _s _s 1661 2175 _m
_sp 1664 2175 1664 2384 1661 2384 3 _pl _pf _np 
_s 0 g 205 264 1665 2175 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 9257 _m
(body)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 2175 2250 2384 2247 2384 3 _pl _pf _np _s _s 1928 2381 _m
_sp 2242 2381 2242 2384 1928 2384 3 _pl _pf _np _s _s 1928 2175 _m
_sp 1931 2175 1931 2384 1928 2384 3 _pl _pf _np _s _s 2239 2175 _m
_sp 2242 2175 2242 2384 2239 2384 3 _pl _pf _np 
_s 0 g 205 306 1932 2175 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8146 9257 _m
(volts)_S gsave 4 4 scale 16 _sr _s 
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_sp 496 1954 496 1957 300 1957 3 _pl _pf _np _s _s 308 2172 _m
_sp 496 2172 496 2175 308 2175 3 _pl _pf _np _s _s 300 1954 _m
_sp 303 1954 303 2175 300 2175 3 _pl _pf _np _s _s 308 1962 _m
_sp 496 1962 496 1965 308 1965 3 _pl _pf _np _s _s 308 1962 _m
_sp 311 1962 311 2175 308 2175 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 749 1954 749 1957 495 1957 3 _pl _pf _np _s _s 495 2172 _m
_sp 749 2172 749 2175 495 2175 3 _pl _pf _np _s _s 495 1962 _m
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_s 0 g 0 0 0 0 _cw 
_s grestore 1752 8422 _m
/Times-BoldItalicR 600 _ff
(V)_S /Times-BoldItalicR 360 _ff
1885 8377 _m
(stern-lateral)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 749 1954 _m
_sp 1661 1954 1661 1957 749 1957 3 _pl _pf _np _s _s 749 2172 _m
_sp 1661 2172 1661 2175 749 2175 3 _pl _pf _np _s _s 749 1962 _m
_sp 752 1962 752 2175 749 2175 3 _pl _pf _np _s _s 749 1962 _m
_sp 1661 1962 1661 1965 749 1965 3 _pl _pf _np 
_s 0 g 205 908 753 1966 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3112 8423 _m
/Times-RomanR 600 _ff
(Volts,)_S 67 _t
(stern)_S 67 _t
(lateral)_S 67 _t
(cross-body)_S 67 _t
(thruster)_S 3112 8074 _m
(\(\01524)_S 67 _t
(V)_S 67 _t
(corresponds)_S 67 _t
(to)_S 67 _t
(\0152.0)_S 67 _t
(lb\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1661 1954 _m
_sp 1929 1954 1929 1957 1661 1957 3 _pl _pf _np _s _s 1661 2172 _m
_sp 1929 2172 1929 2175 1661 2175 3 _pl _pf _np _s _s 1661 1962 _m
_sp 1664 1962 1664 2175 1661 2175 3 _pl _pf _np _s _s 1661 1962 _m
_sp 1929 1962 1929 1965 1661 1965 3 _pl _pf _np 
_s 0 g 205 264 1665 1966 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 6986 8423 _m
(body)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1954 2250 1957 1928 1957 3 _pl _pf _np _s _s 2247 1954 _m
_sp 2250 1954 2250 2175 2247 2175 3 _pl _pf _np _s _s 1928 2172 _m
_sp 2242 2172 2242 2175 1928 2175 3 _pl _pf _np _s _s 1928 1962 _m
_sp 1931 1962 1931 2175 1928 2175 3 _pl _pf _np _s _s 1928 1962 _m
_sp 2242 1962 2242 1965 1928 1965 3 _pl _pf _np _s _s 2239 1962 _m
_sp 2242 1962 2242 2175 2239 2175 3 _pl _pf _np 
_s 0 g 205 306 1932 1966 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8146 8423 _m
(volts)_S 4950 1288 _m
(129)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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/Times-BoldR 600 _ff
(Table)_S 67 _t
(6.2.)_S 134 _t
(Hydrodynamics)_S 67 _t
(Model)_S 67 _t
(Coefficients)_S /Times-RomanR 600 _ff
(.)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 2713 555 2716 308 2716 3 _pl _pf _np _s _s 300 2909 _m
_sp 555 2909 555 2912 300 2912 3 _pl _pf _np _s _s 300 2713 _m
_sp 303 2713 303 2912 300 2912 3 _pl _pf _np _s _s 308 2721 _m
_sp 555 2721 555 2724 308 2724 3 _pl _pf _np _s _s 308 2901 _m
_sp 555 2901 555 2904 308 2904 3 _pl _pf _np _s _s 308 2721 _m
_sp 311 2721 311 2904 308 2904 3 _pl _pf _np 
_s 0 g 175 243 312 2725 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-BoldR 480 _ff
1360 11078 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2713 _m
_sp 805 2713 805 2716 554 2716 3 _pl _pf _np _s _s 554 2909 _m
_sp 805 2909 805 2912 554 2912 3 _pl _pf _np _s _s 554 2721 _m
_sp 557 2721 557 2904 554 2904 3 _pl _pf _np _s _s 554 2909 _m
_sp 557 2909 557 2912 554 2912 3 _pl _pf _np _s _s 554 2721 _m
_sp 805 2721 805 2724 554 2724 3 _pl _pf _np _s _s 554 2901 _m
_sp 805 2901 805 2904 554 2904 3 _pl _pf _np 
_s 0 g 175 247 558 2725 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11078 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2713 _m
_sp 1853 2713 1853 2716 804 2716 3 _pl _pf _np _s _s 804 2909 _m
_sp 1853 2909 1853 2912 804 2912 3 _pl _pf _np _s _s 804 2721 _m
_sp 807 2721 807 2904 804 2904 3 _pl _pf _np _s _s 804 2909 _m
_sp 807 2909 807 2912 804 2912 3 _pl _pf _np _s _s 804 2721 _m
_sp 1853 2721 1853 2724 804 2724 3 _pl _pf _np _s _s 804 2901 _m
_sp 1853 2901 1853 2904 804 2904 3 _pl _pf _np 
_s 0 g 175 1045 808 2725 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11078 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2713 _m
_sp 2242 2713 2242 2716 1852 2716 3 _pl _pf _np _s _s 2247 2713 _m
_sp 2250 2713 2250 2912 2247 2912 3 _pl _pf _np _s _s 1852 2909 _m
_sp 2250 2909 2250 2912 1852 2912 3 _pl _pf _np _s _s 1852 2721 _m
_sp 1855 2721 1855 2904 1852 2904 3 _pl _pf _np _s _s 1852 2909 _m
_sp 1855 2909 1855 2912 1852 2912 3 _pl _pf _np _s _s 1852 2721 _m
_sp 2242 2721 2242 2724 1852 2724 3 _pl _pf _np _s _s 2239 2721 _m
_sp 2242 2721 2242 2904 2239 2904 3 _pl _pf _np _s _s 1852 2901 _m
_sp 2242 2901 2242 2904 1852 2904 3 _pl _pf _np 
_s 0 g 175 382 1856 2725 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11367 _m
(Value)_S 53 _t
(for)_S 7749 11078 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2711 _m
_sp 555 2711 555 2714 308 2714 3 _pl _pf _np _s _s 300 2504 _m
_sp 303 2504 303 2714 300 2714 3 _pl _pf _np _s _s 308 2504 _m
_sp 311 2504 311 2714 308 2714 3 _pl _pf _np 
_s 0 g 206 243 312 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1644 10575 _m
/Times-BoldItalicR 600 _ff
(W)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2711 _m
_sp 805 2711 805 2714 554 2714 3 _pl _pf _np _s _s 554 2504 _m
_sp 557 2504 557 2714 554 2714 3 _pl _pf _np 
_s 0 g 206 247 558 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2454 10576 _m
/Times-RomanR 600 _ff
(weight)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2711 _m
_sp 1853 2711 1853 2714 804 2714 3 _pl _pf _np _s _s 804 2504 _m
_sp 807 2504 807 2714 804 2714 3 _pl _pf _np 
_s 0 g 206 1045 808 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10576 _m
(Submerged)_S 67 _t
(weight)_S 67 _t
(of)_S 67 _t
(vehicle,)_S 67 _t
(including)_S 67 _t
(water)_S 3333 10227 _m
(in)_S 67 _t
(contained)_S 67 _t
(free-flood)_S 67 _t
(spaces,)_S 67 _t
(neutral)_S 67 _t
(ballast.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2504 _m
_sp 2250 2504 2250 2714 2247 2714 3 _pl _pf _np _s _s 1852 2711 _m
_sp 2242 2711 2242 2714 1852 2714 3 _pl _pf _np _s _s 1852 2504 _m
_sp 1855 2504 1855 2714 1852 2714 3 _pl _pf _np _s _s 2239 2504 _m
_sp 2242 2504 2242 2714 2239 2714 3 _pl _pf _np 
_s 0 g 206 382 1856 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7928 10576 _m
(435)_S 67 _t
(lb)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2502 _m
_sp 555 2502 555 2505 308 2505 3 _pl _pf _np _s _s 300 2121 _m
_sp 303 2121 303 2505 300 2505 3 _pl _pf _np _s _s 308 2121 _m
_sp 311 2121 311 2505 308 2505 3 _pl _pf _np 
_s 0 g 380 243 312 2121 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1666 9741 _m
/Times-BoldItalicR 600 _ff
(B)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2502 _m
_sp 805 2502 805 2505 554 2505 3 _pl _pf _np _s _s 554 2121 _m
_sp 557 2121 557 2505 554 2505 3 _pl _pf _np 
_s 0 g 380 247 558 2121 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2337 9742 _m
/Times-RomanR 600 _ff
(buoyancy)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2502 _m
_sp 1853 2502 1853 2505 804 2505 3 _pl _pf _np _s _s 804 2121 _m
_sp 807 2121 807 2505 804 2505 3 _pl _pf _np 
_s 0 g 380 1045 808 2121 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 9742 _m
(Weight)_S 67 _t
(of)_S 67 _t
(water)_S 67 _t
(displaced)_S 67 _t
(by)_S 67 _t
(vehicle,)_S 67 _t
(including)_S 3333 9393 _m
(water)_S 67 _t
(in)_S 67 _t
(contained)_S 67 _t
(free-flood)_S 67 _t
(spaces.)_S 134 _t
3333 9044 _m
(Can)_S 67 _t
(vary)_S 67 _t
(with)_S 67 _t
(depth)_S 67 _t
(\(due)_S 67 _t
(to)_S 67 _t
(hull)_S 67 _t
(compression\))_S 3333 8695 _m
(and)_S 67 _t
(with)_S 67 _t
(changes)_S 67 _t
(in)_S 67 _t
(water)_S 67 _t
(density)_S 67 _t
/Symbol 600 _ff
(r)_S /Times-RomanR 600 _ff
(.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2121 _m
_sp 2250 2121 2250 2505 2247 2505 3 _pl _pf _np _s _s 1852 2502 _m
_sp 2242 2502 2242 2505 1852 2505 3 _pl _pf _np _s _s 1852 2121 _m
_sp 1855 2121 1855 2505 1852 2505 3 _pl _pf _np _s _s 2239 2121 _m
_sp 2242 2121 2242 2505 2239 2505 3 _pl _pf _np 
_s 0 g 380 382 1856 2121 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7928 9742 _m
(435)_S 67 _t
(lb)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2119 _m
_sp 555 2119 555 2122 308 2122 3 _pl _pf _np _s _s 300 1389 _m
_sp 303 1389 303 2122 300 2122 3 _pl _pf _np _s _s 308 1389 _m
_sp 311 1389 311 2122 308 2122 3 _pl _pf _np 
_s 0 g 729 243 312 1389 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1672 8209 _m
/Times-BoldItalicR 600 _ff
(L)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2119 _m
_sp 805 2119 805 2122 554 2122 3 _pl _pf _np _s _s 554 1389 _m
_sp 557 1389 557 2122 554 2122 3 _pl _pf _np 
_s 0 g 729 247 558 1389 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2476 8210 _m
/Times-RomanR 600 _ff
(length)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2119 _m
_sp 1853 2119 1853 2122 804 2122 3 _pl _pf _np _s _s 804 1389 _m
_sp 807 1389 807 2122 804 2122 3 _pl _pf _np 
_s 0 g 729 1045 808 1389 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8210 _m
(Vehicle)_S 67 _t
(length,)_S 67 _t
(also)_S 67 _t
(known)_S 67 _t
(as)_S 67 _t
(characteristic)_S 3333 7861 _m
(length.)_S 134 _t
(Dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(are)_S 3333 7511 _m
(written)_S 67 _t
(to)_S 67 _t
(explicitly)_S 67 _t
(utilize)_S 67 _t
/Times-BoldItalicR 600 _ff
(L)_S /Times-RomanR 600 _ff
67 _t
(as)_S 67 _t
(a)_S 67 _t
(normalization)_S 3333 7161 _m
(coefficient.)_S 134 _t
(This)_S 67 _t
(approach)_S 67 _t
(makes)_S 67 _t
(most)_S 67 _t
(other)_S 3333 6812 _m
(coefficients)_S 67 _t
(dimensionless)_S 67 _t
(and)_S 67 _t
(quantitatively)_S 3333 6463 _m
(independent)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(dimensions,)_S 67 _t
(permitting)_S 3333 6114 _m
(comparison)_S 67 _t
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(relative)_S 67 _t
(effects)_S 67 _t
(between)_S 67 _t
(different)_S 3333 5765 _m
(forces)_S 67 _t
(and)_S 67 _t
(dissimilar)_S 67 _t
(vehicles.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1389 _m
_sp 2250 1389 2250 2122 2247 2122 3 _pl _pf _np _s _s 1852 2119 _m
_sp 2242 2119 2242 2122 1852 2122 3 _pl _pf _np _s _s 1852 1389 _m
_sp 1855 1389 1855 2122 1852 2122 3 _pl _pf _np _s _s 2239 1389 _m
_sp 2242 1389 2242 2122 2239 2122 3 _pl _pf _np 
_s 0 g 729 382 1856 1389 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7869 8210 _m
(7.302)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1387 _m
_sp 555 1387 555 1390 308 1390 3 _pl _pf _np _s _s 300 1268 _m
_sp 303 1268 303 1390 300 1390 3 _pl _pf _np _s _s 308 1268 _m
_sp 311 1268 311 1390 308 1390 3 _pl _pf _np 
_s 0 g 118 243 312 1268 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1683 5279 _m
/Times-BoldItalicR 600 _ff
(g)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1387 _m
_sp 805 1387 805 1390 554 1390 3 _pl _pf _np _s _s 554 1268 _m
_sp 557 1268 557 1390 554 1390 3 _pl _pf _np 
_s 0 g 118 247 558 1268 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1387 _m
_sp 1853 1387 1853 1390 804 1390 3 _pl _pf _np _s _s 804 1268 _m
_sp 807 1268 807 1390 804 1390 3 _pl _pf _np 
_s 0 g 118 1045 808 1268 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 5280 _m
(Acceleration)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(gravity)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1268 _m
_sp 2250 1268 2250 1390 2247 1390 3 _pl _pf _np _s _s 1852 1387 _m
_sp 2242 1387 2242 1390 1852 1390 3 _pl _pf _np _s _s 1852 1268 _m
_sp 1855 1268 1855 1390 1852 1390 3 _pl _pf _np _s _s 2239 1268 _m
_sp 2242 1268 2242 1390 2239 1390 3 _pl _pf _np 
_s 0 g 118 382 1856 1268 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7634 5280 _m
(32.174)_S 67 _t
(ft/sec)_S /Times-RomanR 360 _ff
8684 5362 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1265 _m
_sp 555 1265 555 1268 308 1268 3 _pl _pf _np _s _s 300 1059 _m
_sp 303 1059 303 1268 300 1268 3 _pl _pf _np _s _s 308 1059 _m
_sp 311 1059 311 1268 308 1268 3 _pl _pf _np 
_s 0 g 205 243 312 1059 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1678 4794 _m
/Symbol 600 _ff
(r)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1265 _m
_sp 805 1265 805 1268 554 1268 3 _pl _pf _np _s _s 554 1059 _m
_sp 557 1059 557 1268 554 1268 3 _pl _pf _np 
_s 0 g 205 247 558 1059 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2593 4795 _m
/Times-RomanR 600 _ff
(rho)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1265 _m
_sp 1853 1265 1853 1268 804 1268 3 _pl _pf _np _s _s 804 1059 _m
_sp 807 1059 807 1268 804 1268 3 _pl _pf _np 
_s 0 g 205 1045 808 1059 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 4795 _m
(Mass)_S 67 _t
(density)_S 67 _t
(of)_S 67 _t
(fresh)_S 67 _t
(water:)_S 3333 4446 _m
(Mass)_S 67 _t
(density)_S 67 _t
(of)_S 67 _t
(sea)_S 67 _t
(water)_S 67 _t
(\(representative\):)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1059 _m
_sp 2250 1059 2250 1268 2247 1268 3 _pl _pf _np _s _s 1852 1265 _m
_sp 2242 1265 2242 1268 1852 1268 3 _pl _pf _np _s _s 1852 1059 _m
_sp 1855 1059 1855 1268 1852 1268 3 _pl _pf _np _s _s 2239 1059 _m
_sp 2242 1059 2242 1268 2239 1268 3 _pl _pf _np 
_s 0 g 205 382 1856 1059 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7656 4795 _m
(1.94)_S 67 _t
(slugs/ft)_S /Times-RomanR 360 _ff
8662 4877 _m
(3)_S /Times-RomanR 600 _ff
7656 4446 _m
(1.99)_S 67 _t
(slugs/ft)_S /Times-RomanR 360 _ff
8662 4528 _m
(3)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1057 _m
_sp 555 1057 555 1060 308 1060 3 _pl _pf _np _s _s 300 850 _m
_sp 303 850 303 1060 300 1060 3 _pl _pf _np _s _s 308 850 _m
_sp 311 850 311 1060 308 1060 3 _pl _pf _np 
_s 0 g 206 243 312 850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1655 3960 _m
/Times-BoldItalicR 600 _ff
(m)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1057 _m
_sp 805 1057 805 1060 554 1060 3 _pl _pf _np _s _s 554 850 _m
_sp 557 850 557 1060 554 1060 3 _pl _pf _np 
_s 0 g 206 247 558 850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 3961 _m
/Times-RomanR 600 _ff
(mass)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1057 _m
_sp 1853 1057 1853 1060 804 1060 3 _pl _pf _np _s _s 804 850 _m
_sp 807 850 807 1060 804 1060 3 _pl _pf _np 
_s 0 g 206 1045 808 850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 3961 _m
(Vehicle)_S 67 _t
(mass,)_S 67 _t
(including)_S 67 _t
(water)_S 67 _t
(contained)_S 67 _t
(in)_S 3333 3612 _m
(enclosed)_S 67 _t
(free-flood)_S 67 _t
(spaces,)_S 67 _t
(neutral)_S 67 _t
(ballast.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 850 _m
_sp 2250 850 2250 1060 2247 1060 3 _pl _pf _np _s _s 1852 1057 _m
_sp 2242 1057 2242 1060 1852 1060 3 _pl _pf _np _s _s 1852 850 _m
_sp 1855 850 1855 1060 1852 1060 3 _pl _pf _np _s _s 2239 850 _m
_sp 2242 850 2242 1060 2239 1060 3 _pl _pf _np 
_s 0 g 206 382 1856 850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7607 3960 _m
/Times-BoldItalicR 600 _ff
(W)_S 67 _t
(/)_S 67 _t
(g)_S /Times-RomanR 600 _ff
67 _t
(=)_S 67 _t
(13.52)_S gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 1997 920 _m
_sp 1997 920 1998 918 2000 917 2002 918 2003 920 2002 922 2000 923 1998 922 8 _pl _cp _f _s _s grestore _s grestore 7739 3610 _m
(\(lb)_S 7961 3610 _m
8013 3610 _m
67 _t
(sec)_S /Times-RomanR 360 _ff
8335 3692 _m
(2)_S 8395 3692 _m
/Times-RomanR 600 _ff
8395 3610 _m
(\)/ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 848 _m
_sp 555 848 555 851 308 851 3 _pl _pf _np _s _s 300 642 _m
_sp 303 642 303 851 300 851 3 _pl _pf _np _s _s 308 642 _m
_sp 311 642 311 851 308 851 3 _pl _pf _np 
_s 0 g 205 243 312 642 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1664 3124 _m
/Times-BoldItalicR 600 _ff
(I)_S /Times-BoldItalicR 360 _ff
1742 3079 _m
(x)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 848 _m
_sp 805 848 805 851 554 851 3 _pl _pf _np _s _s 554 642 _m
_sp 557 642 557 851 554 851 3 _pl _pf _np 
_s 0 g 205 247 558 642 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 848 _m
_sp 1853 848 1853 851 804 851 3 _pl _pf _np _s _s 804 642 _m
_sp 807 642 807 851 804 851 3 _pl _pf _np 
_s 0 g 205 1045 808 642 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 3125 _m
(Mass)_S 67 _t
(moment)_S 67 _t
(of)_S 67 _t
(inertia)_S 67 _t
(coefficient)_S 67 _t
(about)_S 67 _t
(body)_S 3333 2776 _m
(longitudinal)_S 67 _t
(axis,)_S 67 _t
(Equation)_S 67 _t
(\(6.55\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 642 _m
_sp 2250 642 2250 851 2247 851 3 _pl _pf _np _s _s 1852 848 _m
_sp 2242 848 2242 851 1852 851 3 _pl _pf _np _s _s 1852 642 _m
_sp 1855 642 1855 851 1852 851 3 _pl _pf _np _s _s 2239 642 _m
_sp 2242 642 2242 851 2239 851 3 _pl _pf _np 
_s 0 g 205 382 1856 642 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2029 799 _m
_sp 2029 799 2030 797 2032 796 2034 797 2035 799 2034 801 2032 802 2030 801 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2080 799 _m
_sp 2080 799 2081 797 2083 796 2085 797 2086 799 2085 801 2083 802 2081 801 8 _pl _cp _f _s _s grestore _s grestore 7649 3125 _m
(2.7)_S 67 _t
(ft)_S 8088 3125 _m
8140 3125 _m
(lb)_S 8295 3125 _m
8347 3125 _m
67 _t
(sec)_S /Times-RomanR 360 _ff
8669 3207 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 638 _m
_sp 555 638 555 641 300 641 3 _pl _pf _np _s _s 300 638 _m
_sp 303 638 303 642 300 642 3 _pl _pf _np _s _s 308 638 _m
_sp 311 638 311 642 308 642 3 _pl _pf _np _s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 638 _m
_sp 805 638 805 641 554 641 3 _pl _pf _np _s _s 554 638 _m
_sp 557 638 557 642 554 642 3 _pl _pf _np _s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 638 _m
_sp 1853 638 1853 641 804 641 3 _pl _pf _np _s _s 804 638 _m
_sp 807 638 807 642 804 642 3 _pl _pf _np _s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 638 _m
_sp 2250 638 2250 641 1852 641 3 _pl _pf _np _s _s 2247 638 _m
_sp 2250 638 2250 642 2247 642 3 _pl _pf _np _s _s 1852 638 _m
_sp 1855 638 1855 642 1852 642 3 _pl _pf _np _s _s 2239 638 _m
_sp 2242 638 2242 642 2239 642 3 _pl _pf _np _s grestore 4950 1288 _m
(130)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 243 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2592 _m
_sp 303 2592 303 2801 300 2801 3 _pl _pf _np _s _s 308 2592 _m
_sp 311 2592 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 205 243 312 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1668 10924 _m
/Times-BoldItalicR 600 _ff
(I)_S /Times-BoldItalicR 360 _ff
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(y)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2798 _m
_sp 805 2798 805 2801 554 2801 3 _pl _pf _np _s _s 554 2592 _m
_sp 557 2592 557 2801 554 2801 3 _pl _pf _np 
_s 0 g 205 247 558 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2798 _m
_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np _s _s 804 2592 _m
_sp 807 2592 807 2801 804 2801 3 _pl _pf _np 
_s 0 g 205 1045 808 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10925 _m
(Mass)_S 67 _t
(moment)_S 67 _t
(of)_S 67 _t
(inertia)_S 67 _t
(coefficient)_S 67 _t
(about)_S 67 _t
(body)_S 3333 10576 _m
(lateral)_S 67 _t
(axis,)_S 67 _t
(Equation)_S 67 _t
(\(6.56\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2592 _m
_sp 2250 2592 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 1852 2592 _m
_sp 1855 2592 1855 2801 1852 2801 3 _pl _pf _np _s _s 2239 2592 _m
_sp 2242 2592 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 205 382 1856 2592 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2050 2749 _m
_sp 2050 2749 2051 2747 2053 2746 2055 2747 2056 2749 2055 2751 2053 2752 2051 2751 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2101 2749 _m
_sp 2101 2749 2102 2747 2104 2746 2106 2747 2107 2749 2106 2751 2104 2752 2102 2751 8 _pl _cp _f _s _s grestore _s grestore 7632 10925 _m
(42.0)_S 67 _t
(ft)_S 8172 10925 _m
8223 10925 _m
(lb)_S 8379 10925 _m
8430 10925 _m
(sec)_S /Times-RomanR 360 _ff
8686 11007 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2589 _m
_sp 555 2589 555 2592 308 2592 3 _pl _pf _np _s _s 300 2383 _m
_sp 303 2383 303 2592 300 2592 3 _pl _pf _np _s _s 308 2383 _m
_sp 311 2383 311 2592 308 2592 3 _pl _pf _np 
_s 0 g 205 243 312 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1671 10090 _m
/Times-BoldItalicR 600 _ff
(I)_S /Times-BoldItalicR 360 _ff
1749 10045 _m
(z)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2589 _m
_sp 805 2589 805 2592 554 2592 3 _pl _pf _np _s _s 554 2383 _m
_sp 557 2383 557 2592 554 2592 3 _pl _pf _np 
_s 0 g 205 247 558 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2589 _m
_sp 1853 2589 1853 2592 804 2592 3 _pl _pf _np _s _s 804 2383 _m
_sp 807 2383 807 2592 804 2592 3 _pl _pf _np 
_s 0 g 205 1045 808 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10091 _m
(Mass)_S 67 _t
(moment)_S 67 _t
(of)_S 67 _t
(inertia)_S 67 _t
(coefficient)_S 67 _t
(about)_S 67 _t
(body)_S 3333 9742 _m
(vertical)_S 67 _t
(axis,)_S 67 _t
(Equation)_S 67 _t
(\(6.57\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2383 _m
_sp 2250 2383 2250 2592 2247 2592 3 _pl _pf _np _s _s 1852 2589 _m
_sp 2242 2589 2242 2592 1852 2592 3 _pl _pf _np _s _s 1852 2383 _m
_sp 1855 2383 1855 2592 1852 2592 3 _pl _pf _np _s _s 2239 2383 _m
_sp 2242 2383 2242 2592 2239 2592 3 _pl _pf _np 
_s 0 g 205 382 1856 2383 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2050 2541 _m
_sp 2050 2541 2051 2539 2053 2538 2055 2539 2056 2541 2055 2543 2053 2544 2051 2543 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2101 2541 _m
_sp 2101 2541 2102 2539 2104 2538 2106 2539 2107 2541 2106 2543 2104 2544 2102 2543 8 _pl _cp _f _s _s grestore _s grestore 7632 10091 _m
(45.0)_S 67 _t
(ft)_S 8172 10091 _m
8223 10091 _m
(lb)_S 8379 10091 _m
8430 10091 _m
(sec)_S /Times-RomanR 360 _ff
8686 10173 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2381 _m
_sp 555 2381 555 2384 308 2384 3 _pl _pf _np _s _s 300 2087 _m
_sp 303 2087 303 2384 300 2384 3 _pl _pf _np _s _s 308 2087 _m
_sp 311 2087 311 2384 308 2384 3 _pl _pf _np 
_s 0 g 293 243 312 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1638 9256 _m
/Times-BoldItalicR 600 _ff
(I)_S /Times-BoldItalicR 360 _ff
1715 9211 _m
(xy)_S /Times-BoldItalicR 600 _ff
1547 8907 _m
(=)_S 67 _t
(I)_S /Times-BoldItalicR 360 _ff
1806 8862 _m
(yx)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2381 _m
_sp 805 2381 805 2384 554 2384 3 _pl _pf _np _s _s 554 2087 _m
_sp 557 2087 557 2384 554 2384 3 _pl _pf _np 
_s 0 g 293 247 558 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2381 _m
_sp 1853 2381 1853 2384 804 2384 3 _pl _pf _np _s _s 804 2087 _m
_sp 807 2087 807 2384 804 2384 3 _pl _pf _np 
_s 0 g 293 1045 808 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 9257 _m
(Cross)_S 67 _t
(product)_S 67 _t
(of)_S 67 _t
(inertia)_S 67 _t
(coefficient,)_S 67 _t
(due)_S 67 _t
(to)_S 3333 8908 _m
(asymmetric)_S 67 _t
(mass)_S 67 _t
(distribution)_S 67 _t
(about)_S 67 _t
(body)_S 3333 8559 _m
(longitudinal/lateral)_S 67 _t
(axes,)_S 67 _t
(Equation)_S 67 _t
(\(6.58\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2087 _m
_sp 2250 2087 2250 2384 2247 2384 3 _pl _pf _np _s _s 1852 2381 _m
_sp 2242 2381 2242 2384 1852 2384 3 _pl _pf _np _s _s 1852 2087 _m
_sp 1855 2087 1855 2384 1852 2384 3 _pl _pf _np _s _s 2239 2087 _m
_sp 2242 2087 2242 2384 2239 2384 3 _pl _pf _np 
_s 0 g 293 382 1856 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2029 2332 _m
_sp 2029 2332 2030 2330 2032 2329 2034 2330 2035 2332 2034 2334 2032 2335 2030 2334 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2080 2332 _m
_sp 2080 2332 2081 2330 2083 2329 2085 2330 2086 2332 2085 2334 2083 2335 2081 2334 8 _pl _cp _f _s _s grestore _s grestore 7649 9257 _m
(0.0)_S 67 _t
(ft)_S 8088 9257 _m
8140 9257 _m
(lb)_S 8295 9257 _m
8347 9257 _m
67 _t
(sec)_S /Times-RomanR 360 _ff
8669 9339 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2085 _m
_sp 555 2085 555 2088 308 2088 3 _pl _pf _np _s _s 300 1792 _m
_sp 303 1792 303 2088 300 2088 3 _pl _pf _np _s _s 308 1792 _m
_sp 311 1792 311 2088 308 2088 3 _pl _pf _np 
_s 0 g 292 243 312 1792 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1641 8073 _m
/Times-BoldItalicR 600 _ff
(I)_S /Times-BoldItalicR 360 _ff
1719 8028 _m
(xz)_S /Times-BoldItalicR 600 _ff
1550 7724 _m
(=)_S 67 _t
(I)_S /Times-BoldItalicR 360 _ff
1809 7679 _m
(zx)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2085 _m
_sp 805 2085 805 2088 554 2088 3 _pl _pf _np _s _s 554 1792 _m
_sp 557 1792 557 2088 554 2088 3 _pl _pf _np 
_s 0 g 292 247 558 1792 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2085 _m
_sp 1853 2085 1853 2088 804 2088 3 _pl _pf _np _s _s 804 1792 _m
_sp 807 1792 807 2088 804 2088 3 _pl _pf _np 
_s 0 g 292 1045 808 1792 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8074 _m
(Cross)_S 67 _t
(product)_S 67 _t
(of)_S 67 _t
(inertia)_S 67 _t
(coefficient,)_S 67 _t
(due)_S 67 _t
(to)_S 3333 7725 _m
(asymmetric)_S 67 _t
(mass)_S 67 _t
(distribution)_S 67 _t
(about)_S 67 _t
(body)_S 3333 7376 _m
(longitudinal/vertical)_S 67 _t
(axes,)_S 67 _t
(Equation)_S 67 _t
(\(6.59\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1792 _m
_sp 2250 1792 2250 2088 2247 2088 3 _pl _pf _np _s _s 1852 2085 _m
_sp 2242 2085 2242 2088 1852 2088 3 _pl _pf _np _s _s 1852 1792 _m
_sp 1855 1792 1855 2088 1852 2088 3 _pl _pf _np _s _s 2239 1792 _m
_sp 2242 1792 2242 2088 2239 2088 3 _pl _pf _np 
_s 0 g 292 382 1856 1792 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2029 2036 _m
_sp 2029 2036 2030 2034 2032 2033 2034 2034 2035 2036 2034 2038 2032 2039 2030 2038 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2080 2036 _m
_sp 2080 2036 2081 2034 2083 2033 2085 2034 2086 2036 2085 2038 2083 2039 2081 2038 8 _pl _cp _f _s _s grestore _s grestore 7649 8074 _m
(0.0)_S 67 _t
(ft)_S 8088 8074 _m
8140 8074 _m
(lb)_S 8295 8074 _m
8347 8074 _m
67 _t
(sec)_S /Times-RomanR 360 _ff
8669 8156 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1789 _m
_sp 555 1789 555 1792 308 1792 3 _pl _pf _np _s _s 300 1496 _m
_sp 303 1496 303 1792 300 1792 3 _pl _pf _np _s _s 308 1496 _m
_sp 311 1496 311 1792 308 1792 3 _pl _pf _np 
_s 0 g 292 243 312 1496 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1644 6890 _m
/Times-BoldItalicR 600 _ff
(I)_S /Times-BoldItalicR 360 _ff
1722 6845 _m
(yz)_S /Times-BoldItalicR 600 _ff
1554 6541 _m
(=)_S 67 _t
(I)_S /Times-BoldItalicR 360 _ff
1812 6496 _m
(zy)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1789 _m
_sp 805 1789 805 1792 554 1792 3 _pl _pf _np _s _s 554 1496 _m
_sp 557 1496 557 1792 554 1792 3 _pl _pf _np 
_s 0 g 292 247 558 1496 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1789 _m
_sp 1853 1789 1853 1792 804 1792 3 _pl _pf _np _s _s 804 1496 _m
_sp 807 1496 807 1792 804 1792 3 _pl _pf _np 
_s 0 g 292 1045 808 1496 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 6891 _m
(Cross)_S 67 _t
(product)_S 67 _t
(of)_S 67 _t
(inertia)_S 67 _t
(coefficient,)_S 67 _t
(due)_S 67 _t
(to)_S 3333 6542 _m
(asymmetric)_S 67 _t
(mass)_S 67 _t
(distribution)_S 67 _t
(about)_S 67 _t
(body)_S 3333 6193 _m
(lateral/vertical)_S 67 _t
(axes,)_S 67 _t
(Equation)_S 67 _t
(\(6.60\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1496 _m
_sp 2250 1496 2250 1792 2247 1792 3 _pl _pf _np _s _s 1852 1789 _m
_sp 2242 1789 2242 1792 1852 1792 3 _pl _pf _np _s _s 1852 1496 _m
_sp 1855 1496 1855 1792 1852 1792 3 _pl _pf _np _s _s 2239 1496 _m
_sp 2242 1496 2242 1792 2239 1792 3 _pl _pf _np 
_s 0 g 292 382 1856 1496 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2029 1741 _m
_sp 2029 1741 2030 1739 2032 1738 2034 1739 2035 1741 2034 1743 2032 1744 2030 1743 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2080 1741 _m
_sp 2080 1741 2081 1739 2083 1738 2085 1739 2086 1741 2085 1743 2083 1744 2081 1743 8 _pl _cp _f _s _s grestore _s grestore 7649 6891 _m
(0.0)_S 67 _t
(ft)_S 8088 6891 _m
8140 6891 _m
(lb)_S 8295 6891 _m
8347 6891 _m
67 _t
(sec)_S /Times-RomanR 360 _ff
8669 6973 _m
(2)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1494 _m
_sp 555 1494 555 1497 308 1497 3 _pl _pf _np _s _s 300 1200 _m
_sp 303 1200 303 1497 300 1497 3 _pl _pf _np _s _s 308 1200 _m
_sp 311 1200 311 1497 308 1497 3 _pl _pf _np 
_s 0 g 293 243 312 1200 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1594 5707 _m
/Times-BoldItalicR 600 _ff
(CG)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1494 _m
_sp 805 1494 805 1497 554 1497 3 _pl _pf _np _s _s 554 1200 _m
_sp 557 1200 557 1497 554 1497 3 _pl _pf _np 
_s 0 g 293 247 558 1200 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2365 5708 _m
/Times-RomanR 600 _ff
(center)_S 67 _t
(of)_S 2443 5359 _m
(gravity)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1494 _m
_sp 1853 1494 1853 1497 804 1497 3 _pl _pf _np _s _s 804 1200 _m
_sp 807 1200 807 1497 804 1497 3 _pl _pf _np 
_s 0 g 293 1045 808 1200 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 5708 _m
(Mass)_S 67 _t
(centroid)_S 67 _t
(of)_S 67 _t
(vehicle.)_S 134 _t
(The)_S 67 _t
(CG)_S 67 _t
(is)_S 67 _t
(the)_S 3333 5359 _m
(apparent)_S 67 _t
(point)_S 67 _t
(where)_S 67 _t
(forces)_S 67 _t
(and)_S 67 _t
(moments)_S 67 _t
(are)_S 3333 5010 _m
(applied.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1200 _m
_sp 2250 1200 2250 1497 2247 1497 3 _pl _pf _np _s _s 1852 1494 _m
_sp 2242 1494 2242 1497 1852 1497 3 _pl _pf _np _s _s 1852 1200 _m
_sp 1855 1200 1855 1497 1852 1497 3 _pl _pf _np _s _s 2239 1200 _m
_sp 2242 1200 2242 1497 2239 1497 3 _pl _pf _np 
_s 0 g 293 382 1856 1200 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7742 5707 _m
(\()_S /Times-BoldItalicR 600 _ff
(x)_S /Times-BoldItalicR 360 _ff
7909 5662 _m
(G)_S 7995 5662 _m
/Times-RomanR 600 _ff
7995 5707 _m
(,)_S 67 _t
/Times-BoldItalicR 600 _ff
(y)_S /Times-BoldItalicR 360 _ff
8201 5662 _m
(G)_S 8288 5662 _m
/Times-RomanR 600 _ff
8288 5707 _m
(,)_S 67 _t
/Times-BoldItalicR 600 _ff
(z)_S /Times-BoldItalicR 360 _ff
8483 5662 _m
(G)_S 8569 5662 _m
/Times-RomanR 600 _ff
8569 5707 _m
(\))_S gsave 4 4 scale 16 _sr _s 
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_sp 555 1198 555 1201 308 1201 3 _pl _pf _np _s _s 300 904 _m
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/Times-BoldItalicR 600 _ff
(x)_S /Times-BoldItalicR 360 _ff
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(G)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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(y)_S /Times-BoldItalicR 360 _ff
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_s 0 g 0 0 0 0 _cw 
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_bp /Times-RomanR 600 _ff
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_s 0 g 0 0 0 0 _cw 
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(Name)_S gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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_s 0 g 0 0 0 0 _cw 
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gsave 4 4 scale 16 _sr _s 
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_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 555 2118 555 2121 308 2121 3 _pl _pf _np _s _s 300 1912 _m
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_s 0 g 0 0 0 0 _cw 
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gsave 4 4 scale 16 _sr _s 
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_sp 805 2118 805 2121 554 2121 3 _pl _pf _np _s _s 554 1912 _m
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_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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gsave 4 4 scale 16 _sr _s 
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gsave 4 4 scale 16 _sr _s 
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_sp 555 1405 555 1408 308 1408 3 _pl _pf _np _s _s 300 1111 _m
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_s grestore gsave 4 4 scale 16 _sr _s 
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(bow-vertical)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 1853 1405 1853 1408 804 1408 3 _pl _pf _np _s _s 804 1111 _m
_sp 807 1111 807 1408 804 1408 3 _pl _pf _np 
_s 0 g 293 1045 808 1111 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 5353 _m
/Times-RomanR 600 _ff
(Distance)_S 67 _t
(from)_S 67 _t
(nominal)_S 67 _t
(vehicle)_S 67 _t
(centroid)_S 67 _t
(to)_S 3333 5004 _m
(centerline)_S 67 _t
(of)_S 67 _t
(bow)_S 67 _t
(vertical)_S 67 _t
(thruster)_S 67 _t
(tunnel)_S 67 _t
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(body)_S 67 _t
(longitudinal)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1111 2250 1408 2247 1408 3 _pl _pf _np _s _s 1852 1405 _m
_sp 2242 1405 2242 1408 1852 1408 3 _pl _pf _np _s _s 1852 1111 _m
_sp 1855 1111 1855 1408 1852 1408 3 _pl _pf _np _s _s 2239 1111 _m
_sp 2242 1111 2242 1408 2239 1408 3 _pl _pf _np 
_s 0 g 293 382 1856 1111 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7852 5353 _m
67 _t
67 _t
(1.41)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 1109 555 1112 308 1112 3 _pl _pf _np _s _s 300 816 _m
_sp 303 816 303 1112 300 1112 3 _pl _pf _np _s _s 308 816 _m
_sp 311 816 311 1112 308 1112 3 _pl _pf _np 
_s 0 g 292 243 312 816 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1109 _m
_sp 805 1109 805 1112 554 1112 3 _pl _pf _np 
_s 0 g 292 251 554 816 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1855 4169 _m
/Times-BoldItalicR 600 _ff
(x)_S /Times-BoldItalicR 360 _ff
1955 4124 _m
(stern-vertical)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1109 _m
_sp 1853 1109 1853 1112 804 1112 3 _pl _pf _np _s _s 804 816 _m
_sp 807 816 807 1112 804 1112 3 _pl _pf _np 
_s 0 g 292 1045 808 816 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 4170 _m
/Times-RomanR 600 _ff
(Distance)_S 67 _t
(from)_S 67 _t
(nominal)_S 67 _t
(vehicle)_S 67 _t
(centroid)_S 67 _t
(to)_S 3333 3821 _m
(centerline)_S 67 _t
(of)_S 67 _t
(stern)_S 67 _t
(vertical)_S 67 _t
(thruster)_S 67 _t
(tunnel)_S 67 _t
(along)_S 3333 3472 _m
(body)_S 67 _t
(longitudinal)_S 67 _t
(axis.)_S 134 _t
(Note)_S 67 _t
(negative.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 816 _m
_sp 2250 816 2250 1112 2247 1112 3 _pl _pf _np _s _s 1852 1109 _m
_sp 2242 1109 2242 1112 1852 1112 3 _pl _pf _np _s _s 1852 816 _m
_sp 1855 816 1855 1112 1852 1112 3 _pl _pf _np _s _s 2239 816 _m
_sp 2242 816 2242 1112 2239 1112 3 _pl _pf _np 
_s 0 g 292 382 1856 816 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7853 4170 _m
/Times-BoldR 600 _ff
(-)_S /Times-RomanR 600 _ff
67 _t
(1.41)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 813 _m
_sp 555 813 555 816 308 816 3 _pl _pf _np _s _s 300 520 _m
_sp 303 520 303 816 300 816 3 _pl _pf _np _s _s 308 520 _m
_sp 311 520 311 816 308 816 3 _pl _pf _np 
_s 0 g 292 243 312 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 813 _m
_sp 805 813 805 816 554 816 3 _pl _pf _np 
_s 0 g 292 251 554 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1902 2986 _m
/Times-BoldItalicR 600 _ff
(x)_S /Times-BoldItalicR 360 _ff
2002 2941 _m
(bow-lateral)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 813 _m
_sp 1853 813 1853 816 804 816 3 _pl _pf _np _s _s 804 520 _m
_sp 807 520 807 816 804 816 3 _pl _pf _np 
_s 0 g 292 1045 808 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 2987 _m
/Times-RomanR 600 _ff
(Distance)_S 67 _t
(from)_S 67 _t
(nominal)_S 67 _t
(vehicle)_S 67 _t
(centroid)_S 67 _t
(to)_S 3333 2638 _m
(centerline)_S 67 _t
(of)_S 67 _t
(bow)_S 67 _t
(lateral)_S 67 _t
(thruster)_S 67 _t
(tunnel)_S 67 _t
(along)_S 3333 2289 _m
(body)_S 67 _t
(longitudinal)_S 67 _t
(axis.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 520 _m
_sp 2250 520 2250 816 2247 816 3 _pl _pf _np _s _s 1852 813 _m
_sp 2242 813 2242 816 1852 816 3 _pl _pf _np _s _s 1852 520 _m
_sp 1855 520 1855 816 1852 816 3 _pl _pf _np _s _s 2239 520 _m
_sp 2242 520 2242 816 2239 816 3 _pl _pf _np 
_s 0 g 292 382 1856 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7852 2987 _m
67 _t
67 _t
(1.92)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 516 _m
_sp 555 516 555 519 300 519 3 _pl _pf _np _s _s 300 516 _m
_sp 303 516 303 521 300 521 3 _pl _pf _np _s _s 308 516 _m
_sp 311 516 311 521 308 521 3 _pl _pf _np 
_s 0 g 1 243 312 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 516 _m
_sp 805 516 805 519 554 519 3 _pl _pf _np 
_s 0 g 1 251 554 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 516 _m
_sp 1853 516 1853 519 804 519 3 _pl _pf _np _s _s 804 516 _m
_sp 807 516 807 521 804 521 3 _pl _pf _np 
_s 0 g 1 1045 808 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 516 _m
_sp 2250 516 2250 519 1852 519 3 _pl _pf _np _s _s 2247 516 _m
_sp 2250 516 2250 521 2247 521 3 _pl _pf _np _s _s 1852 516 _m
_sp 1855 516 1855 521 1852 521 3 _pl _pf _np _s _s 2239 516 _m
_sp 2242 516 2242 521 2239 521 3 _pl _pf _np 
_s 0 g 1 382 1856 520 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(132)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 243 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2504 _m
_sp 303 2504 303 2801 300 2801 3 _pl _pf _np _s _s 308 2504 _m
_sp 311 2504 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 293 243 312 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2798 _m
_sp 805 2798 805 2801 554 2801 3 _pl _pf _np 
_s 0 g 293 251 554 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1879 10924 _m
/Times-BoldItalicR 600 _ff
(x)_S /Times-BoldItalicR 360 _ff
1979 10879 _m
(stern-lateral)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2798 _m
_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np _s _s 804 2504 _m
_sp 807 2504 807 2801 804 2801 3 _pl _pf _np 
_s 0 g 293 1045 808 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10925 _m
/Times-RomanR 600 _ff
(Distance)_S 67 _t
(from)_S 67 _t
(nominal)_S 67 _t
(vehicle)_S 67 _t
(centroid)_S 67 _t
(to)_S 3333 10576 _m
(centerline)_S 67 _t
(of)_S 67 _t
(stern)_S 67 _t
(lateral)_S 67 _t
(thruster)_S 67 _t
(tunnel)_S 67 _t
(along)_S 3333 10227 _m
(body)_S 67 _t
(longitudinal)_S 67 _t
(axis.)_S 134 _t
(Note)_S 67 _t
(negative.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2504 _m
_sp 2250 2504 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 1852 2504 _m
_sp 1855 2504 1855 2801 1852 2801 3 _pl _pf _np _s _s 2239 2504 _m
_sp 2242 2504 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 293 382 1856 2504 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7853 10925 _m
/Times-BoldR 600 _ff
(-)_S /Times-RomanR 600 _ff
67 _t
(1.92)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2502 _m
_sp 555 2502 555 2505 308 2505 3 _pl _pf _np _s _s 300 2296 _m
_sp 303 2296 303 2505 300 2505 3 _pl _pf _np _s _s 308 2296 _m
_sp 311 2296 311 2505 308 2505 3 _pl _pf _np 
_s 0 g 205 243 312 2296 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2502 _m
_sp 805 2502 805 2505 554 2505 3 _pl _pf _np 
_s 0 g 205 251 554 2296 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1844 9741 _m
/Times-BoldItalicR 600 _ff
(y)_S /Times-BoldItalicR 360 _ff
1933 9696 _m
(port-propeller)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2502 _m
_sp 1853 2502 1853 2505 804 2505 3 _pl _pf _np _s _s 804 2296 _m
_sp 807 2296 807 2505 804 2505 3 _pl _pf _np 
_s 0 g 205 1045 808 2296 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 9742 _m
/Times-RomanR 600 _ff
(Port)_S 67 _t
(propeller)_S 67 _t
(shaft)_S 67 _t
(offset)_S 67 _t
(from)_S 3333 9393 _m
(longitudinal)_S 67 _t
(centerline)_S 67 _t
(of)_S 67 _t
(vehicle)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2296 _m
_sp 2250 2296 2250 2505 2247 2505 3 _pl _pf _np _s _s 1852 2502 _m
_sp 2242 2502 2242 2505 1852 2505 3 _pl _pf _np _s _s 1852 2296 _m
_sp 1855 2296 1855 2505 1852 2505 3 _pl _pf _np _s _s 2239 2296 _m
_sp 2242 2296 2242 2505 2239 2505 3 _pl _pf _np 
_s 0 g 205 382 1856 2296 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7836 9742 _m
(-)_S 67 _t
(3.75)_S 67 _t
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(0.313)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2294 _m
_sp 555 2294 555 2297 308 2297 3 _pl _pf _np _s _s 300 2087 _m
_sp 303 2087 303 2297 300 2297 3 _pl _pf _np _s _s 308 2087 _m
_sp 311 2087 311 2297 308 2297 3 _pl _pf _np 
_s 0 g 206 243 312 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2294 _m
_sp 805 2294 805 2297 554 2297 3 _pl _pf _np 
_s 0 g 206 251 554 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1844 8907 _m
/Times-BoldItalicR 600 _ff
(y)_S /Times-BoldItalicR 360 _ff
1933 8862 _m
(stbd-propeller)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2294 _m
_sp 1853 2294 1853 2297 804 2297 3 _pl _pf _np _s _s 804 2087 _m
_sp 807 2087 807 2297 804 2297 3 _pl _pf _np 
_s 0 g 206 1045 808 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8908 _m
/Times-RomanR 600 _ff
(Starboard)_S 67 _t
(propeller)_S 67 _t
(shaft)_S 67 _t
(offset)_S 67 _t
(from)_S 3333 8559 _m
(longitudinal)_S 67 _t
(centerline)_S 67 _t
(of)_S 67 _t
(vehicle)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 2087 2250 2297 2247 2297 3 _pl _pf _np _s _s 1852 2294 _m
_sp 2242 2294 2242 2297 1852 2297 3 _pl _pf _np _s _s 1852 2087 _m
_sp 1855 2087 1855 2297 1852 2297 3 _pl _pf _np _s _s 2239 2087 _m
_sp 2242 2087 2242 2297 2239 2297 3 _pl _pf _np 
_s 0 g 206 382 1856 2087 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7802 8908 _m
67 _t
67 _t
67 _t
(3.75)_S 67 _t
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(0.313)_S 67 _t
(ft)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2085 _m
_sp 555 2085 555 2088 308 2088 3 _pl _pf _np _s _s 300 1791 _m
_sp 303 1791 303 2088 300 2088 3 _pl _pf _np _s _s 308 1791 _m
_sp 311 1791 311 2088 308 2088 3 _pl _pf _np 
_s 0 g 293 243 312 1791 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1527 8073 _m
/Times-BoldItalicR 600 _ff
(h)_S 67 _t
(\(x\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2085 _m
_sp 805 2085 805 2088 554 2088 3 _pl _pf _np _s _s 554 1791 _m
_sp 557 1791 557 2088 554 2088 3 _pl _pf _np 
_s 0 g 293 247 558 1791 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2085 _m
_sp 1853 2085 1853 2088 804 2088 3 _pl _pf _np _s _s 804 1791 _m
_sp 807 1791 807 2088 804 2088 3 _pl _pf _np 
_s 0 g 293 1045 808 1791 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8074 _m
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/Times-BoldItalicR 600 _ff
(y)_S /Times-RomanR 600 _ff
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/Times-BoldItalicR 600 _ff
(x)_S /Times-RomanR 600 _ff
67 _t
(measured)_S 67 _t
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(longitudinal)_S 67 _t
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(axis)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1791 2250 2088 2247 2088 3 _pl _pf _np _s _s 1852 2085 _m
_sp 2242 2085 2242 2088 1852 2088 3 _pl _pf _np _s _s 1852 1791 _m
_sp 1855 1791 1855 2088 1852 2088 3 _pl _pf _np _s _s 2239 1791 _m
_sp 2242 1791 2242 2088 2239 2088 3 _pl _pf _np 
_s 0 g 293 382 1856 1791 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7900 8074 _m
(vehicle)_S 7811 7725 _m
(geometry)_S 7711 7376 _m
(tabular)_S 67 _t
(data)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1789 _m
_sp 555 1789 555 1792 308 1792 3 _pl _pf _np _s _s 300 1495 _m
_sp 303 1495 303 1792 300 1792 3 _pl _pf _np _s _s 308 1495 _m
_sp 311 1495 311 1792 308 1792 3 _pl _pf _np 
_s 0 g 293 243 312 1495 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1533 6888 _m
/Times-BoldItalicR 600 _ff
(b)_S 67 _t
(\(x\))_S gsave 4 4 scale 16 _sr _s 
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_sp 805 1789 805 1792 554 1792 3 _pl _pf _np _s _s 554 1495 _m
_sp 557 1495 557 1792 554 1792 3 _pl _pf _np 
_s 0 g 293 247 558 1495 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 1853 1789 1853 1792 804 1792 3 _pl _pf _np _s _s 804 1495 _m
_sp 807 1495 807 1792 804 1792 3 _pl _pf _np 
_s 0 g 293 1045 808 1495 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 6889 _m
(Height)_S 67 _t
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/Times-BoldItalicR 600 _ff
(z)_S /Times-RomanR 600 _ff
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(a)_S 67 _t
(given)_S 67 _t
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/Times-BoldItalicR 600 _ff
(x)_S /Times-RomanR 600 _ff
67 _t
(measured)_S 67 _t
(on)_S 67 _t
(the)_S 3333 6189 _m
(longitudinal)_S 67 _t
(body)_S 67 _t
(axis)_S gsave 4 4 scale 16 _sr _s 
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_sp 2250 1495 2250 1792 2247 1792 3 _pl _pf _np _s _s 1852 1789 _m
_sp 2242 1789 2242 1792 1852 1792 3 _pl _pf _np _s _s 1852 1495 _m
_sp 1855 1495 1855 1792 1852 1792 3 _pl _pf _np _s _s 2239 1495 _m
_sp 2242 1495 2242 1792 2239 1792 3 _pl _pf _np 
_s 0 g 293 382 1856 1495 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7900 6889 _m
(vehicle)_S 7811 6540 _m
(geometry)_S 7711 6191 _m
(tabular)_S 67 _t
(data)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1493 _m
_sp 555 1493 555 1496 308 1496 3 _pl _pf _np _s _s 300 1286 _m
_sp 303 1286 303 1496 300 1496 3 _pl _pf _np _s _s 308 1286 _m
_sp 311 1286 311 1496 308 1496 3 _pl _pf _np 
_s 0 g 206 243 312 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1464 5703 _m
/Times-BoldItalicR 600 _ff
(U)_S /Times-BoldItalicR 360 _ff
1609 5658 _m
(cf)_S 1702 5658 _m
/Times-BoldItalicR 600 _ff
1702 5703 _m
67 _t
(\(x\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1493 _m
_sp 805 1493 805 1496 554 1496 3 _pl _pf _np _s _s 554 1286 _m
_sp 557 1286 557 1496 554 1496 3 _pl _pf _np 
_s 0 g 206 247 558 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1493 _m
_sp 1853 1493 1853 1496 804 1496 3 _pl _pf _np _s _s 804 1286 _m
_sp 807 1286 807 1496 804 1496 3 _pl _pf _np 
_s 0 g 206 1045 808 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 5704 _m
(Total)_S 67 _t
(cross-flow)_S 67 _t
(velocity)_S 67 _t
(across)_S 67 _t
(body)_S 67 _t
(at)_S 67 _t
(a)_S 67 _t
(given)_S 3333 5354 _m
(body)_S 67 _t
(position)_S 67 _t
/Times-BoldItalicR 600 _ff
(x)_S /Times-RomanR 600 _ff
67 _t
(along)_S 67 _t
(longitudinal)_S 67 _t
(axis)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1286 _m
_sp 2250 1286 2250 1496 2247 1496 3 _pl _pf _np _s _s 1852 1493 _m
_sp 2242 1493 2242 1496 1852 1496 3 _pl _pf _np _s _s 1852 1286 _m
_sp 1855 1286 1855 1496 1852 1496 3 _pl _pf _np _s _s 2239 1286 _m
_sp 2242 1286 2242 1496 2239 1496 3 _pl _pf _np 
_s 0 g 206 382 1856 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8061 5704 _m
(see)_S 7553 5355 _m
(Equation)_S 67 _t
(\(6.47\))_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 1282 _m
_sp 555 1282 555 1285 300 1285 3 _pl _pf _np _s _s 300 1282 _m
_sp 303 1282 303 1287 300 1287 3 _pl _pf _np _s _s 308 1282 _m
_sp 311 1282 311 1287 308 1287 3 _pl _pf _np 
_s 0 g 1 243 312 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1282 _m
_sp 805 1282 805 1285 554 1285 3 _pl _pf _np _s _s 554 1282 _m
_sp 557 1282 557 1287 554 1287 3 _pl _pf _np 
_s 0 g 1 247 558 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1282 _m
_sp 1853 1282 1853 1285 804 1285 3 _pl _pf _np _s _s 804 1282 _m
_sp 807 1282 807 1287 804 1287 3 _pl _pf _np 
_s 0 g 1 1045 808 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 1282 _m
_sp 2250 1282 2250 1285 1852 1285 3 _pl _pf _np _s _s 2247 1282 _m
_sp 2250 1282 2250 1287 2247 1287 3 _pl _pf _np _s _s 1852 1282 _m
_sp 1855 1282 1855 1287 1852 1287 3 _pl _pf _np _s _s 2239 1282 _m
_sp 2242 1282 2242 1287 2239 1287 3 _pl _pf _np 
_s 0 g 1 382 1856 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(133)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 243 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2679 _m
_sp 303 2679 303 2801 300 2801 3 _pl _pf _np _s _s 308 2679 _m
_sp 311 2679 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 118 243 312 2679 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2798 _m
_sp 805 2798 805 2801 554 2801 3 _pl _pf _np 
_s 0 g 118 251 554 2679 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2798 _m
_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np 
_s 0 g 118 1049 804 2679 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2679 _m
_sp 2250 2679 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 2239 2679 _m
_sp 2242 2679 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 118 386 1852 2679 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4105 10924 _m
/Times-BoldItalicR 600 _ff
(Surge)_S 67 _t
(force)_S 67 _t
(coefficients)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2677 _m
_sp 555 2677 555 2680 308 2680 3 _pl _pf _np _s _s 300 2180 _m
_sp 303 2180 303 2680 300 2680 3 _pl _pf _np _s _s 308 2180 _m
_sp 311 2180 311 2680 308 2680 3 _pl _pf _np 
_s 0 g 496 243 312 2180 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2677 _m
_sp 805 2677 805 2680 554 2680 3 _pl _pf _np 
_s 0 g 496 251 554 2180 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1493 10090 _m
(steady-state)_S 67 _t
(speed)_S 1648 9741 _m
(per)_S 67 _t
(maximum)_S 1660 9392 _m
(propeller)_S 67 _t
(rpm)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2677 _m
_sp 1853 2677 1853 2680 804 2680 3 _pl _pf _np _s _s 804 2180 _m
_sp 807 2180 807 2680 804 2680 3 _pl _pf _np 
_s 0 g 496 1045 808 2180 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10440 _m
/Times-RomanR 600 _ff
(Average)_S 67 _t
(forward)_S 67 _t
(velocity)_S 67 _t
(based)_S 67 _t
(on)_S 67 _t
(combined)_S 3333 10091 _m
(propeller)_S 67 _t
(revolutions)_S 67 _t
(per)_S 67 _t
(minute)_S 67 _t
(\(rpm\),)_S 3333 9742 _m
(typically)_S 67 _t
(measured)_S 67 _t
(at)_S 67 _t
(maximum)_S 67 _t
(steady-state)_S 3333 9393 _m
(speed.)_S 134 _t
(Analogous)_S 67 _t
(to)_S 67 _t
(turns-per-knot)_S 67 _t
(\(TPK\))_S 67 _t
(ratio)_S 3333 9044 _m
(for)_S 67 _t
(ships)_S 67 _t
(with)_S 67 _t
(fixed-pitch)_S 67 _t
(propellers.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2180 _m
_sp 2250 2180 2250 2680 2247 2680 3 _pl _pf _np _s _s 1852 2677 _m
_sp 2242 2677 2242 2680 1852 2680 3 _pl _pf _np _s _s 1852 2180 _m
_sp 1855 2180 1855 2680 1852 2680 3 _pl _pf _np _s _s 2239 2180 _m
_sp 2242 2180 2242 2680 2239 2680 3 _pl _pf _np 
_s 0 g 496 382 1856 2180 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7714 10042 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 136 238 1928 2510 _cw 
_s 1938 2575 _m
_sp 1938 2575 1935 2575 1935 2587 1935 2592 1935 2596 1935 2600 1935 2605 1936 2609 1937 2612 1938 2616 1939 2619 1941 2622 1942 2625 1945 2629 1948 2634 
1949 2634 1946 2629 1944 2624 1942 2621 1941 2617 1940 2614 1939 2611 1939 2607 1938 2602 1938 2598 1938 2594 1938 2590 1938 2586 28 _pl _cp 
0 g _f _s _s 
0 g 1938 2575 _m
_sp 1938 2575 1935 2575 1935 2561 1935 2556 1935 2552 1935 2547 1935 2543 1936 2539 1937 2535 1938 2532 1939 2529 1941 2526 1942 2522 1945 2518 1948 2514 
1949 2514 1946 2519 1944 2524 1942 2527 1941 2530 1940 2534 1939 2537 1939 2541 1938 2545 1938 2550 1938 2554 1938 2558 1938 2562 28 _pl _cp 
0 g _f _s _s 
0 g 2154 2575 _m
_sp 2154 2575 2157 2575 2157 2587 2157 2592 2157 2596 2157 2600 2156 2605 2156 2609 2155 2612 2154 2616 2153 2619 2152 2622 2150 2625 2147 2629 2144 2634 
2143 2634 2146 2629 2148 2624 2150 2621 2151 2617 2152 2614 2153 2611 2153 2607 2154 2602 2154 2598 2154 2594 2154 2590 2154 2586 28 _pl _cp 
0 g _f _s _s 
0 g 2154 2575 _m
_sp 2154 2575 2157 2575 2157 2561 2157 2556 2157 2552 2157 2547 2156 2543 2156 2539 2155 2535 2154 2532 2153 2529 2152 2526 2150 2522 2147 2518 2144 2514 
2143 2514 2146 2519 2148 2524 2150 2527 2151 2530 2152 2534 2153 2537 2153 2541 2154 2545 2154 2550 2154 2554 2154 2558 2154 2562 28 _pl _cp 
0 g _f _s _s 
0 g 1953 2579 _m
_sp 1953 2579 1953 2577 2137 2577 2137 2579 4 _pl _cp 
0 g _f _s _s 
0 g 1976 2599 _m
_sp 1976 2599 1978 2601 1982 2605 1983 2606 1984 2607 1985 2609 1986 2610 1988 2613 1989 2615 1990 2617 1990 2619 1989 2623 1988 2626 1985 2627 1981 2628 
1979 2628 1977 2627 1976 2627 1974 2626 1973 2624 1972 2623 1971 2621 1971 2618 1972 2618 1973 2620 1974 2622 1976 2623 1979 2624 1982 2623 1984 2622 
1985 2620 1986 2617 1986 2614 1984 2611 1982 2608 1979 2604 1975 2600 1970 2595 1970 2595 1990 2595 1993 2601 1992 2602 1991 2601 1990 2600 1990 2599 
1988 2599 1986 2599 47 _pl _cp 
0 g _f _s _s 
0 g 2021 2617 _m
_sp 2021 2617 2017 2617 2017 2615 2021 2615 2021 2599 2021 2596 2018 2596 2018 2596 2018 2595 2030 2595 2030 2596 2029 2596 2026 2596 2026 2599 2026 2615 
2032 2615 2032 2617 2026 2617 2026 2618 2026 2623 2027 2626 2028 2627 2030 2627 2031 2626 2032 2624 2033 2624 2035 2624 2036 2626 2035 2627 2034 2628 
2032 2629 2030 2629 2026 2628 2024 2626 2022 2623 2021 2618 36 _pl _cp 
0 g _f _s _s 
0 g 2034 2616 _m
_sp 2034 2616 2034 2615 2037 2615 2037 2601 2037 2598 2038 2596 2039 2594 2041 2594 2043 2594 2044 2595 2046 2596 2047 2598 2046 2599 2045 2597 2044 2596 
2042 2597 2041 2600 2041 2615 2046 2615 2046 2617 2041 2617 2041 2623 2040 2623 2039 2622 2038 2621 2037 2619 2036 2618 2035 2617 28 _pl _cp 
0 g _f _s _s 
0 g 2057 2628 _m
_sp 2057 2628 2046 2586 2050 2586 2061 2628 4 _pl _cp 
0 g _f _s _s 
0 g 2063 2595 _m
_sp 2063 2595 2064 2595 2064 2595 2065 2595 2066 2595 2067 2595 2070 2594 2072 2594 2075 2595 2078 2596 2079 2598 2080 2600 2079 2603 2078 2605 2077 2606 
2075 2606 2074 2607 2071 2608 2069 2609 2067 2611 2066 2612 2066 2613 2067 2615 2070 2616 2073 2616 2075 2615 2076 2613 2077 2610 2078 2610 2078 2617 
2077 2617 2077 2617 2076 2616 2076 2617 2075 2617 2073 2617 2072 2617 2070 2617 2067 2617 2065 2616 2064 2614 2063 2611 2063 2609 2064 2608 2066 2606 
2068 2605 2072 2603 2075 2601 2076 2599 2076 2598 2075 2596 2073 2595 2071 2595 2069 2596 2066 2597 2065 2599 2064 2602 2063 2602 58 _pl _cp 
0 g _f _s _s 
0 g 2086 2608 _m
_sp 2086 2608 2101 2608 2100 2612 2099 2615 2096 2616 2092 2617 2088 2616 2085 2614 2083 2610 2082 2605 2083 2600 2085 2597 2088 2595 2092 2594 2095 2595 
2098 2596 2100 2599 2102 2602 2101 2603 2100 2601 2098 2599 2096 2598 2094 2597 2091 2598 2088 2600 2087 2604 2086 2608 2086 2608 28 _pl _cp 2096 2610 _m
_sp 2096 2610 2096 2613 2095 2615 2093 2616 2091 2616 2089 2616 2087 2615 2086 2613 2086 2610 9 _pl _cp 
0 g _f _s _s 
0 g 2123 2602 _m
_sp 2123 2602 2121 2600 2120 2599 2118 2598 2116 2598 2113 2599 2111 2601 2109 2603 2108 2607 2109 2611 2110 2613 2112 2615 2115 2616 2117 2615 2118 2613 
2119 2611 2121 2610 2122 2611 2123 2612 2122 2614 2121 2616 2119 2617 2116 2617 2112 2616 2109 2615 2106 2612 2104 2609 2104 2605 2105 2601 2107 2597 
2110 2595 2114 2594 2116 2594 2118 2595 2119 2596 2121 2597 2122 2598 2122 2599 2123 2600 2124 2602 40 _pl _cp 
0 g _f _s _s 
0 g 1960 2552 _m
_sp 1960 2552 1961 2552 1962 2554 1964 2555 1967 2556 1977 2556 1967 2527 1971 2527 1982 2560 1963 2560 10 _pl _cp 
0 g _f _s _s 
0 g 1985 2543 _m
_sp 1985 2543 1985 2541 1985 2539 1985 2536 1986 2534 1987 2533 1988 2532 1989 2530 1990 2529 1991 2528 1992 2527 1994 2527 1996 2527 2000 2528 2003 2530 
2006 2533 2007 2538 2008 2544 2007 2549 2006 2554 2003 2558 2000 2560 1996 2561 1992 2560 1989 2558 1987 2554 1985 2549 27 _pl _cp 1990 2544 _m
_sp 1990 2544 1990 2538 1991 2534 1992 2531 1994 2529 1996 2529 1998 2529 1999 2530 2000 2532 2001 2535 2002 2539 2002 2544 2002 2549 2001 2553 2000 2556 
1998 2558 1996 2559 1994 2558 1992 2556 1991 2553 1990 2549 21 _pl _cp 
0 g _f _s _s 
0 g 2010 2543 _m
_sp 2010 2543 2010 2541 2010 2539 2010 2536 2011 2534 2012 2533 2013 2532 2014 2530 2015 2529 2016 2528 2017 2527 2019 2527 2021 2527 2025 2528 2028 2530 
2031 2533 2032 2538 2033 2544 2032 2549 2031 2554 2028 2558 2025 2560 2021 2561 2017 2560 2014 2558 2012 2554 2010 2549 27 _pl _cp 2015 2544 _m
_sp 2015 2544 2015 2538 2016 2534 2017 2531 2019 2529 2021 2529 2023 2529 2024 2530 2025 2532 2026 2535 2027 2539 2027 2544 2027 2549 2026 2553 2025 2556 
2023 2558 2021 2559 2019 2558 2017 2556 2016 2553 2015 2549 21 _pl _cp 
0 g _f _s _s 
0 g 2064 2551 _m
_sp 2064 2551 2063 2551 2056 2548 2056 2546 2056 2546 2059 2546 2059 2543 2059 2532 2059 2529 2056 2528 2056 2528 2056 2527 2068 2527 2068 2528 2067 2528 
2064 2529 2064 2532 2064 2543 2065 2545 2066 2546 2067 2546 2068 2546 2069 2545 2070 2545 2071 2546 2072 2547 2071 2549 2069 2550 2068 2550 2067 2549 
2065 2548 2064 2546 32 _pl _cp 
0 g _f _s _s 
0 g 2081 2546 _m
_sp 2081 2546 2081 2551 2080 2551 2072 2547 2072 2546 2073 2546 2076 2546 2076 2543 2076 2522 2076 2519 2073 2518 2072 2518 2072 2517 2085 2517 2085 2518 
2083 2518 2081 2519 2081 2522 2081 2528 2083 2527 2085 2527 2088 2527 2091 2529 2094 2532 2095 2535 2096 2539 2095 2543 2094 2547 2091 2549 2088 2550 
2086 2550 2084 2549 2083 2548 33 _pl _cp 2081 2544 _m
_sp 2081 2544 2081 2531 2083 2529 2085 2528 2088 2529 2090 2531 2091 2533 2091 2537 2091 2541 2090 2544 2088 2546 2085 2547 2083 2546 13 _pl _cp 
0 g _f _s _s 
0 g 2106 2551 _m
_sp 2106 2551 2105 2551 2098 2548 2098 2546 2098 2546 2101 2546 2101 2543 2101 2532 2101 2529 2098 2528 2097 2528 2097 2527 2109 2527 2109 2528 2109 2528 
2106 2529 2106 2532 2106 2544 2107 2545 2109 2546 2110 2547 2111 2547 2112 2547 2114 2546 2115 2544 2115 2541 2115 2532 2114 2529 2112 2528 2111 2528 
2111 2527 2122 2527 2122 2528 2122 2528 2119 2529 2119 2532 2119 2544 2120 2545 2122 2546 2123 2547 2124 2547 2126 2547 2127 2546 2128 2544 2128 2542 
2128 2532 2127 2529 2125 2528 2125 2528 2125 2527 2136 2527 2136 2528 2135 2528 2133 2529 2132 2532 2132 2542 2132 2545 2131 2548 2129 2549 2126 2550 
2124 2550 2122 2549 2120 2548 2118 2546 2117 2548 2116 2549 2115 2550 2113 2550 2111 2550 2110 2549 2108 2548 2106 2546 72 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 7861 9626 _m
(for)_S 67 _t
(twin)_S 7764 9277 _m
(propellers,)_S 7717 8928 _m
(steady)_S 67 _t
(state)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2177 _m
_sp 555 2177 555 2180 308 2180 3 _pl _pf _np _s _s 300 1621 _m
_sp 303 1621 303 2180 300 2180 3 _pl _pf _np _s _s 308 1621 _m
_sp 311 1621 311 2180 308 2180 3 _pl _pf _np 
_s 0 g 555 243 312 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1553 8442 _m
/Times-BoldItalicR 600 _ff
(X)_S /Times-BoldItalicR 360 _ff
1686 8397 _m
(prop)_S /Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2177 _m
_sp 805 2177 805 2180 554 2180 3 _pl _pf _np _s _s 554 1621 _m
_sp 557 1621 557 2180 554 2180 3 _pl _pf _np 
_s 0 g 555 247 558 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2177 _m
_sp 1853 2177 1853 2180 804 2180 3 _pl _pf _np _s _s 804 1621 _m
_sp 807 1621 807 2180 804 2180 3 _pl _pf _np 
_s 0 g 555 1045 808 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8442 _m
(No)_S 67 _t
(longer)_S 67 _t
(used,)_S 67 _t
(since)_S 67 _t
/Times-BoldItalicR 600 _ff
(X)_S /Times-BoldItalicR 360 _ff
5317 8397 _m
(prop)_S 5544 8397 _m
/Times-RomanR 600 _ff
5544 8442 _m
67 _t
(term)_S 67 _t
(is)_S 67 _t
(not)_S 67 _t
(a)_S 67 _t
(true)_S 3333 8091 _m
(coefficient.)_S 134 _t
/Times-BoldItalicR 600 _ff
(X)_S /Times-BoldItalicR 360 _ff
4506 8046 _m
(prop)_S 4732 8046 _m
/Times-RomanR 600 _ff
4732 8091 _m
67 _t
(is)_S 67 _t
(now)_S 67 _t
(decomposed)_S 67 _t
(in)_S 3333 7741 _m
(Equation)_S 67 _t
(\(6.43\))_S 67 _t
(to)_S 67 _t
(explicitly)_S 67 _t
(show)_S 67 _t
(individual)_S 3333 7392 _m
(contributing)_S 67 _t
(propulsion-related)_S 67 _t
(variables,)_S 67 _t
(which)_S 3333 7043 _m
(are)_S 67 _t
(then)_S 67 _t
(included)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(revised)_S 67 _t
(surge)_S 3333 6694 _m
(equation)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(\(6.48\).)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1621 _m
_sp 2250 1621 2250 2180 2247 2180 3 _pl _pf _np _s _s 1852 2177 _m
_sp 2242 2177 2242 2180 1852 2180 3 _pl _pf _np _s _s 1852 1621 _m
_sp 1855 1621 1855 2180 1852 2180 3 _pl _pf _np _s _s 2239 1621 _m
_sp 2242 1621 2242 2180 2239 2180 3 _pl _pf _np 
_s 0 g 555 382 1856 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7764 8443 _m
(Not)_S 67 _t
(used.)_S 67 _t
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(Previous)_S 67 _t
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(are)_S 67 _t
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(applicable.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 1617 _m
_sp 555 1617 555 1620 300 1620 3 _pl _pf _np _s _s 300 1617 _m
_sp 303 1617 303 1622 300 1622 3 _pl _pf _np _s _s 308 1617 _m
_sp 311 1617 311 1622 308 1622 3 _pl _pf _np 
_s 0 g 1 243 312 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1617 _m
_sp 805 1617 805 1620 554 1620 3 _pl _pf _np _s _s 554 1617 _m
_sp 557 1617 557 1622 554 1622 3 _pl _pf _np 
_s 0 g 1 247 558 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1617 _m
_sp 1853 1617 1853 1620 804 1620 3 _pl _pf _np _s _s 804 1617 _m
_sp 807 1617 807 1622 804 1622 3 _pl _pf _np 
_s 0 g 1 1045 808 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 1617 _m
_sp 2250 1617 2250 1620 1852 1620 3 _pl _pf _np _s _s 2247 1617 _m
_sp 2250 1617 2250 1622 2247 1622 3 _pl _pf _np _s _s 1852 1617 _m
_sp 1855 1617 1855 1622 1852 1622 3 _pl _pf _np _s _s 2239 1617 _m
_sp 2242 1617 2242 1622 2239 1622 3 _pl _pf _np 
_s 0 g 1 382 1856 1621 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(134)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 243 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2653 _m
_sp 303 2653 303 2801 300 2801 3 _pl _pf _np _s _s 308 2653 _m
_sp 311 2653 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 144 243 312 2653 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1616 10768 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 58 404 2692 _cw 
_s 424 2737 _m
_sp 424 2737 417 2727 415 2725 413 2723 412 2722 410 2722 410 2721 419 2721 419 2722 418 2722 417 2723 417 2723 418 2725 419 2727 425 2734 
427 2727 428 2726 428 2725 428 2724 428 2723 427 2722 425 2722 425 2721 437 2721 437 2722 436 2722 434 2723 433 2726 432 2727 428 2739 
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434 2752 434 2751 433 2750 432 2749 432 2748 427 2741 425 2748 424 2750 424 2751 423 2751 424 2752 425 2753 426 2753 427 2754 415 2754 
415 2753 416 2753 417 2753 418 2752 419 2750 420 2748 66 _pl _cp 
0 g _f _s _s 
0 g 452 2720 _m
_sp 452 2720 452 2718 451 2716 450 2715 450 2714 449 2712 448 2711 446 2708 444 2707 444 2707 444 2707 444 2708 444 2709 447 2720 442 2719 
442 2719 442 2719 443 2719 444 2718 444 2717 443 2716 441 2710 441 2709 441 2708 441 2708 441 2707 442 2706 443 2705 445 2705 446 2707 
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452 2706 452 2707 452 2707 452 2708 452 2708 452 2709 452 2710 453 2712 453 2714 454 2718 455 2720 56 _pl _cp 
0 g _f _s _s 
0 g 449 2725 _m
_sp 449 2725 450 2724 451 2723 452 2724 453 2725 452 2726 451 2727 450 2726 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2798 _m
_sp 805 2798 805 2801 554 2801 3 _pl _pf _np _s _s 554 2653 _m
_sp 557 2653 557 2801 554 2801 3 _pl _pf _np 
_s 0 g 144 247 558 2653 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2798 _m
_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np _s _s 804 2653 _m
_sp 807 2653 807 2801 804 2801 3 _pl _pf _np 
_s 0 g 144 1045 808 2653 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10925 _m
(Coefficients)_S 67 _t
(describing)_S 67 _t
(surge)_S 67 _t
(forces)_S 67 _t
(from)_S 3333 10506 _m
(resolved)_S 67 _t
(lift,)_S 67 _t
(drag)_S 67 _t
(and)_S 67 _t
(fluid)_S 67 _t
(inertia)_S 67 _t
(along)_S 67 _t
(body)_S 3333 10087 _m
(longitudinal)_S 67 _t
(axis.)_S 134 _t
(These)_S 67 _t
(occur)_S 67 _t
(in)_S 67 _t
(response)_S 67 _t
(to)_S 3333 9668 _m
(individual)_S 67 _t
(\(or)_S 67 _t
(multiple\))_S 67 _t
(velocity,)_S 67 _t
(acceleration)_S 3333 9249 _m
(and)_S 67 _t
(plane)_S 67 _t
(surface)_S 67 _t
(components,)_S 67 _t
(as)_S 67 _t
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(the)_S 67 _t
(corresponding)_S 67 _t
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(For)_S 67 _t
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67 _t
67 _t
67 _t
67 _t
3601 7715 _m
3836 7835 _m
67 _t
(describes)_S 67 _t
(the)_S 67 _t
(drag)_S 67 _t
(contribution)_S 67 _t
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 76 58 900 1928 _cw 
_s 920 1973 _m
_sp 920 1973 913 1963 911 1961 909 1959 908 1958 906 1958 906 1957 915 1957 915 1958 914 1958 913 1959 913 1959 914 1961 915 1963 921 1970 
923 1963 924 1962 924 1961 924 1960 924 1959 923 1958 921 1958 921 1957 933 1957 933 1958 932 1958 930 1959 929 1962 928 1963 924 1975 
925 1977 926 1978 927 1980 928 1981 929 1982 931 1984 932 1985 933 1986 935 1988 937 1989 937 1990 928 1990 928 1989 928 1989 930 1989 
930 1988 930 1987 929 1986 928 1985 928 1984 923 1977 921 1984 920 1986 920 1987 919 1987 920 1988 921 1989 922 1989 923 1990 911 1990 
911 1989 912 1989 913 1989 914 1988 915 1986 916 1984 66 _pl _cp 
0 g _f _s _s 
0 g 948 1956 _m
_sp 948 1956 948 1954 947 1952 946 1951 946 1950 945 1948 944 1947 942 1944 940 1943 940 1943 940 1943 940 1944 940 1945 943 1956 938 1955 
938 1955 938 1955 939 1955 940 1954 940 1953 939 1952 937 1946 937 1945 937 1944 937 1944 937 1943 938 1942 939 1941 941 1941 942 1943 
943 1944 944 1945 945 1946 946 1948 945 1945 945 1944 945 1942 946 1941 947 1941 949 1942 951 1945 951 1945 950 1945 949 1943 949 1943 
948 1942 948 1943 948 1943 948 1944 948 1944 948 1945 948 1946 949 1948 949 1950 950 1954 951 1956 56 _pl _cp 
0 g _f _s _s 
0 g 945 1961 _m
_sp 945 1961 946 1960 947 1959 948 1960 949 1961 948 1962 947 1963 946 1962 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 3333 7289 _m
67 _t
67 _t
67 _t
67 _t
(in)_S 67 _t
(the)_S 67 _t
(longitudinal)_S 67 _t
/Times-BoldItalicR 600 _ff
(X)_S /Times-RomanR 600 _ff
67 _t
(direction)_S 67 _t
3333 6869 _m
67 _t
67 _t
67 _t
67 _t
(due)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 3333 6341 _m
67 _t
67 _t
67 _t
67 _t
(surge)_S 67 _t
(velocity)_S 67 _t
(\()_S 4879 6269 _m
5036 6341 _m
(\))_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 39 1219 1567 _cw 
_s 1246 1615 _m
_sp 1246 1615 1245 1617 1242 1618 1240 1617 1239 1615 1240 1613 1242 1612 1245 1613 8 _pl _cp 
0 g _f _s _s 
0 g 1238 1607 _m
_sp 1238 1607 1235 1606 1234 1606 1232 1606 1229 1606 1227 1605 1227 1604 1229 1604 1230 1603 1230 1602 1230 1601 1230 1599 1228 1592 1227 1590 1227 1587 
1228 1585 1231 1584 1233 1584 1236 1586 1237 1587 1238 1589 1239 1590 1240 1592 1239 1589 1239 1587 1240 1585 1243 1584 1245 1584 1247 1586 1249 1588 
1250 1590 1249 1591 1247 1588 1246 1587 1245 1588 1245 1588 1245 1590 1246 1592 1250 1606 1244 1606 1242 1599 1241 1597 1240 1595 1239 1593 1238 1591 
1236 1588 1234 1587 1233 1588 1233 1589 1233 1590 1233 1591 51 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 3333 5835 _m
(Note)_S 67 _t
(that)_S 67 _t
(any)_S 67 _t
(coefficient)_S 67 _t
(may)_S 67 _t
(be)_S 67 _t
(non-zero,)_S 3333 5416 _m
(depending)_S 67 _t
(principally)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(geometry)_S 67 _t
(of)_S 67 _t
(the)_S 3333 4997 _m
(vehicle)_S 67 _t
(being)_S 67 _t
(modeled.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2653 _m
_sp 2250 2653 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 1852 2653 _m
_sp 1855 2653 1855 2801 1852 2801 3 _pl _pf _np _s _s 2239 2653 _m
_sp 2242 2653 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 144 382 1856 2653 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 10925 _m
(-2.82)_S 67 _t
(E-3)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2651 _m
_sp 555 2651 555 2654 308 2654 3 _pl _pf _np _s _s 300 2543 _m
_sp 303 2543 303 2654 300 2654 3 _pl _pf _np _s _s 308 2543 _m
_sp 311 2543 311 2654 308 2654 3 _pl _pf _np 
_s 0 g 107 243 312 2543 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1620 10179 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 76 56 405 2544 _cw 
_s 425 2589 _m
_sp 425 2589 418 2579 416 2577 414 2575 413 2574 411 2574 411 2573 420 2573 420 2574 419 2574 418 2575 418 2575 419 2577 420 2579 426 2586 
428 2579 429 2578 429 2577 429 2576 429 2575 428 2574 426 2574 426 2573 438 2573 438 2574 437 2574 435 2575 434 2578 433 2579 429 2591 
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416 2605 417 2605 418 2605 419 2604 420 2602 421 2600 66 _pl _cp 
0 g _f _s _s 
0 g 441 2571 _m
_sp 441 2571 441 2571 442 2571 442 2571 443 2570 444 2569 445 2567 445 2565 445 2564 446 2562 446 2559 446 2557 446 2557 447 2557 447 2558 
449 2560 451 2562 452 2563 453 2565 454 2566 455 2567 456 2569 456 2570 455 2571 454 2572 453 2572 452 2571 453 2570 453 2569 454 2569 
454 2568 454 2567 453 2566 452 2565 451 2564 450 2562 448 2560 448 2561 448 2564 448 2565 448 2567 447 2568 447 2570 446 2572 44 _pl _cp 
0 g _f _s _s 
0 g 449 2577 _m
_sp 449 2577 450 2576 451 2575 452 2576 453 2577 452 2578 451 2579 450 2578 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2651 _m
_sp 805 2651 805 2654 554 2654 3 _pl _pf _np _s _s 554 2543 _m
_sp 557 2543 557 2654 554 2654 3 _pl _pf _np 
_s 0 g 107 247 558 2543 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2543 _m
_sp 807 2543 807 2654 804 2654 3 _pl _pf _np 
_s 0 g 111 1045 808 2543 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2543 _m
_sp 2250 2543 2250 2654 2247 2654 3 _pl _pf _np _s _s 1852 2651 _m
_sp 2242 2651 2242 2654 1852 2654 3 _pl _pf _np _s _s 1852 2543 _m
_sp 1855 2543 1855 2654 1852 2654 3 _pl _pf _np _s _s 2239 2543 _m
_sp 2242 2543 2242 2654 2239 2654 3 _pl _pf _np 
_s 0 g 107 382 1856 2543 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8064 10336 _m
(0.0)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2541 _m
_sp 555 2541 555 2544 308 2544 3 _pl _pf _np _s _s 300 2434 _m
_sp 303 2434 303 2544 300 2544 3 _pl _pf _np _s _s 308 2434 _m
_sp 311 2434 311 2544 308 2544 3 _pl _pf _np 
_s 0 g 106 243 312 2434 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1605 9741 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 64 401 2435 _cw 
_s 421 2480 _m
_sp 421 2480 414 2470 412 2468 410 2466 409 2465 407 2465 407 2464 416 2464 416 2465 415 2465 414 2466 414 2466 415 2468 416 2470 422 2477 
424 2470 425 2469 425 2468 425 2467 425 2466 424 2465 422 2465 422 2464 434 2464 434 2465 433 2465 431 2466 430 2469 429 2470 425 2482 
426 2484 427 2485 428 2487 429 2488 430 2489 432 2491 433 2492 434 2493 436 2495 438 2496 438 2497 429 2497 429 2496 429 2496 431 2496 
431 2495 431 2494 430 2493 429 2492 429 2491 424 2484 422 2491 421 2493 421 2494 420 2494 421 2495 422 2496 423 2496 424 2497 412 2497 
412 2496 413 2496 414 2496 415 2495 416 2493 417 2491 66 _pl _cp 
0 g _f _s _s 
0 g 444 2452 _m
_sp 444 2452 443 2454 443 2456 443 2457 443 2459 442 2461 442 2463 438 2462 437 2462 438 2462 440 2461 440 2460 441 2457 441 2454 441 2451 
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456 2461 456 2461 457 2460 457 2459 457 2459 457 2458 456 2456 454 2454 453 2452 452 2451 451 2463 450 2463 42 _pl _cp 
0 g _f _s _s 
0 g 449 2468 _m
_sp 449 2468 450 2467 451 2466 452 2467 452 2468 452 2469 451 2470 450 2469 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2541 _m
_sp 805 2541 805 2544 554 2544 3 _pl _pf _np _s _s 554 2434 _m
_sp 557 2434 557 2544 554 2544 3 _pl _pf _np 
_s 0 g 106 247 558 2434 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2434 _m
_sp 807 2434 807 2544 804 2544 3 _pl _pf _np 
_s 0 g 110 1045 808 2434 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2434 _m
_sp 2250 2434 2250 2544 2247 2544 3 _pl _pf _np _s _s 1852 2541 _m
_sp 2242 2541 2242 2544 1852 2544 3 _pl _pf _np _s _s 1852 2434 _m
_sp 1855 2434 1855 2544 1852 2544 3 _pl _pf _np _s _s 2239 2434 _m
_sp 2242 2434 2242 2544 2239 2544 3 _pl _pf _np 
_s 0 g 106 382 1856 2434 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8064 9898 _m
(0.0)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2432 _m
_sp 555 2432 555 2435 308 2435 3 _pl _pf _np _s _s 300 2324 _m
_sp 303 2324 303 2435 300 2435 3 _pl _pf _np _s _s 308 2324 _m
_sp 311 2324 311 2435 308 2435 3 _pl _pf _np 
_s 0 g 107 243 312 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1616 9303 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 76 58 404 2325 _cw 
_s 424 2370 _m
_sp 424 2370 417 2360 415 2358 413 2356 412 2355 410 2355 410 2354 419 2354 419 2355 418 2355 417 2356 417 2356 418 2358 419 2360 425 2367 
427 2360 428 2359 428 2358 428 2357 428 2356 427 2355 425 2355 425 2354 437 2354 437 2355 436 2355 434 2356 433 2359 432 2360 428 2372 
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0 g 446 2350 _m
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455 2345 456 2347 456 2349 455 2352 452 2353 451 2353 449 2352 448 2351 38 _pl _cp 444 2341 _m
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447 2349 447 2348 446 2346 445 2344 19 _pl _cp 
0 g _f _s _s 
0 g 449 2358 _m
_sp 449 2358 450 2357 451 2356 452 2357 453 2358 452 2359 451 2360 450 2359 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2432 _m
_sp 805 2432 805 2435 554 2435 3 _pl _pf _np _s _s 554 2324 _m
_sp 557 2324 557 2435 554 2435 3 _pl _pf _np 
_s 0 g 107 247 558 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2324 _m
_sp 807 2324 807 2435 804 2435 3 _pl _pf _np 
_s 0 g 111 1045 808 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2324 _m
_sp 2250 2324 2250 2435 2247 2435 3 _pl _pf _np _s _s 1852 2432 _m
_sp 2242 2432 2242 2435 1852 2435 3 _pl _pf _np _s _s 1852 2324 _m
_sp 1855 2324 1855 2435 1852 2435 3 _pl _pf _np _s _s 2239 2324 _m
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/Times-BoldItalicR 600 _ff
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/Times-BoldItalicR 600 _ff
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gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 78 394 1925 _cw 
_s 428 1962 _m
_sp 428 1962 425 1959 423 1958 420 1956 417 1956 415 1956 413 1957 412 1957 411 1958 410 1960 409 1962 408 1964 408 1966 408 1971 410 1976 
412 1980 415 1983 418 1985 422 1986 424 1986 425 1985 427 1984 428 1983 429 1982 429 1981 430 1979 430 1977 431 1977 433 1988 432 1988 
431 1987 430 1987 430 1987 429 1987 427 1987 425 1988 424 1988 422 1988 417 1987 413 1986 409 1983 406 1980 404 1976 403 1972 402 1967 
402 1964 403 1962 404 1959 406 1957 408 1956 410 1955 413 1954 416 1954 419 1954 421 1955 423 1956 425 1957 427 1959 429 1961 59 _pl _cp 
0 g _f _s _s 
0 g 443 1942 _m
_sp 443 1942 442 1941 442 1940 442 1939 443 1938 444 1938 445 1938 446 1938 447 1939 449 1941 448 1942 448 1941 446 1940 446 1940 445 1940 
445 1940 445 1941 445 1942 451 1961 445 1960 445 1960 446 1960 447 1960 447 1959 447 1958 447 1957 445 1952 444 1953 443 1953 442 1953 
440 1952 439 1951 437 1950 435 1948 434 1946 433 1944 433 1942 434 1939 437 1938 439 1938 441 1940 442 1941 42 _pl _cp 436 1942 _m
_sp 436 1942 437 1940 438 1939 440 1940 442 1943 443 1944 443 1945 444 1948 445 1950 444 1951 443 1952 442 1952 441 1951 439 1950 438 1949 
437 1947 437 1946 436 1944 436 1942 436 1942 20 _pl _cp 
0 g _f _s _s 
0 g 451 1945 _m
_sp 451 1945 451 1942 452 1940 454 1938 456 1938 459 1939 462 1941 464 1944 465 1948 466 1952 466 1955 465 1958 463 1959 461 1960 458 1959 
455 1957 453 1954 452 1950 451 1945 451 1945 20 _pl _cp 454 1943 _m
_sp 454 1943 455 1940 456 1939 458 1940 460 1942 461 1945 462 1948 463 1951 463 1954 463 1956 462 1958 461 1959 460 1959 459 1958 457 1957 
456 1954 455 1950 454 1947 454 1943 454 1943 20 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2031 _m
_sp 805 2031 805 2034 554 2034 3 _pl _pf _np _s _s 554 1924 _m
_sp 557 1924 557 2034 554 2034 3 _pl _pf _np 
_s 0 g 106 247 558 1924 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2031 _m
_sp 1853 2031 1853 2034 804 2034 3 _pl _pf _np _s _s 804 1924 _m
_sp 807 1924 807 2034 804 2034 3 _pl _pf _np 
_s 0 g 106 1045 808 1924 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 7859 _m
(Drag)_S 67 _t
(coefficient)_S 67 _t
(along)_S 67 _t
(body)_S 67 _t
(longitudinal)_S 67 _t
(axis)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1924 _m
_sp 2250 1924 2250 2034 2247 2034 3 _pl _pf _np _s _s 1852 2031 _m
_sp 2242 2031 2242 2034 1852 2034 3 _pl _pf _np _s _s 1852 1924 _m
_sp 1855 1924 1855 2034 1852 2034 3 _pl _pf _np _s _s 2239 1924 _m
_sp 2242 1924 2242 2034 2239 2034 3 _pl _pf _np 
_s 0 g 106 382 1856 1924 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7864 7859 _m
(0.00778)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1922 _m
_sp 555 1922 555 1925 308 1925 3 _pl _pf _np _s _s 300 1715 _m
_sp 303 1715 303 1925 300 1925 3 _pl _pf _np _s _s 308 1715 _m
_sp 311 1715 311 1925 308 1925 3 _pl _pf _np 
_s 0 g 206 243 312 1715 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1922 _m
_sp 805 1922 805 1925 554 1925 3 _pl _pf _np 
_s 0 g 206 251 554 1715 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1922 _m
_sp 1853 1922 1853 1925 804 1925 3 _pl _pf _np 
_s 0 g 206 1049 804 1715 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1715 _m
_sp 2250 1715 2250 1925 2247 1925 3 _pl _pf _np _s _s 1852 1922 _m
_sp 2242 1922 2242 1925 1852 1925 3 _pl _pf _np _s _s 2239 1715 _m
_sp 2242 1715 2242 1925 2239 1925 3 _pl _pf _np 
_s 0 g 206 386 1852 1715 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1715 7188 _m
(Note:)_S 134 _t
(for)_S 67 _t
(remaining)_S 67 _t
(coefficients,)_S 67 _t
(only)_S 67 _t
(non-negligible)_S 67 _t
(NPS)_S 67 _t
(AUV)_S 67 _t
(values)_S 67 _t
(are)_S 67 _t
(listed.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1713 _m
_sp 555 1713 555 1716 308 1716 3 _pl _pf _np _s _s 300 1623 _m
_sp 303 1623 303 1716 300 1716 3 _pl _pf _np _s _s 308 1623 _m
_sp 311 1623 311 1716 308 1716 3 _pl _pf _np 
_s 0 g 89 243 312 1623 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1713 _m
_sp 805 1713 805 1716 554 1716 3 _pl _pf _np 
_s 0 g 89 251 554 1623 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1713 _m
_sp 1853 1713 1853 1716 804 1716 3 _pl _pf _np 
_s 0 g 89 1049 804 1623 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1623 _m
_sp 2250 1623 2250 1716 2247 1716 3 _pl _pf _np _s _s 1852 1713 _m
_sp 2242 1713 2242 1716 1852 1716 3 _pl _pf _np _s _s 2239 1623 _m
_sp 2242 1623 2242 1716 2239 1716 3 _pl _pf _np 
_s 0 g 89 386 1852 1623 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4133 6585 _m
/Times-BoldItalicR 600 _ff
(Sway)_S 67 _t
(force)_S 67 _t
(coefficients)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1621 _m
_sp 555 1621 555 1624 308 1624 3 _pl _pf _np _s _s 300 1511 _m
_sp 303 1511 303 1624 300 1624 3 _pl _pf _np _s _s 308 1511 _m
_sp 311 1511 311 1624 308 1624 3 _pl _pf _np 
_s 0 g 109 243 312 1511 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1625 6060 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 54 406 1515 _cw 
_s 424 1559 _m
_sp 424 1559 421 1551 421 1549 419 1546 417 1545 416 1545 415 1544 429 1544 430 1545 428 1545 427 1546 426 1547 426 1548 426 1549 427 1551 
429 1559 430 1561 434 1566 437 1570 439 1573 441 1575 442 1575 443 1576 444 1577 434 1577 434 1576 435 1576 436 1576 437 1575 436 1574 
435 1572 434 1570 432 1568 431 1566 430 1565 429 1563 428 1562 425 1572 425 1573 425 1573 425 1574 424 1574 425 1575 427 1576 428 1576 
428 1577 416 1577 416 1576 418 1575 420 1572 50 _pl _cp 
0 g _f _s _s 
0 g 440 1542 _m
_sp 440 1542 439 1542 440 1542 440 1542 441 1541 442 1540 443 1538 443 1536 444 1535 444 1533 444 1530 444 1528 445 1528 445 1528 446 1529 
448 1531 450 1533 451 1534 452 1536 452 1537 453 1538 454 1540 454 1541 453 1542 452 1543 451 1543 451 1542 451 1541 451 1540 452 1540 
452 1539 452 1538 451 1537 451 1536 450 1535 448 1533 447 1531 447 1532 446 1535 446 1536 446 1538 446 1539 445 1541 445 1543 44 _pl _cp 
0 g _f _s _s 
0 g 447 1548 _m
_sp 447 1548 448 1547 449 1546 450 1547 451 1548 450 1549 449 1550 448 1549 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1621 _m
_sp 805 1621 805 1624 554 1624 3 _pl _pf _np _s _s 554 1511 _m
_sp 557 1511 557 1624 554 1624 3 _pl _pf _np 
_s 0 g 109 247 558 1511 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1621 _m
_sp 1853 1621 1853 1624 804 1624 3 _pl _pf _np _s _s 804 1511 _m
_sp 807 1511 807 1624 804 1624 3 _pl _pf _np 
_s 0 g 109 1045 808 1511 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 6217 _m
(Coefficients)_S 67 _t
(describing)_S 67 _t
(sway)_S 67 _t
(forces)_S 67 _t
(from)_S 3333 5798 _m
(resolved)_S 67 _t
(lift,)_S 67 _t
(drag)_S 67 _t
(and)_S 67 _t
(fluid)_S 67 _t
(inertia)_S 67 _t
(along)_S 67 _t
(body)_S 3333 5379 _m
(lateral)_S 67 _t
(axis.)_S 134 _t
(These)_S 67 _t
(occur)_S 67 _t
(in)_S 67 _t
(response)_S 67 _t
(to)_S 3333 4960 _m
(individual)_S 67 _t
(\(or)_S 67 _t
(multiple\))_S 67 _t
(velocity,)_S 67 _t
(acceleration)_S 3333 4541 _m
(and)_S 67 _t
(plane)_S 67 _t
(surface)_S 67 _t
(components,)_S 67 _t
(as)_S 67 _t
(indicated)_S 67 _t
(by)_S 3333 4122 _m
(the)_S 67 _t
(corresponding)_S 67 _t
(subscripts.)_S 67 _t
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1511 _m
_sp 2250 1511 2250 1624 2247 1624 3 _pl _pf _np _s _s 1852 1621 _m
_sp 2242 1621 2242 1624 1852 1624 3 _pl _pf _np _s _s 1852 1511 _m
_sp 1855 1511 1855 1624 1852 1624 3 _pl _pf _np _s _s 2239 1511 _m
_sp 2242 1511 2242 1624 2239 1624 3 _pl _pf _np 
_s 0 g 109 382 1856 1511 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 6217 _m
(-3.43)_S 67 _t
(E-2)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1508 _m
_sp 555 1508 555 1511 308 1511 3 _pl _pf _np _s _s 300 1398 _m
_sp 303 1398 303 1511 300 1511 3 _pl _pf _np _s _s 308 1398 _m
_sp 311 1398 311 1511 308 1511 3 _pl _pf _np 
_s 0 g 109 243 312 1398 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1629 5610 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 52 407 1402 _cw 
_s 425 1446 _m
_sp 425 1446 422 1438 422 1436 420 1433 418 1432 417 1432 416 1431 430 1431 431 1432 429 1432 428 1433 427 1434 427 1435 427 1436 428 1438 
430 1446 431 1448 435 1453 438 1457 440 1460 442 1462 443 1462 444 1463 445 1464 435 1464 435 1463 436 1463 437 1463 438 1462 437 1461 
436 1459 435 1457 433 1455 432 1453 431 1452 430 1450 429 1449 426 1459 426 1460 426 1460 426 1461 425 1461 426 1462 428 1463 429 1463 
429 1464 417 1464 417 1463 419 1462 421 1459 50 _pl _cp 
0 g _f _s _s 
0 g 441 1415 _m
_sp 441 1415 444 1415 445 1418 445 1420 446 1421 447 1424 448 1426 449 1427 450 1428 450 1428 451 1427 451 1427 452 1426 453 1427 453 1428 
453 1429 452 1430 451 1430 449 1429 448 1427 447 1425 447 1425 446 1424 448 1430 442 1429 442 1429 443 1429 444 1429 444 1428 444 1427 
444 1426 31 _pl _cp 
0 g _f _s _s 
0 g 447 1435 _m
_sp 447 1435 448 1434 449 1433 450 1434 451 1435 450 1436 449 1437 448 1436 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1508 _m
_sp 805 1508 805 1511 554 1511 3 _pl _pf _np _s _s 554 1398 _m
_sp 557 1398 557 1511 554 1511 3 _pl _pf _np 
_s 0 g 109 247 558 1398 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1398 _m
_sp 807 1398 807 1511 804 1511 3 _pl _pf _np 
_s 0 g 113 1045 808 1398 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1398 _m
_sp 2250 1398 2250 1511 2247 1511 3 _pl _pf _np _s _s 1852 1508 _m
_sp 2242 1508 2242 1511 1852 1511 3 _pl _pf _np _s _s 1852 1398 _m
_sp 1855 1398 1855 1511 1852 1511 3 _pl _pf _np _s _s 2239 1398 _m
_sp 2242 1398 2242 1511 2239 1511 3 _pl _pf _np 
_s 0 g 109 382 1856 1398 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 5767 _m
(-1.78)_S 67 _t
(E-1)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1396 _m
_sp 555 1396 555 1399 308 1399 3 _pl _pf _np _s _s 300 1286 _m
_sp 303 1286 303 1399 300 1399 3 _pl _pf _np _s _s 308 1286 _m
_sp 311 1286 311 1399 308 1399 3 _pl _pf _np 
_s 0 g 109 243 312 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1592 5160 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 70 398 1290 _cw 
_s 416 1334 _m
_sp 416 1334 413 1326 413 1324 411 1321 409 1320 408 1320 407 1319 421 1319 422 1320 420 1320 419 1321 418 1322 418 1323 418 1324 419 1326 
421 1334 422 1336 426 1341 429 1345 431 1348 433 1350 434 1350 435 1351 436 1352 426 1352 426 1351 427 1351 428 1351 429 1350 428 1349 
427 1347 426 1345 424 1343 423 1341 422 1340 421 1338 420 1337 417 1347 417 1348 417 1348 417 1349 416 1349 417 1350 419 1351 420 1351 
420 1352 408 1352 408 1351 410 1350 412 1347 50 _pl _cp 
0 g _f _s _s 
0 g 444 1318 _m
_sp 444 1318 443 1316 442 1314 441 1312 440 1309 439 1307 437 1306 436 1305 435 1305 435 1305 435 1305 435 1306 435 1307 438 1318 433 1317 
433 1317 434 1317 435 1317 435 1316 435 1315 434 1314 433 1308 433 1307 432 1306 432 1306 432 1305 433 1304 434 1303 436 1303 438 1305 
439 1306 439 1307 440 1308 441 1310 441 1307 440 1306 440 1304 441 1303 442 1303 443 1303 444 1304 446 1305 447 1307 446 1307 446 1307 
445 1305 444 1305 443 1304 443 1305 443 1305 443 1306 443 1306 443 1307 444 1308 444 1310 445 1312 446 1316 446 1318 58 _pl _cp 
0 g _f _s _s 
0 g 448 1317 _m
_sp 448 1317 448 1317 449 1317 449 1317 450 1316 451 1315 452 1313 452 1311 452 1310 453 1308 453 1305 453 1303 453 1303 454 1303 454 1304 
456 1306 458 1308 459 1309 460 1311 461 1312 462 1313 463 1315 463 1316 462 1317 461 1318 460 1318 459 1317 460 1316 460 1315 461 1315 
461 1314 461 1313 460 1312 459 1311 458 1310 457 1308 455 1306 455 1307 455 1310 455 1311 455 1313 454 1314 454 1316 453 1318 44 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1396 _m
_sp 805 1396 805 1399 554 1399 3 _pl _pf _np _s _s 554 1286 _m
_sp 557 1286 557 1399 554 1399 3 _pl _pf _np 
_s 0 g 109 247 558 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1286 _m
_sp 807 1286 807 1399 804 1399 3 _pl _pf _np 
_s 0 g 113 1045 808 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1286 _m
_sp 2250 1286 2250 1399 2247 1399 3 _pl _pf _np _s _s 1852 1396 _m
_sp 2242 1396 2242 1399 1852 1399 3 _pl _pf _np _s _s 1852 1286 _m
_sp 1855 1286 1855 1399 1852 1399 3 _pl _pf _np _s _s 2239 1286 _m
_sp 2242 1286 2242 1399 2239 1399 3 _pl _pf _np 
_s 0 g 109 382 1856 1286 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 5317 _m
(-1.07)_S 67 _t
(E-1)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1283 _m
_sp 555 1283 555 1286 308 1286 3 _pl _pf _np _s _s 300 1173 _m
_sp 303 1173 303 1286 300 1286 3 _pl _pf _np _s _s 308 1173 _m
_sp 311 1173 311 1286 308 1286 3 _pl _pf _np 
_s 0 g 109 243 312 1173 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1595 4710 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 69 398 1177 _cw 
_s 416 1221 _m
_sp 416 1221 413 1213 413 1211 411 1208 409 1207 408 1207 407 1206 421 1206 422 1207 420 1207 419 1208 418 1209 418 1210 418 1211 419 1213 
421 1221 422 1223 426 1228 429 1232 431 1235 433 1237 434 1237 435 1238 436 1239 426 1239 426 1238 427 1238 428 1238 429 1237 428 1236 
427 1234 426 1232 424 1230 423 1228 422 1227 421 1225 420 1224 417 1234 417 1235 417 1235 417 1236 416 1236 417 1237 419 1238 420 1238 
420 1239 408 1239 408 1238 410 1237 412 1234 50 _pl _cp 
0 g _f _s _s 
0 g 444 1205 _m
_sp 444 1205 443 1203 442 1201 441 1199 440 1196 439 1194 437 1193 436 1192 435 1192 435 1192 435 1192 435 1193 435 1194 438 1205 433 1204 
433 1204 434 1204 435 1204 435 1203 435 1202 434 1201 433 1195 433 1194 432 1193 432 1193 432 1192 433 1191 434 1190 436 1190 438 1192 
439 1193 439 1194 440 1195 441 1197 441 1194 440 1193 440 1191 441 1190 442 1190 443 1190 444 1191 446 1192 447 1194 446 1194 446 1194 
445 1192 444 1192 443 1191 443 1192 443 1192 443 1193 443 1193 443 1194 444 1195 444 1197 445 1199 446 1203 446 1205 58 _pl _cp 
0 g _f _s _s 
0 g 449 1190 _m
_sp 449 1190 452 1190 452 1193 453 1195 453 1196 454 1197 455 1199 455 1200 456 1201 457 1202 458 1203 458 1203 458 1202 459 1202 460 1201 
461 1202 461 1203 460 1204 459 1205 458 1205 457 1204 456 1202 455 1200 454 1200 454 1199 455 1205 450 1204 450 1204 451 1204 452 1204 
452 1203 452 1202 452 1201 33 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1283 _m
_sp 805 1283 805 1286 554 1286 3 _pl _pf _np _s _s 554 1173 _m
_sp 557 1173 557 1286 554 1286 3 _pl _pf _np 
_s 0 g 109 247 558 1173 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1173 _m
_sp 807 1173 807 1286 804 1286 3 _pl _pf _np 
_s 0 g 113 1045 808 1173 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1173 _m
_sp 2250 1173 2250 1286 2247 1286 3 _pl _pf _np _s _s 1852 1283 _m
_sp 2242 1283 2242 1286 1852 1286 3 _pl _pf _np _s _s 1852 1173 _m
_sp 1855 1173 1855 1286 1852 1286 3 _pl _pf _np _s _s 2239 1173 _m
_sp 2242 1173 2242 1286 2239 1286 3 _pl _pf _np 
_s 0 g 109 382 1856 1173 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8064 4867 _m
(0.0)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1171 _m
_sp 555 1171 555 1174 308 1174 3 _pl _pf _np _s _s 300 1061 _m
_sp 303 1061 303 1174 300 1174 3 _pl _pf _np _s _s 308 1061 _m
_sp 311 1061 311 1174 308 1174 3 _pl _pf _np 
_s 0 g 109 243 312 1061 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1427 4260 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 153 356 1065 _cw 
_s 374 1109 _m
_sp 374 1109 371 1101 371 1099 369 1096 367 1095 366 1095 365 1094 379 1094 380 1095 378 1095 377 1096 376 1097 376 1098 376 1099 377 1101 
379 1109 380 1111 384 1116 387 1120 389 1123 391 1125 392 1125 393 1126 394 1127 384 1127 384 1126 385 1126 386 1126 387 1125 386 1124 
385 1122 384 1120 382 1118 381 1116 380 1115 379 1113 378 1112 375 1122 375 1123 375 1123 375 1124 374 1124 375 1125 377 1126 378 1126 
378 1127 366 1127 366 1126 368 1125 370 1122 50 _pl _cp 
0 g _f _s _s 
0 g 402 1093 _m
_sp 402 1093 401 1091 400 1089 399 1087 398 1084 397 1082 395 1081 394 1080 393 1080 393 1080 393 1080 393 1081 393 1082 396 1093 391 1092 
391 1092 392 1092 393 1092 393 1091 393 1090 392 1089 391 1083 391 1082 390 1081 390 1081 390 1080 391 1079 392 1078 394 1078 396 1080 
397 1081 397 1082 398 1083 399 1085 399 1082 398 1081 398 1079 399 1078 400 1078 401 1078 402 1079 404 1080 405 1082 404 1082 404 1082 
403 1080 402 1080 401 1079 401 1080 401 1080 401 1081 401 1081 401 1082 402 1083 402 1085 403 1087 404 1091 404 1093 58 _pl _cp 
0 g _f _s _s 
0 g 432 1093 _m
_sp 432 1093 431 1091 430 1089 429 1087 428 1084 427 1082 425 1081 424 1080 423 1080 423 1080 423 1080 423 1081 423 1082 426 1093 421 1092 
421 1092 422 1092 423 1092 423 1091 423 1090 422 1089 421 1083 421 1082 420 1081 420 1081 420 1080 421 1079 422 1078 424 1078 426 1080 
427 1081 427 1082 428 1083 429 1085 429 1082 428 1081 428 1079 429 1078 430 1078 431 1078 432 1079 434 1080 435 1082 434 1082 434 1082 
433 1080 432 1080 431 1079 431 1080 431 1080 431 1081 431 1081 431 1082 432 1083 432 1085 433 1087 434 1091 434 1093 58 _pl _cp 
0 g _f _s _s 
0 g 474 1078 _m
_sp 474 1078 477 1078 478 1081 478 1083 479 1084 480 1087 481 1089 482 1090 483 1091 483 1091 484 1090 484 1090 485 1089 486 1090 486 1091 
486 1092 485 1093 484 1093 482 1092 481 1090 480 1088 480 1088 479 1087 481 1093 475 1092 475 1092 476 1092 477 1092 477 1091 477 1090 
477 1089 31 _pl _cp 
0 g _f _s _s 
0 g 493 1089 _m
_sp 493 1089 496 1101 490 1100 490 1100 491 1100 492 1100 492 1099 492 1098 492 1097 488 1081 487 1080 487 1080 487 1080 487 1079 488 1079 
490 1078 492 1078 494 1078 496 1079 497 1080 499 1081 500 1083 501 1085 502 1087 502 1089 501 1092 499 1093 498 1093 497 1093 495 1091 
30 _pl _cp 490 1080 _m
_sp 490 1080 491 1079 492 1079 494 1079 496 1081 497 1083 498 1085 499 1087 499 1089 499 1090 497 1091 496 1091 494 1090 493 1088 492 1086 
491 1084 491 1082 490 1081 18 _pl _cp 
0 g _f _s _s 
0 g 413 1103 _m
_sp 413 1103 413 1070 414 1070 414 1103 4 _pl _cp 
0 g _f _s _s 
0 g 443 1103 _m
_sp 443 1103 443 1070 444 1070 444 1103 4 _pl _cp 
0 g _f _s _s 
0 g 467 1097 _m
_sp 467 1097 465 1099 463 1100 461 1101 459 1100 458 1098 458 1097 459 1096 461 1094 462 1093 459 1092 458 1091 456 1088 456 1085 457 1082 
458 1080 460 1079 462 1078 465 1079 467 1080 468 1082 469 1085 469 1087 469 1088 468 1089 467 1091 466 1092 464 1093 462 1095 461 1096 
460 1097 460 1098 460 1099 461 1099 462 1098 464 1097 465 1095 37 _pl _cp 466 1085 _m
_sp 466 1085 466 1083 465 1081 464 1080 462 1079 461 1080 460 1081 459 1083 459 1085 459 1088 460 1090 461 1091 462 1091 464 1091 465 1090 
466 1088 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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(coefficient)_S 67 _t
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_sp 311 835 311 839 308 839 3 _pl _pf _np _s grestore gsave 4 4 scale 16 _sr _s 
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_sp 2250 835 2250 838 1852 838 3 _pl _pf _np _s _s 2247 835 _m
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_sp 2242 835 2242 839 2239 839 3 _pl _pf _np _s grestore 4950 1288 _m
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_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
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(Coefficient)_S gsave 4 4 scale 16 _sr _s 
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(Name)_S gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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(Description)_S gsave 4 4 scale 16 _sr _s 
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(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
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_s 0 g 0 0 0 0 _cw 
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_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 557 2587 557 2709 554 2709 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
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gsave 4 4 scale 16 _sr _s 
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_s 0 g 0 0 0 0 _cw 
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(multiple\))_S 67 _t
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(the)_S 67 _t
(corresponding)_S 67 _t
(subscripts.)_S 67 _t
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_s 0 g 0 0 0 0 _cw 
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(E-2)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 2584 555 2587 308 2587 3 _pl _pf _np _s _s 300 2439 _m
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_s 0 g 0 0 0 0 _cw 
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/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
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0 g 451 2504 _m
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_s grestore gsave 4 4 scale 16 _sr _s 
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(E-3)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 2437 555 2440 308 2440 3 _pl _pf _np _s _s 300 2292 _m
_sp 303 2292 303 2440 300 2440 3 _pl _pf _np _s _s 308 2292 _m
_sp 311 2292 311 2440 308 2440 3 _pl _pf _np 
_s 0 g 144 243 312 2292 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1577 9325 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 78 394 2331 _cw 
_s 399 2361 _m
_sp 399 2361 399 2360 423 2360 426 2369 424 2369 423 2367 422 2365 420 2364 418 2363 415 2362 412 2362 406 2362 429 2392 429 2393 406 2393 
404 2385 405 2385 406 2387 407 2389 409 2390 410 2390 413 2391 416 2391 422 2391 24 _pl _cp 
0 g _f _s _s 
0 g 440 2359 _m
_sp 440 2359 439 2357 438 2355 437 2353 436 2350 435 2348 433 2347 432 2346 431 2346 431 2346 431 2346 431 2347 431 2348 434 2359 429 2358 
429 2358 430 2358 431 2358 431 2357 431 2356 430 2355 429 2349 429 2348 428 2347 428 2347 428 2346 429 2345 430 2344 432 2344 434 2346 
435 2347 435 2348 436 2349 437 2351 437 2348 436 2347 436 2345 437 2344 438 2344 439 2344 440 2345 442 2346 443 2348 442 2348 442 2348 
441 2346 440 2346 439 2345 439 2346 439 2346 439 2347 439 2347 439 2348 440 2349 440 2351 441 2353 442 2357 442 2359 58 _pl _cp 
0 g _f _s _s 
0 g 451 2348 _m
_sp 451 2348 450 2350 450 2352 450 2353 450 2355 449 2357 449 2359 445 2358 444 2358 445 2358 447 2357 447 2356 448 2353 448 2350 448 2347 
448 2344 449 2344 456 2355 457 2344 458 2344 460 2346 461 2348 463 2350 464 2352 465 2355 466 2357 465 2358 464 2359 463 2359 463 2358 
463 2357 463 2357 464 2356 464 2355 464 2355 464 2354 463 2352 461 2350 460 2348 459 2347 458 2359 457 2359 42 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2437 _m
_sp 805 2437 805 2440 554 2440 3 _pl _pf _np _s _s 554 2292 _m
_sp 557 2292 557 2440 554 2440 3 _pl _pf _np 
_s 0 g 144 247 558 2292 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2292 _m
_sp 807 2292 807 2440 804 2440 3 _pl _pf _np 
_s 0 g 148 1045 808 2292 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2292 _m
_sp 2250 2292 2250 2440 2247 2440 3 _pl _pf _np _s _s 1852 2437 _m
_sp 2242 2437 2242 2440 1852 2440 3 _pl _pf _np _s _s 1852 2292 _m
_sp 1855 2292 1855 2440 1852 2440 3 _pl _pf _np _s _s 2239 2292 _m
_sp 2242 2292 2242 2440 2239 2440 3 _pl _pf _np 
_s 0 g 144 382 1856 2292 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7753 9482 _m
(-7.844)_S 67 _t
(E-1)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2290 _m
_sp 555 2290 555 2293 308 2293 3 _pl _pf _np _s _s 300 2145 _m
_sp 303 2145 303 2293 300 2293 3 _pl _pf _np _s _s 308 2145 _m
_sp 311 2145 311 2293 308 2293 3 _pl _pf _np 
_s 0 g 144 243 312 2145 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1588 8736 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 72 397 2184 _cw 
_s 402 2214 _m
_sp 402 2214 402 2213 426 2213 429 2222 427 2222 426 2220 425 2218 423 2217 421 2216 418 2215 415 2215 409 2215 432 2245 432 2246 409 2246 
407 2238 408 2238 409 2240 410 2242 412 2243 413 2243 416 2244 419 2244 425 2244 24 _pl _cp 
0 g _f _s _s 
0 g 443 2212 _m
_sp 443 2212 442 2210 441 2208 440 2206 439 2203 438 2201 436 2200 435 2199 434 2199 434 2199 434 2199 434 2200 434 2201 437 2212 432 2211 
432 2211 433 2211 434 2211 434 2210 434 2209 433 2208 432 2202 432 2201 431 2200 431 2200 431 2199 432 2198 433 2197 435 2197 437 2199 
438 2200 438 2201 439 2202 440 2204 440 2201 439 2200 439 2198 440 2197 441 2197 442 2197 443 2198 445 2199 446 2201 445 2201 445 2201 
444 2199 443 2199 442 2198 442 2199 442 2199 442 2200 442 2200 442 2201 443 2202 443 2204 444 2206 445 2210 445 2212 58 _pl _cp 
0 g _f _s _s 
0 g 460 2210 _m
_sp 460 2210 459 2212 457 2212 456 2212 454 2211 453 2210 451 2209 450 2207 449 2205 448 2203 448 2201 449 2198 451 2197 452 2197 453 2197 
455 2199 457 2201 455 2194 454 2192 453 2191 452 2191 452 2191 460 2191 460 2191 459 2191 458 2192 458 2192 458 2193 458 2194 463 2212 
460 2212 31 _pl _cp 451 2201 _m
_sp 451 2201 451 2199 452 2199 453 2199 455 2200 456 2201 457 2203 458 2205 458 2206 459 2208 459 2209 458 2210 457 2211 456 2211 454 2209 
453 2207 452 2205 451 2203 451 2201 451 2201 20 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2290 _m
_sp 805 2290 805 2293 554 2293 3 _pl _pf _np _s _s 554 2145 _m
_sp 557 2145 557 2293 554 2293 3 _pl _pf _np 
_s 0 g 144 247 558 2145 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2145 _m
_sp 807 2145 807 2293 804 2293 3 _pl _pf _np 
_s 0 g 148 1045 808 2145 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2145 _m
_sp 2250 2145 2250 2293 2247 2293 3 _pl _pf _np _s _s 1852 2290 _m
_sp 2242 2290 2242 2293 1852 2293 3 _pl _pf _np _s _s 1852 2145 _m
_sp 1855 2145 1855 2293 1852 2293 3 _pl _pf _np _s _s 2239 2145 _m
_sp 2242 2145 2242 2293 2239 2293 3 _pl _pf _np 
_s 0 g 144 382 1856 2145 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7753 8893 _m
(-7.013)_S 67 _t
(E-2)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2143 _m
_sp 555 2143 555 2146 308 2146 3 _pl _pf _np _s _s 300 1998 _m
_sp 303 1998 303 2146 300 2146 3 _pl _pf _np _s _s 308 1998 _m
_sp 311 1998 311 2146 308 2146 3 _pl _pf _np 
_s 0 g 144 243 312 1998 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1420 8147 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 76 156 355 2036 _cw 
_s 360 2066 _m
_sp 360 2066 360 2065 384 2065 387 2074 385 2074 384 2072 383 2070 381 2069 379 2068 376 2067 373 2067 367 2067 390 2097 390 2098 367 2098 
365 2090 366 2090 367 2092 368 2094 370 2095 371 2095 374 2096 377 2096 383 2096 24 _pl _cp 
0 g _f _s _s 
0 g 401 2064 _m
_sp 401 2064 400 2062 399 2060 398 2058 397 2055 396 2053 394 2052 393 2051 392 2051 392 2051 392 2051 392 2052 392 2053 395 2064 390 2063 
390 2063 391 2063 392 2063 392 2062 392 2061 391 2060 390 2054 390 2053 389 2052 389 2052 389 2051 390 2050 391 2049 393 2049 395 2051 
396 2052 396 2053 397 2054 398 2056 398 2053 397 2052 397 2050 398 2049 399 2049 400 2049 401 2050 403 2051 404 2053 403 2053 403 2053 
402 2051 401 2051 400 2050 400 2051 400 2051 400 2052 400 2052 400 2053 401 2054 401 2056 402 2058 403 2062 403 2064 58 _pl _cp 
0 g _f _s _s 
0 g 431 2064 _m
_sp 431 2064 430 2062 429 2060 428 2058 427 2055 426 2053 424 2052 423 2051 422 2051 422 2051 422 2051 422 2052 422 2053 425 2064 420 2063 
420 2063 421 2063 422 2063 422 2062 422 2061 421 2060 420 2054 420 2053 419 2052 419 2052 419 2051 420 2050 421 2049 423 2049 425 2051 
426 2052 426 2053 427 2054 428 2056 428 2053 427 2052 427 2050 428 2049 429 2049 430 2049 431 2050 433 2051 434 2053 433 2053 433 2053 
432 2051 431 2051 430 2050 430 2051 430 2051 430 2052 430 2052 430 2053 431 2054 431 2056 432 2058 433 2062 433 2064 58 _pl _cp 
0 g _f _s _s 
0 g 479 2061 _m
_sp 479 2061 480 2064 474 2063 474 2063 475 2063 476 2063 476 2062 476 2061 476 2060 472 2046 471 2044 470 2043 470 2043 470 2043 476 2043 
476 2043 475 2043 475 2044 474 2044 474 2045 474 2045 475 2046 476 2049 477 2049 478 2049 480 2049 481 2050 483 2051 484 2052 485 2054 
487 2056 488 2058 488 2060 487 2063 484 2064 483 2064 481 2063 480 2062 38 _pl _cp 476 2052 _m
_sp 476 2052 476 2051 476 2051 477 2050 478 2050 480 2050 481 2051 482 2053 484 2056 485 2058 485 2060 484 2062 483 2063 482 2062 480 2061 
479 2060 479 2059 478 2057 477 2055 19 _pl _cp 
0 g _f _s _s 
0 g 495 2060 _m
_sp 495 2060 499 2072 493 2071 493 2071 494 2071 495 2071 495 2070 495 2069 495 2068 490 2052 490 2051 490 2051 490 2051 490 2050 490 2050 
492 2049 494 2049 496 2049 498 2050 500 2051 502 2052 503 2054 504 2056 505 2058 505 2060 504 2063 501 2064 501 2064 500 2064 499 2063 
498 2062 496 2061 32 _pl _cp 493 2051 _m
_sp 493 2051 494 2050 495 2050 497 2050 499 2052 500 2054 501 2056 502 2058 502 2060 501 2061 500 2062 499 2062 497 2061 496 2059 495 2057 
494 2055 494 2053 493 2052 18 _pl _cp 
0 g _f _s _s 
0 g 412 2074 _m
_sp 412 2074 412 2041 413 2041 413 2074 4 _pl _cp 
0 g _f _s _s 
0 g 442 2074 _m
_sp 442 2074 442 2041 443 2041 443 2074 4 _pl _cp 
0 g _f _s _s 
0 g 466 2068 _m
_sp 466 2068 464 2070 462 2071 460 2072 458 2071 457 2069 457 2068 458 2067 460 2065 461 2064 458 2063 457 2062 455 2059 455 2056 456 2053 
457 2051 459 2050 461 2049 464 2050 466 2051 467 2053 468 2056 468 2058 468 2059 467 2060 466 2062 465 2063 463 2064 461 2066 460 2067 
459 2068 459 2069 459 2070 460 2070 461 2069 463 2068 464 2066 37 _pl _cp 465 2056 _m
_sp 465 2056 465 2054 464 2052 463 2051 461 2050 460 2051 459 2052 458 2054 458 2056 458 2059 459 2061 460 2062 461 2062 463 2062 464 2061 
465 2059 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2143 _m
_sp 805 2143 805 2146 554 2146 3 _pl _pf _np _s _s 554 1998 _m
_sp 557 1998 557 2146 554 2146 3 _pl _pf _np 
_s 0 g 144 247 558 1998 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1998 _m
_sp 807 1998 807 2146 804 2146 3 _pl _pf _np 
_s 0 g 148 1045 808 1998 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1998 _m
_sp 2250 1998 2250 2146 2247 2146 3 _pl _pf _np _s _s 1852 2143 _m
_sp 2242 2143 2242 2146 1852 2146 3 _pl _pf _np _s _s 1852 1998 _m
_sp 1855 1998 1855 2146 1852 2146 3 _pl _pf _np _s _s 2239 1998 _m
_sp 2242 1998 2242 2146 2239 2146 3 _pl _pf _np 
_s 0 g 144 382 1856 1998 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 8304 _m
(-2.11)_S 67 _t
(E-2)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1995 _m
_sp 555 1995 555 1998 308 1998 3 _pl _pf _np _s _s 300 1850 _m
_sp 303 1850 303 1998 300 1998 3 _pl _pf _np _s _s 308 1850 _m
_sp 311 1850 311 1998 308 1998 3 _pl _pf _np 
_s 0 g 144 243 312 1850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1427 7558 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 153 356 1889 _cw 
_s 361 1919 _m
_sp 361 1919 361 1918 385 1918 388 1927 386 1927 385 1925 384 1923 382 1922 380 1921 377 1920 374 1920 368 1920 391 1950 391 1951 368 1951 
366 1943 367 1943 368 1945 369 1947 371 1948 372 1948 375 1949 378 1949 384 1949 24 _pl _cp 
0 g _f _s _s 
0 g 402 1917 _m
_sp 402 1917 401 1915 400 1913 399 1911 398 1908 397 1906 395 1905 394 1904 393 1904 393 1904 393 1904 393 1905 393 1906 396 1917 391 1916 
391 1916 392 1916 393 1916 393 1915 393 1914 392 1913 391 1907 391 1906 390 1905 390 1905 390 1904 391 1903 392 1902 394 1902 396 1904 
397 1905 397 1906 398 1907 399 1909 399 1906 398 1905 398 1903 399 1902 400 1902 401 1902 402 1903 404 1904 405 1906 404 1906 404 1906 
403 1904 402 1904 401 1903 401 1904 401 1904 401 1905 401 1905 401 1906 402 1907 402 1909 403 1911 404 1915 404 1917 58 _pl _cp 
0 g _f _s _s 
0 g 432 1917 _m
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421 1916 422 1916 423 1916 423 1915 423 1914 422 1913 421 1907 421 1906 420 1905 420 1905 420 1904 421 1903 422 1902 424 1902 426 1904 
427 1905 427 1906 428 1907 429 1909 429 1906 428 1905 428 1903 429 1902 430 1902 431 1902 432 1903 434 1904 435 1906 434 1906 434 1906 
433 1904 432 1904 431 1903 431 1904 431 1904 431 1905 431 1905 431 1906 432 1907 432 1909 433 1911 434 1915 434 1917 58 _pl _cp 
0 g _f _s _s 
0 g 480 1914 _m
_sp 480 1914 481 1917 475 1916 475 1916 476 1916 477 1916 477 1915 477 1914 477 1913 473 1899 472 1897 471 1896 471 1896 471 1896 477 1896 
477 1896 476 1896 476 1897 475 1897 475 1898 475 1898 476 1899 477 1902 478 1902 479 1902 481 1902 482 1903 484 1904 485 1905 486 1907 
488 1909 489 1911 489 1913 488 1916 485 1917 484 1917 482 1916 481 1915 38 _pl _cp 477 1905 _m
_sp 477 1905 477 1904 477 1904 478 1903 479 1903 481 1903 482 1904 483 1906 485 1909 486 1911 486 1913 485 1915 484 1916 483 1915 481 1914 
480 1913 480 1912 479 1910 478 1908 19 _pl _cp 
0 g _f _s _s 
0 g 490 1907 _m
_sp 490 1907 490 1902 490 1902 491 1902 491 1902 491 1902 491 1902 492 1902 493 1902 494 1902 495 1902 497 1902 499 1903 500 1904 501 1906 
501 1907 500 1908 499 1909 498 1911 496 1913 495 1915 496 1916 497 1916 500 1915 501 1912 502 1912 503 1917 502 1917 502 1917 501 1917 
500 1917 499 1917 498 1917 497 1917 494 1916 493 1914 493 1913 493 1911 494 1910 496 1908 498 1907 498 1905 497 1904 495 1903 492 1904 
491 1907 46 _pl _cp 
0 g _f _s _s 
0 g 413 1927 _m
_sp 413 1927 413 1894 414 1894 414 1927 4 _pl _cp 
0 g _f _s _s 
0 g 443 1927 _m
_sp 443 1927 443 1894 444 1894 444 1927 4 _pl _cp 
0 g _f _s _s 
0 g 467 1921 _m
_sp 467 1921 465 1923 463 1924 461 1925 459 1924 458 1922 458 1921 459 1920 461 1918 462 1917 459 1916 458 1915 456 1912 456 1909 457 1906 
458 1904 460 1903 462 1902 465 1903 467 1904 468 1906 469 1909 469 1911 469 1912 468 1913 467 1915 466 1916 464 1917 462 1919 461 1920 
460 1921 460 1922 460 1923 461 1923 462 1922 464 1921 465 1919 37 _pl _cp 466 1909 _m
_sp 466 1909 466 1907 465 1905 464 1904 462 1903 461 1904 460 1905 459 1907 459 1909 459 1912 460 1914 461 1915 462 1915 464 1915 465 1914 
466 1912 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1995 _m
_sp 805 1995 805 1998 554 1998 3 _pl _pf _np _s _s 554 1850 _m
_sp 557 1850 557 1998 554 1998 3 _pl _pf _np 
_s 0 g 144 247 558 1850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1850 _m
_sp 807 1850 807 1998 804 1998 3 _pl _pf _np 
_s 0 g 148 1045 808 1850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1850 _m
_sp 2250 1850 2250 1998 2247 1998 3 _pl _pf _np _s _s 1852 1995 _m
_sp 2242 1995 2242 1998 1852 1998 3 _pl _pf _np _s _s 1852 1850 _m
_sp 1855 1850 1855 1998 1852 1998 3 _pl _pf _np _s _s 2239 1850 _m
_sp 2242 1850 2242 1998 2239 1998 3 _pl _pf _np 
_s 0 g 144 382 1856 1850 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 7715 _m
(-2.11)_S 67 _t
(E-2)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1848 _m
_sp 555 1848 555 1851 308 1851 3 _pl _pf _np _s _s 300 1703 _m
_sp 303 1703 303 1851 300 1851 3 _pl _pf _np _s _s 308 1703 _m
_sp 311 1703 311 1851 308 1851 3 _pl _pf _np 
_s 0 g 144 243 312 1703 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1581 6969 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 76 395 1742 _cw 
_s 429 1779 _m
_sp 429 1779 426 1776 424 1775 421 1773 418 1773 416 1773 414 1774 413 1774 412 1775 411 1777 410 1779 409 1781 409 1783 409 1788 411 1793 
413 1797 416 1800 419 1802 423 1803 425 1803 426 1802 428 1801 429 1800 430 1799 430 1798 431 1796 431 1794 432 1794 434 1805 433 1805 
432 1804 431 1804 431 1804 430 1804 428 1804 426 1805 425 1805 423 1805 418 1804 414 1803 410 1800 407 1797 405 1793 404 1789 403 1784 
403 1781 404 1779 405 1776 407 1774 409 1773 411 1772 414 1771 417 1771 420 1771 422 1772 424 1773 426 1774 428 1776 430 1778 59 _pl _cp 
0 g _f _s _s 
0 g 444 1759 _m
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446 1757 446 1758 446 1759 452 1778 446 1777 446 1777 447 1777 448 1777 448 1776 448 1775 448 1774 446 1769 445 1770 444 1770 443 1770 
441 1769 440 1768 438 1767 436 1765 435 1763 434 1761 434 1759 435 1756 438 1755 440 1755 442 1757 443 1758 42 _pl _cp 437 1759 _m
_sp 437 1759 438 1757 439 1756 441 1757 443 1760 444 1761 444 1762 445 1765 446 1767 445 1768 444 1769 443 1769 442 1768 440 1767 439 1766 
438 1764 438 1763 437 1761 437 1759 437 1759 20 _pl _cp 
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0 g 451 1769 _m
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453 1750 453 1750 453 1751 452 1751 452 1751 452 1751 451 1751 450 1751 450 1750 450 1749 451 1748 453 1749 454 1749 456 1751 457 1753 
459 1756 460 1757 461 1759 462 1761 463 1764 464 1765 465 1767 465 1768 464 1769 463 1770 462 1770 461 1769 462 1768 462 1768 463 1767 
463 1766 463 1766 463 1765 463 1764 462 1763 462 1762 461 1760 461 1760 460 1759 460 1758 459 1758 459 1759 459 1759 458 1761 458 1763 
458 1765 457 1767 456 1769 456 1770 64 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 1848 805 1851 554 1851 3 _pl _pf _np _s _s 554 1703 _m
_sp 557 1703 557 1851 554 1851 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1848 _m
_sp 1853 1848 1853 1851 804 1851 3 _pl _pf _np _s _s 804 1703 _m
_sp 807 1703 807 1851 804 1851 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3333 7126 _m
(Drag)_S 67 _t
(coefficient)_S 67 _t
(along)_S 67 _t
(body)_S 67 _t
(vertical)_S 67 _t
(axis)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1703 _m
_sp 2250 1703 2250 1851 2247 1851 3 _pl _pf _np _s _s 1852 1848 _m
_sp 2242 1848 2242 1851 1852 1851 3 _pl _pf _np _s _s 1852 1703 _m
_sp 1855 1703 1855 1851 1852 1851 3 _pl _pf _np _s _s 2239 1703 _m
_sp 2242 1703 2242 1851 2239 1851 3 _pl _pf _np 
_s 0 g 144 382 1856 1703 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 8064 7126 _m
(0.6)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1701 _m
_sp 555 1701 555 1704 308 1704 3 _pl _pf _np _s _s 300 1582 _m
_sp 303 1582 303 1704 300 1704 3 _pl _pf _np _s _s 308 1582 _m
_sp 311 1582 311 1704 308 1704 3 _pl _pf _np 
_s 0 g 118 243 312 1582 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 1701 805 1704 554 1704 3 _pl _pf _np 
_s 0 g 118 251 554 1582 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1701 _m
_sp 1853 1701 1853 1704 804 1704 3 _pl _pf _np 
_s 0 g 118 1049 804 1582 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1582 _m
_sp 2250 1582 2250 1704 2247 1704 3 _pl _pf _np _s _s 1852 1701 _m
_sp 2242 1701 2242 1704 1852 1704 3 _pl _pf _np _s _s 2239 1582 _m
_sp 2242 1582 2242 1704 2239 1704 3 _pl _pf _np 
_s 0 g 118 386 1852 1582 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4055 6536 _m
/Times-BoldItalicR 600 _ff
(Roll)_S 67 _t
(moment)_S 67 _t
(coefficients)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1580 _m
_sp 555 1580 555 1583 308 1583 3 _pl _pf _np _s _s 300 1332 _m
_sp 303 1332 303 1583 300 1583 3 _pl _pf _np _s _s 308 1332 _m
_sp 311 1332 311 1583 308 1583 3 _pl _pf _np 
_s 0 g 247 243 312 1332 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1610 5895 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 76 61 402 1473 _cw 
_s 421 1521 _m
_sp 421 1521 423 1529 424 1531 425 1533 426 1534 427 1534 428 1534 428 1535 416 1535 415 1534 417 1534 418 1533 419 1532 419 1531 419 1531 
418 1529 413 1508 412 1506 411 1504 410 1503 409 1503 408 1503 408 1502 420 1502 421 1503 419 1503 418 1504 417 1505 417 1506 418 1508 
421 1519 427 1508 428 1507 428 1506 428 1505 428 1504 427 1503 425 1503 425 1502 438 1502 439 1503 438 1503 437 1503 435 1504 434 1506 
432 1508 425 1521 432 1526 438 1531 440 1532 441 1533 442 1533 443 1534 444 1535 432 1535 432 1534 435 1533 435 1532 435 1531 432 1529 
430 1527 428 1525 427 1524 425 1523 424 1522 65 _pl _cp 
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0 g 447 1498 _m
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445 1480 444 1480 443 1481 443 1481 443 1482 443 1482 443 1483 444 1486 445 1486 446 1486 448 1486 450 1487 451 1488 453 1489 454 1491 
455 1493 456 1495 456 1497 455 1500 453 1501 452 1501 450 1500 449 1499 38 _pl _cp 445 1489 _m
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448 1497 447 1496 447 1494 446 1492 19 _pl _cp 
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0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 1580 805 1583 554 1583 3 _pl _pf _np _s _s 554 1332 _m
_sp 557 1332 557 1583 554 1583 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1580 _m
_sp 1853 1580 1853 1583 804 1583 3 _pl _pf _np _s _s 804 1332 _m
_sp 807 1332 807 1583 804 1583 3 _pl _pf _np 
_s 0 g 247 1045 808 1332 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 6052 _m
(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(longitudinal)_S 67 _t
(body)_S 3333 5594 _m
(axis)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(roll)_S 67 _t
(rate)_S 67 _t
(\()_S 6969 5534 _m
7115 5594 _m
(\))_S gsave 4 4 scale 16 _sr 
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_s 1761 1430 _m
_sp 1761 1430 1762 1428 1764 1427 1766 1428 1767 1430 1766 1432 1764 1433 1762 1432 8 _pl _cp 
0 g _f _s _s 
0 g 1757 1418 _m
_sp 1757 1418 1759 1423 1750 1422 1750 1421 1752 1421 1753 1420 1754 1419 1754 1418 1753 1417 1747 1395 1746 1392 1744 1391 1744 1391 1743 1390 1754 1390 
1754 1391 1752 1391 1751 1392 1751 1393 1751 1393 1751 1394 1751 1395 1753 1400 1755 1400 1756 1400 1758 1400 1761 1401 1764 1402 1766 1404 1768 1407 
1770 1410 1771 1413 1771 1416 1771 1419 1770 1421 1768 1422 1766 1423 1763 1423 1761 1422 1759 1420 40 _pl _cp 1754 1404 _m
_sp 1754 1404 1754 1404 1753 1403 1754 1402 1756 1401 1757 1401 1758 1402 1760 1403 1761 1404 1763 1407 1765 1410 1766 1413 1767 1417 1766 1419 1764 1420 
1762 1420 1759 1418 1758 1417 1757 1415 1756 1413 1755 1410 21 _pl _cp 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1332 _m
_sp 2250 1332 2250 1583 2247 1583 3 _pl _pf _np _s _s 1852 1580 _m
_sp 2242 1580 2242 1583 1852 1583 3 _pl _pf _np _s _s 1852 1332 _m
_sp 1855 1332 1855 1583 1852 1583 3 _pl _pf _np _s _s 2239 1332 _m
_sp 2242 1332 2242 1583 2239 1583 3 _pl _pf _np 
_s 0 g 247 382 1856 1332 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7853 6052 _m
(-2.4)_S 67 _t
(E-4)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 1330 555 1333 308 1333 3 _pl _pf _np _s _s 300 1036 _m
_sp 303 1036 303 1333 300 1333 3 _pl _pf _np _s _s 308 1036 _m
_sp 311 1036 311 1333 308 1333 3 _pl _pf _np 
_s 0 g 293 243 312 1036 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1524 4897 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
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_s 400 1272 _m
_sp 400 1272 402 1280 403 1282 404 1284 405 1285 406 1285 407 1285 407 1286 395 1286 394 1285 396 1285 397 1284 398 1283 398 1282 398 1282 
397 1280 392 1259 391 1257 390 1255 389 1254 388 1254 387 1254 387 1253 399 1253 400 1254 398 1254 397 1255 396 1256 396 1257 397 1259 
400 1270 406 1259 407 1258 407 1257 407 1256 407 1255 406 1254 404 1254 404 1253 417 1253 418 1254 417 1254 416 1254 414 1255 413 1257 
411 1259 404 1272 411 1277 417 1282 419 1283 420 1284 421 1284 422 1285 423 1286 411 1286 411 1285 414 1284 414 1283 414 1282 411 1280 
409 1278 407 1276 406 1275 404 1274 403 1273 65 _pl _cp 
0 g _f _s _s 
0 g 445 1252 _m
_sp 445 1252 445 1250 444 1248 443 1247 443 1246 442 1244 441 1243 439 1240 437 1239 437 1239 437 1239 437 1240 437 1241 440 1252 435 1251 
435 1251 435 1251 436 1251 437 1250 437 1249 436 1248 434 1242 434 1241 434 1240 434 1240 434 1239 435 1238 436 1237 438 1237 439 1239 
440 1240 441 1241 442 1242 443 1244 442 1241 442 1240 442 1238 443 1237 444 1237 446 1238 448 1241 448 1241 447 1241 446 1239 446 1239 
445 1238 445 1239 445 1239 445 1240 445 1240 445 1241 445 1242 446 1244 446 1246 447 1250 448 1252 56 _pl _cp 
0 g _f _s _s 
0 g 469 1249 _m
_sp 469 1249 470 1252 465 1251 465 1251 466 1251 467 1251 467 1250 467 1249 467 1248 463 1234 462 1232 461 1231 460 1231 460 1231 467 1231 
467 1231 466 1231 465 1232 465 1232 465 1233 465 1233 465 1234 466 1237 468 1237 469 1237 471 1237 472 1238 474 1239 475 1240 476 1242 
478 1244 479 1246 479 1248 478 1251 475 1252 474 1252 472 1251 471 1250 38 _pl _cp 467 1240 _m
_sp 467 1240 467 1239 467 1239 467 1238 468 1238 470 1238 472 1239 473 1241 475 1244 476 1246 476 1248 475 1250 474 1251 473 1250 471 1249 
470 1248 470 1247 469 1245 468 1243 19 _pl _cp 
0 g _f _s _s 
0 g 427 1262 _m
_sp 427 1262 427 1229 428 1229 428 1262 4 _pl _cp 
0 g _f _s _s 
0 g 457 1262 _m
_sp 457 1262 457 1229 458 1229 458 1262 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1330 _m
_sp 805 1330 805 1333 554 1333 3 _pl _pf _np _s _s 554 1036 _m
_sp 557 1036 557 1333 554 1333 3 _pl _pf _np 
_s 0 g 293 247 558 1036 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1330 _m
_sp 1853 1330 1853 1333 804 1333 3 _pl _pf _np _s _s 804 1036 _m
_sp 807 1036 807 1333 804 1333 3 _pl _pf _np 
_s 0 g 293 1045 808 1036 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 5054 _m
(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(longitudinal)_S 67 _t
(body)_S 3333 4704 _m
(axis)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(existing)_S 67 _t
(roll)_S 67 _t
/Times-BoldItalicR 600 _ff
(p)_S /Times-RomanR 600 _ff
67 _t
(and)_S 67 _t
(magnitude)_S 67 _t
(of)_S 3333 4353 _m
(surge)_S 67 _t
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1036 _m
_sp 2250 1036 2250 1333 2247 1333 3 _pl _pf _np _s _s 1852 1330 _m
_sp 2242 1330 2242 1333 1852 1333 3 _pl _pf _np _s _s 1852 1036 _m
_sp 1855 1036 1855 1333 1852 1333 3 _pl _pf _np _s _s 2239 1036 _m
_sp 2242 1036 2242 1333 2239 1333 3 _pl _pf _np 
_s 0 g 293 382 1856 1036 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7853 5054 _m
(-5.4)_S 67 _t
(E-3)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1033 _m
_sp 555 1033 555 1036 308 1036 3 _pl _pf _np _s _s 300 739 _m
_sp 303 739 303 1036 300 1036 3 _pl _pf _np _s _s 308 739 _m
_sp 311 739 311 1036 308 1036 3 _pl _pf _np 
_s 0 g 293 243 312 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1524 3710 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 104 381 927 _cw 
_s 400 975 _m
_sp 400 975 402 983 403 985 404 987 405 988 406 988 407 988 407 989 395 989 394 988 396 988 397 987 398 986 398 985 398 985 
397 983 392 962 391 960 390 958 389 957 388 957 387 957 387 956 399 956 400 957 398 957 397 958 396 959 396 960 397 962 
400 973 406 962 407 961 407 960 407 959 407 958 406 957 404 957 404 956 417 956 418 957 417 957 416 957 414 958 413 960 
411 962 404 975 411 980 417 985 419 986 420 987 421 987 422 988 423 989 411 989 411 988 414 987 414 986 414 985 411 983 
409 981 407 979 406 978 404 977 403 976 65 _pl _cp 
0 g _f _s _s 
0 g 426 952 _m
_sp 426 952 427 955 422 954 421 954 423 954 424 954 424 953 424 952 423 951 420 937 419 935 418 934 417 934 417 934 424 934 
424 934 423 934 422 935 422 935 422 936 422 936 422 937 423 940 424 940 425 940 427 940 429 941 430 942 432 943 433 945 
434 947 435 949 435 951 434 954 432 955 431 955 429 954 428 953 38 _pl _cp 424 943 _m
_sp 424 943 424 942 424 942 424 941 425 941 427 941 429 942 430 944 431 947 432 949 432 951 432 953 430 954 429 953 428 952 
427 951 426 950 426 948 425 946 19 _pl _cp 
0 g _f _s _s 
0 g 456 952 _m
_sp 456 952 457 955 452 954 451 954 453 954 454 954 454 953 454 952 453 951 450 937 449 935 448 934 447 934 447 934 454 934 
454 934 453 934 452 935 452 935 452 936 452 936 452 937 453 940 454 940 455 940 457 940 459 941 460 942 462 943 463 945 
464 947 465 949 465 951 464 954 462 955 461 955 459 954 458 953 38 _pl _cp 454 943 _m
_sp 454 943 454 942 454 942 454 941 455 941 457 941 459 942 460 944 461 947 462 949 462 951 462 953 460 954 459 953 458 952 
457 951 456 950 456 948 455 946 19 _pl _cp 
0 g _f _s _s 
0 g 444 965 _m
_sp 444 965 444 932 445 932 445 965 4 _pl _cp 
0 g _f _s _s 
0 g 474 965 _m
_sp 474 965 474 932 475 932 475 965 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1033 _m
_sp 805 1033 805 1036 554 1036 3 _pl _pf _np _s _s 554 739 _m
_sp 557 739 557 1036 554 1036 3 _pl _pf _np 
_s 0 g 293 247 558 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1033 _m
_sp 1853 1033 1853 1036 804 1036 3 _pl _pf _np _s _s 804 739 _m
_sp 807 739 807 1036 804 1036 3 _pl _pf _np 
_s 0 g 293 1045 808 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 3867 _m
(Drag)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(longitudinal)_S 67 _t
(body)_S 67 _t
(axis)_S 67 _t
(due)_S 3333 3517 _m
(to)_S 67 _t
(signed)_S 67 _t
(square)_S 67 _t
(of)_S 67 _t
(existing)_S 67 _t
(roll)_S 67 _t
/Times-BoldItalicR 600 _ff
(p)_S /Times-RomanR 600 _ff
3333 3167 _m
(corresponding)_S 67 _t
(to)_S 67 _t
(turbulent)_S 67 _t
(flow)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 739 _m
_sp 2250 739 2250 1036 2247 1036 3 _pl _pf _np _s _s 1852 1033 _m
_sp 2242 1033 2242 1036 1852 1036 3 _pl _pf _np _s _s 1852 739 _m
_sp 1855 739 1855 1036 1852 1036 3 _pl _pf _np _s _s 2239 739 _m
_sp 2242 739 2242 1036 2239 1036 3 _pl _pf _np 
_s 0 g 293 382 1856 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 3867 _m
(-2.02)_S 67 _t
(E-2)_S 7856 3518 _m
(estimate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 735 _m
_sp 555 735 555 738 300 738 3 _pl _pf _np _s _s 300 735 _m
_sp 303 735 303 740 300 740 3 _pl _pf _np _s _s 308 735 _m
_sp 311 735 311 740 308 740 3 _pl _pf _np 
_s 0 g 1 243 312 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 735 _m
_sp 805 735 805 738 554 738 3 _pl _pf _np _s _s 554 735 _m
_sp 557 735 557 740 554 740 3 _pl _pf _np 
_s 0 g 1 247 558 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 735 _m
_sp 1853 735 1853 738 804 738 3 _pl _pf _np _s _s 804 735 _m
_sp 807 735 807 740 804 740 3 _pl _pf _np 
_s 0 g 1 1045 808 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 735 _m
_sp 2250 735 2250 738 1852 738 3 _pl _pf _np _s _s 2247 735 _m
_sp 2250 735 2250 740 2247 740 3 _pl _pf _np _s _s 1852 735 _m
_sp 1855 735 1855 740 1852 740 3 _pl _pf _np _s _s 2239 735 _m
_sp 2242 735 2242 740 2239 740 3 _pl _pf _np 
_s 0 g 1 382 1856 739 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(137)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 243 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2445 _m
_sp 303 2445 303 2801 300 2801 3 _pl _pf _np _s _s 308 2445 _m
_sp 311 2445 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 352 243 312 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1608 10768 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 62 402 2692 _cw 
_s 421 2740 _m
_sp 421 2740 423 2748 424 2750 425 2752 426 2753 427 2753 428 2753 428 2754 416 2754 415 2753 417 2753 418 2752 419 2751 419 2750 419 2750 
418 2748 413 2727 412 2725 411 2723 410 2722 409 2722 408 2722 408 2721 420 2721 421 2722 419 2722 418 2723 417 2724 417 2725 418 2727 
421 2738 427 2727 428 2726 428 2725 428 2724 428 2723 427 2722 425 2722 425 2721 438 2721 439 2722 438 2722 437 2722 435 2723 434 2725 
432 2727 425 2740 432 2745 438 2750 440 2751 441 2752 442 2752 443 2753 444 2754 432 2754 432 2753 435 2752 435 2751 435 2750 432 2748 
430 2746 428 2744 427 2743 425 2742 424 2741 65 _pl _cp 
0 g _f _s _s 
0 g 448 2717 _m
_sp 448 2717 449 2720 444 2719 443 2719 445 2719 446 2719 446 2718 446 2717 445 2716 442 2702 441 2700 440 2699 439 2699 439 2699 446 2699 
446 2699 445 2699 444 2700 444 2700 444 2701 444 2701 444 2702 445 2705 446 2705 447 2705 449 2705 451 2706 452 2707 454 2708 455 2710 
456 2712 457 2714 457 2716 456 2719 454 2720 453 2720 451 2719 450 2718 38 _pl _cp 446 2708 _m
_sp 446 2708 446 2707 446 2707 446 2706 447 2706 449 2706 451 2707 452 2709 453 2712 454 2714 454 2716 454 2718 452 2719 451 2718 450 2717 
449 2716 448 2715 448 2713 447 2711 19 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2798 _m
_sp 805 2798 805 2801 554 2801 3 _pl _pf _np _s _s 554 2445 _m
_sp 557 2445 557 2801 554 2801 3 _pl _pf _np 
_s 0 g 352 247 558 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2798 _m
_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np _s _s 804 2445 _m
_sp 807 2445 807 2801 804 2801 3 _pl _pf _np 
_s 0 g 352 1045 808 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10925 _m
(Drag)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(longitudinal)_S 67 _t
(body)_S 67 _t
(axis)_S 67 _t
(due)_S 3333 10575 _m
(to)_S 67 _t
(existing)_S 67 _t
(roll)_S 67 _t
/Times-BoldItalicR 600 _ff
(p)_S /Times-RomanR 600 _ff
67 _t
(corresponding)_S 67 _t
(to)_S 67 _t
(laminar)_S 67 _t
(flow,)_S 3333 10068 _m
(approximately)_S 67 _t
(equals)_S 67 _t
5133 9948 _m
5552 10068 _m
67 _t
(at)_S 67 _t
5831 10008 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 104 1283 2487 _cw 
_s 1302 2535 _m
_sp 1302 2535 1304 2543 1305 2545 1306 2547 1307 2548 1308 2548 1309 2548 1309 2549 1297 2549 1296 2548 1298 2548 1299 2547 1300 2546 1300 2545 1300 2545 
1299 2543 1294 2522 1293 2520 1292 2518 1291 2517 1290 2517 1289 2517 1289 2516 1301 2516 1302 2517 1300 2517 1299 2518 1298 2519 1298 2520 1299 2522 
1302 2533 1308 2522 1309 2521 1309 2520 1309 2519 1309 2518 1308 2517 1306 2517 1306 2516 1319 2516 1320 2517 1319 2517 1318 2517 1316 2518 1315 2520 
1313 2522 1306 2535 1313 2540 1319 2545 1321 2546 1322 2547 1323 2547 1324 2548 1325 2549 1313 2549 1313 2548 1316 2547 1316 2546 1316 2545 1313 2543 
1311 2541 1309 2539 1308 2538 1306 2537 1305 2536 65 _pl _cp 
0 g _f _s _s 
0 g 1328 2512 _m
_sp 1328 2512 1329 2515 1324 2514 1323 2514 1325 2514 1326 2514 1326 2513 1326 2512 1325 2511 1322 2497 1321 2495 1320 2494 1319 2494 1319 2494 1326 2494 
1326 2494 1325 2494 1324 2495 1324 2495 1324 2496 1324 2496 1324 2497 1325 2500 1326 2500 1327 2500 1329 2500 1331 2501 1332 2502 1334 2503 1335 2505 
1336 2507 1337 2509 1337 2511 1336 2514 1334 2515 1333 2515 1331 2514 1330 2513 38 _pl _cp 1326 2503 _m
_sp 1326 2503 1326 2502 1326 2502 1326 2501 1327 2501 1329 2501 1331 2502 1332 2504 1333 2507 1334 2509 1334 2511 1334 2513 1332 2514 1331 2513 1330 2512 
1329 2511 1328 2510 1328 2508 1327 2506 19 _pl _cp 
0 g _f _s _s 
0 g 1358 2512 _m
_sp 1358 2512 1359 2515 1354 2514 1353 2514 1355 2514 1356 2514 1356 2513 1356 2512 1355 2511 1352 2497 1351 2495 1350 2494 1349 2494 1349 2494 1356 2494 
1356 2494 1355 2494 1354 2495 1354 2495 1354 2496 1354 2496 1354 2497 1355 2500 1356 2500 1357 2500 1359 2500 1361 2501 1362 2502 1364 2503 1365 2505 
1366 2507 1367 2509 1367 2511 1366 2514 1364 2515 1363 2515 1361 2514 1360 2513 38 _pl _cp 1356 2503 _m
_sp 1356 2503 1356 2502 1356 2502 1356 2501 1357 2501 1359 2501 1361 2502 1362 2504 1363 2507 1364 2509 1364 2511 1364 2513 1362 2514 1361 2513 1360 2512 
1359 2511 1358 2510 1358 2508 1357 2506 19 _pl _cp 
0 g _f _s _s 
0 g 1346 2525 _m
_sp 1346 2525 1346 2492 1347 2492 1347 2525 4 _pl _cp 
0 g _f _s _s 
0 g 1376 2525 _m
_sp 1376 2525 1376 2492 1377 2492 1377 2525 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 140 1457 2502 _cw 
_s 1468 2548 _m
_sp 1468 2548 1468 2547 1470 2548 1471 2548 1472 2548 1473 2547 1473 2546 1473 2525 1473 2523 1473 2521 1471 2520 1469 2520 1468 2520 1468 2519 1482 2519 
1482 2520 1481 2520 1479 2520 1478 2521 1478 2523 1478 2525 1478 2553 22 _pl _cp 
0 g _f _s _s 
0 g 1522 2552 _m
_sp 1522 2552 1511 2511 1515 2511 1526 2552 4 _pl _cp 
0 g _f _s _s 
0 g 1528 2519 _m
_sp 1528 2519 1529 2519 1529 2519 1530 2519 1531 2519 1532 2519 1535 2519 1537 2519 1540 2519 1543 2521 1544 2522 1545 2525 1544 2527 1543 2529 1542 2530 
1540 2531 1539 2532 1536 2533 1534 2534 1532 2535 1531 2536 1531 2537 1532 2539 1535 2540 1538 2540 1540 2539 1541 2537 1542 2534 1543 2534 1543 2541 
1542 2541 1542 2541 1541 2541 1541 2541 1540 2541 1538 2542 1537 2542 1535 2542 1532 2541 1530 2540 1529 2538 1528 2536 1528 2534 1529 2532 1531 2531 
1533 2529 1537 2527 1540 2525 1541 2523 1541 2522 1540 2521 1538 2520 1536 2520 1534 2521 1531 2522 1530 2524 1529 2527 1528 2527 58 _pl _cp 
0 g _f _s _s 
0 g 1551 2533 _m
_sp 1551 2533 1566 2533 1565 2537 1564 2539 1561 2541 1557 2542 1553 2541 1550 2539 1548 2535 1547 2530 1548 2525 1550 2522 1553 2520 1557 2519 1560 2519 
1563 2521 1565 2523 1567 2527 1566 2527 1565 2525 1563 2523 1561 2522 1559 2521 1556 2522 1553 2524 1552 2528 1551 2532 1551 2532 28 _pl _cp 1561 2534 _m
_sp 1561 2534 1561 2537 1560 2539 1558 2540 1556 2540 1554 2540 1552 2539 1551 2537 1551 2534 9 _pl _cp 
0 g _f _s _s 
0 g 1588 2527 _m
_sp 1588 2527 1586 2525 1585 2523 1583 2522 1581 2522 1578 2523 1576 2525 1574 2528 1573 2532 1574 2535 1575 2538 1577 2539 1580 2540 1582 2540 1583 2537 
1584 2535 1586 2534 1587 2535 1588 2537 1587 2539 1586 2540 1584 2542 1581 2542 1577 2541 1574 2540 1571 2537 1570 2534 1569 2530 1570 2525 1572 2522 
1575 2520 1579 2519 1581 2519 1583 2519 1584 2520 1586 2521 1587 2522 1587 2523 1588 2524 1589 2526 40 _pl _cp 
0 g _f _s _s 
0 g 1490 2548 _m
_sp 1490 2548 1491 2545 1492 2543 1494 2542 1497 2541 1500 2542 1502 2543 1503 2545 1504 2548 1503 2550 1502 2552 1500 2553 1497 2554 1494 2553 1492 2552 
1491 2550 16 _pl _cp 1492 2548 _m
_sp 1492 2548 1492 2549 1493 2551 1495 2552 1497 2552 1499 2552 1501 2551 1502 2549 1502 2548 1502 2546 1501 2544 1499 2543 1497 2543 1495 2543 1493 2544 
1492 2546 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2445 _m
_sp 2250 2445 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 1852 2445 _m
_sp 1855 2445 1855 2801 1852 2801 3 _pl _pf _np _s _s 2239 2445 _m
_sp 2242 2445 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 352 382 1856 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7661 10527 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 136 264 1915 2631 _cw 
_s 1934 2707 _m
_sp 1934 2707 1936 2714 1937 2716 1938 2718 1939 2719 1940 2719 1941 2719 1941 2721 1929 2721 1928 2719 1930 2719 1931 2719 1932 2717 1932 2717 1932 2716 
1931 2714 1926 2694 1925 2692 1924 2690 1923 2689 1922 2689 1921 2689 1921 2688 1933 2688 1934 2689 1932 2689 1931 2690 1930 2691 1930 2692 1931 2694 
1934 2705 1940 2694 1941 2692 1941 2691 1941 2690 1941 2690 1940 2689 1938 2689 1938 2688 1951 2688 1952 2689 1951 2689 1950 2689 1948 2690 1947 2692 
1945 2694 1938 2707 1945 2712 1951 2716 1953 2718 1954 2719 1955 2719 1956 2719 1957 2721 1945 2721 1945 2719 1948 2719 1948 2718 1948 2717 1945 2714 
1943 2713 1941 2711 1940 2710 1938 2709 1937 2708 65 _pl _cp 
0 g _f _s _s 
0 g 1960 2683 _m
_sp 1960 2683 1961 2687 1956 2686 1955 2685 1957 2685 1958 2685 1958 2685 1958 2684 1957 2683 1954 2669 1953 2667 1952 2666 1951 2666 1951 2665 1958 2665 
1958 2666 1957 2666 1956 2666 1956 2667 1956 2667 1956 2668 1956 2669 1957 2672 1958 2672 1959 2672 1961 2672 1963 2673 1964 2674 1966 2675 1967 2677 
1968 2679 1969 2681 1969 2683 1968 2686 1966 2687 1965 2687 1963 2686 1962 2685 38 _pl _cp 1958 2675 _m
_sp 1958 2675 1958 2674 1958 2674 1958 2673 1959 2672 1961 2673 1963 2674 1964 2676 1965 2678 1966 2681 1966 2683 1966 2684 1964 2685 1963 2685 1962 2684 
1961 2683 1960 2682 1960 2680 1959 2678 19 _pl _cp 
0 g _f _s _s 
0 g 1990 2683 _m
_sp 1990 2683 1991 2687 1986 2686 1985 2685 1987 2685 1988 2685 1988 2685 1988 2684 1987 2683 1984 2669 1983 2667 1982 2666 1981 2666 1981 2665 1988 2665 
1988 2666 1987 2666 1986 2666 1986 2667 1986 2667 1986 2668 1986 2669 1987 2672 1988 2672 1989 2672 1991 2672 1993 2673 1994 2674 1996 2675 1997 2677 
1998 2679 1999 2681 1999 2683 1998 2686 1996 2687 1995 2687 1993 2686 1992 2685 38 _pl _cp 1988 2675 _m
_sp 1988 2675 1988 2674 1988 2674 1988 2673 1989 2672 1991 2673 1993 2674 1994 2676 1995 2678 1996 2681 1996 2683 1996 2684 1994 2685 1993 2685 1992 2684 
1991 2683 1990 2682 1990 2680 1989 2678 19 _pl _cp 
0 g _f _s _s 
0 g 1978 2697 _m
_sp 1978 2697 1978 2664 1979 2664 1979 2697 4 _pl _cp 
0 g _f _s _s 
0 g 2008 2697 _m
_sp 2008 2697 2008 2664 2009 2664 2009 2697 4 _pl _cp 
0 g _f _s _s 
0 g 2128 2677 _m
_sp 2128 2677 2129 2674 2130 2672 2132 2671 2135 2670 2137 2671 2139 2672 2140 2674 2141 2677 2140 2679 2139 2681 2137 2682 2135 2683 2132 2682 2130 2681 
2129 2679 16 _pl _cp 2130 2677 _m
_sp 2130 2677 2130 2678 2131 2680 2133 2681 2135 2681 2138 2680 2139 2677 2139 2675 2138 2673 2136 2672 2135 2672 2133 2672 2131 2673 2130 2675 14 _pl _cp 
0 g _f _s _s 
0 g 2029 2696 _m
_sp 2029 2696 2026 2696 2026 2708 2026 2713 2026 2717 2026 2721 2026 2726 2027 2730 2028 2733 2029 2737 2030 2740 2032 2743 2034 2746 2036 2750 2040 2755 
2040 2755 2037 2750 2035 2745 2033 2742 2032 2738 2031 2735 2030 2732 2030 2728 2029 2723 2029 2719 2029 2715 2029 2711 2029 2707 28 _pl _cp 
0 g _f _s _s 
0 g 2029 2696 _m
_sp 2029 2696 2026 2696 2026 2682 2026 2677 2026 2673 2026 2668 2026 2664 2027 2660 2028 2656 2029 2653 2030 2650 2032 2647 2034 2643 2036 2639 2040 2635 
2040 2635 2037 2640 2035 2645 2033 2648 2032 2651 2031 2655 2030 2658 2030 2662 2029 2666 2029 2671 2029 2675 2029 2679 2029 2683 28 _pl _cp 
0 g _f _s _s 
0 g 2168 2696 _m
_sp 2168 2696 2171 2696 2171 2708 2171 2713 2171 2717 2171 2721 2170 2726 2170 2730 2169 2733 2168 2737 2167 2740 2165 2743 2163 2746 2161 2750 2157 2755 
2157 2755 2160 2750 2162 2745 2164 2742 2165 2738 2166 2735 2167 2732 2167 2728 2168 2723 2168 2719 2168 2715 2168 2711 2168 2707 28 _pl _cp 
0 g _f _s _s 
0 g 2168 2696 _m
_sp 2168 2696 2171 2696 2171 2682 2171 2677 2171 2673 2171 2668 2170 2664 2170 2660 2169 2656 2168 2653 2167 2650 2165 2647 2163 2643 2161 2639 2157 2635 
2157 2635 2160 2640 2162 2645 2164 2648 2165 2651 2166 2655 2167 2658 2167 2662 2168 2666 2168 2671 2168 2675 2168 2679 2168 2683 28 _pl _cp 
0 g _f _s _s 
0 g 2045 2700 _m
_sp 2045 2700 2045 2698 2151 2698 2151 2700 4 _pl _cp 
0 g _f _s _s 
0 g 2104 2734 _m
_sp 2104 2734 2110 2734 2110 2737 2096 2737 2093 2737 2091 2737 2090 2736 2089 2735 2088 2734 2086 2732 2088 2731 2089 2732 2090 2733 2091 2734 2093 2734 
2093 2734 2094 2734 2094 2727 2094 2725 2093 2723 2092 2722 2091 2720 2090 2719 2090 2717 2091 2716 2092 2715 2093 2716 2095 2717 2096 2720 2096 2724 
2096 2727 2096 2734 2102 2734 2102 2723 2102 2719 2103 2717 2104 2715 2106 2715 2108 2716 2109 2717 2110 2719 2110 2722 2108 2722 2107 2720 2106 2719 
2104 2720 2104 2723 47 _pl _cp 
0 g _f _s _s 
0 g 2056 2677 _m
_sp 2056 2677 2056 2676 2058 2677 2059 2677 2059 2677 2060 2676 2061 2675 2061 2654 2061 2652 2060 2650 2059 2649 2057 2649 2056 2649 2056 2648 2070 2648 
2070 2649 2069 2649 2067 2649 2066 2650 2065 2652 2065 2654 2065 2682 22 _pl _cp 
0 g _f _s _s 
0 g 2084 2665 _m
_sp 2084 2665 2082 2664 2081 2663 2080 2662 2079 2661 2078 2659 2077 2656 2078 2653 2080 2650 2083 2649 2087 2648 2091 2649 2094 2650 2096 2653 2097 2656 
2097 2658 2096 2659 2096 2661 2095 2662 2094 2663 2093 2664 2092 2665 2090 2667 2092 2668 2093 2669 2094 2670 2095 2671 2096 2673 2096 2675 2095 2678 
2094 2680 2091 2681 2087 2682 2083 2681 2081 2680 2079 2677 2078 2674 2078 2671 2079 2669 2080 2668 2081 2667 2082 2666 42 _pl _cp 2085 2663 _m
_sp 2085 2663 2084 2661 2083 2660 2082 2658 2082 2656 2082 2653 2084 2651 2085 2650 2088 2649 2090 2649 2092 2650 2093 2652 2093 2654 2093 2656 2092 2658 
2090 2660 2088 2662 2087 2663 18 _pl _cp 2088 2668 _m
_sp 2088 2668 2090 2669 2091 2671 2092 2673 2092 2675 2092 2677 2091 2679 2089 2680 2087 2680 2085 2680 2083 2679 2082 2677 2082 2675 2082 2674 2083 2672 
2084 2671 2085 2670 2086 2669 18 _pl _cp 
0 g _f _s _s 
0 g 2101 2664 _m
_sp 2101 2664 2101 2662 2101 2660 2102 2657 2103 2655 2103 2654 2104 2653 2105 2651 2106 2650 2108 2649 2109 2648 2111 2648 2112 2648 2116 2649 2119 2651 
2122 2654 2123 2659 2124 2665 2123 2670 2122 2675 2119 2679 2116 2681 2112 2682 2108 2681 2105 2679 2103 2675 2101 2670 27 _pl _cp 2106 2665 _m
_sp 2106 2665 2106 2659 2107 2655 2108 2652 2110 2650 2112 2650 2114 2650 2116 2651 2117 2653 2118 2656 2119 2660 2119 2665 2119 2670 2118 2674 2116 2677 
2115 2679 2112 2680 2110 2679 2108 2677 2107 2674 2106 2670 21 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 7856 10111 _m
(estimate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2443 _m
_sp 555 2443 555 2446 308 2446 3 _pl _pf _np _s _s 300 2324 _m
_sp 303 2324 303 2446 300 2446 3 _pl _pf _np _s _s 308 2324 _m
_sp 311 2324 311 2446 308 2446 3 _pl _pf _np 
_s 0 g 118 243 312 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2443 _m
_sp 805 2443 805 2446 554 2446 3 _pl _pf _np 
_s 0 g 118 251 554 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2443 _m
_sp 1853 2443 1853 2446 804 2446 3 _pl _pf _np 
_s 0 g 118 1049 804 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2324 _m
_sp 2250 2324 2250 2446 2247 2446 3 _pl _pf _np _s _s 1852 2443 _m
_sp 2242 2443 2242 2446 1852 2446 3 _pl _pf _np _s _s 2239 2324 _m
_sp 2242 2324 2242 2446 2239 2446 3 _pl _pf _np 
_s 0 g 118 386 1852 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4011 9503 _m
/Times-BoldItalicR 600 _ff
(Pitch)_S 67 _t
(moment)_S 67 _t
(coefficients)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2321 _m
_sp 555 2321 555 2324 308 2324 3 _pl _pf _np _s _s 300 2074 _m
_sp 303 2074 303 2324 300 2324 3 _pl _pf _np _s _s 308 2074 _m
_sp 311 2074 311 2324 308 2324 3 _pl _pf _np 
_s 0 g 246 243 312 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1582 8862 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 75 395 2215 _cw 
_s 411 2274 _m
_sp 411 2274 405 2250 404 2248 403 2246 402 2245 401 2245 401 2245 400 2244 410 2244 411 2245 409 2245 408 2246 407 2247 407 2248 407 2249 
408 2249 408 2251 413 2270 416 2244 417 2244 435 2271 429 2250 428 2248 427 2246 426 2245 425 2245 425 2245 425 2244 437 2244 437 2245 
436 2245 435 2246 434 2248 434 2248 434 2249 435 2251 440 2271 441 2273 441 2275 442 2276 443 2276 444 2276 444 2277 436 2277 420 2253 
417 2277 408 2277 408 2276 408 2276 410 2275 50 _pl _cp 
0 g _f _s _s 
0 g 449 2232 _m
_sp 449 2232 449 2234 449 2236 449 2237 448 2239 448 2241 447 2243 443 2242 443 2242 444 2242 445 2241 445 2240 446 2237 446 2234 447 2231 
447 2228 447 2228 454 2239 455 2228 456 2228 458 2230 459 2232 461 2234 462 2236 464 2239 464 2241 463 2242 462 2243 462 2243 461 2242 
461 2241 462 2241 463 2240 463 2239 463 2239 462 2238 461 2236 459 2234 458 2232 457 2231 456 2243 455 2243 42 _pl _cp 
0 g _f _s _s 
0 g 454 2248 _m
_sp 454 2248 455 2247 456 2246 457 2247 458 2248 457 2249 456 2250 455 2249 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2321 _m
_sp 805 2321 805 2324 554 2324 3 _pl _pf _np _s _s 554 2074 _m
_sp 557 2074 557 2324 554 2324 3 _pl _pf _np 
_s 0 g 246 247 558 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2321 _m
_sp 1853 2321 1853 2324 804 2324 3 _pl _pf _np _s _s 804 2074 _m
_sp 807 2074 807 2324 804 2324 3 _pl _pf _np 
_s 0 g 246 1045 808 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 9019 _m
(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(lateral)_S 67 _t
(body)_S 67 _t
(axis)_S 3333 8561 _m
(due)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(heave)_S 67 _t
(rate)_S 67 _t
(\()_S 6768 8501 _m
6947 8561 _m
(\))_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 44 1692 2125 _cw 
_s 1715 2172 _m
_sp 1715 2172 1716 2170 1718 2169 1720 2170 1721 2172 1720 2174 1718 2175 1716 2174 8 _pl _cp 
0 g _f _s _s 
0 g 1708 2149 _m
_sp 1708 2149 1707 2152 1707 2154 1707 2156 1707 2158 1706 2161 1706 2162 1705 2164 1705 2165 1699 2163 1698 2162 1700 2162 1701 2162 1702 2160 1703 2157 
1703 2153 1703 2150 1704 2146 1704 2142 1705 2142 1715 2158 1717 2142 1718 2142 1721 2145 1723 2148 1726 2151 1728 2154 1729 2157 1730 2159 1731 2160 
1731 2162 1730 2164 1728 2165 1727 2164 1726 2163 1726 2162 1727 2161 1728 2160 1728 2159 1728 2158 1727 2157 1727 2156 1726 2154 1725 2153 1723 2151 
1722 2148 1720 2147 1718 2164 1717 2165 49 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2074 _m
_sp 2250 2074 2250 2324 2247 2324 3 _pl _pf _np _s _s 1852 2321 _m
_sp 2242 2321 2242 2324 1852 2324 3 _pl _pf _np _s _s 1852 2074 _m
_sp 1855 2074 1855 2324 1852 2324 3 _pl _pf _np _s _s 2239 2074 _m
_sp 2242 2074 2242 2324 2239 2324 3 _pl _pf _np 
_s 0 g 246 382 1856 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 9019 _m
(-2.53)_S 67 _t
(E-3)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2072 _m
_sp 555 2072 555 2075 308 2075 3 _pl _pf _np _s _s 300 1825 _m
_sp 303 1825 303 2075 300 2075 3 _pl _pf _np _s _s 308 1825 _m
_sp 311 1825 311 2075 308 2075 3 _pl _pf _np 
_s 0 g 246 243 312 1825 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1593 7864 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 70 398 1966 _cw 
_s 414 2025 _m
_sp 414 2025 408 2001 407 1999 406 1997 405 1996 404 1996 404 1996 403 1995 413 1995 414 1996 412 1996 411 1997 410 1998 410 1999 410 2000 
411 2000 411 2002 416 2021 419 1995 420 1995 438 2022 432 2001 431 1999 430 1997 429 1996 428 1996 428 1996 428 1995 440 1995 440 1996 
439 1996 438 1997 437 1999 437 1999 437 2000 438 2002 443 2022 444 2024 444 2026 445 2027 446 2027 447 2027 447 2028 439 2028 423 2004 
420 2028 411 2028 411 2027 411 2027 413 2026 50 _pl _cp 
0 g _f _s _s 
0 g 458 1992 _m
_sp 458 1992 457 1994 455 1994 454 1994 452 1993 451 1992 449 1991 448 1989 447 1987 446 1985 446 1983 447 1980 449 1979 450 1979 451 1979 
453 1981 455 1983 453 1976 452 1974 451 1973 450 1973 450 1973 458 1973 458 1973 457 1973 456 1974 456 1974 456 1975 456 1976 461 1994 
458 1994 31 _pl _cp 449 1983 _m
_sp 449 1983 450 1981 451 1981 453 1982 455 1985 456 1987 456 1988 457 1990 457 1991 457 1992 455 1993 454 1993 452 1991 451 1989 450 1987 
449 1985 449 1983 449 1983 18 _pl _cp 
0 g _f _s _s 
0 g 454 1999 _m
_sp 454 1999 455 1998 456 1997 457 1998 458 1999 457 2000 456 2001 455 2000 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2072 _m
_sp 805 2072 805 2075 554 2075 3 _pl _pf _np _s _s 554 1825 _m
_sp 557 1825 557 2075 554 2075 3 _pl _pf _np 
_s 0 g 246 247 558 1825 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2072 _m
_sp 1853 2072 1853 2075 804 2075 3 _pl _pf _np _s _s 804 1825 _m
_sp 807 1825 807 2075 804 2075 3 _pl _pf _np 
_s 0 g 246 1045 808 1825 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8021 _m
(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(lateral)_S 67 _t
(body)_S 67 _t
(axis)_S 3333 7563 _m
(due)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(pitch)_S 67 _t
(rate)_S 67 _t
(\()_S 6702 7503 _m
6848 7563 _m
(\))_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 64 36 1675 1875 _cw 
_s 1694 1922 _m
_sp 1694 1922 1695 1920 1697 1919 1699 1920 1700 1922 1699 1924 1697 1925 1695 1924 8 _pl _cp 
0 g _f _s _s 
0 g 1700 1912 _m
_sp 1700 1912 1698 1914 1696 1915 1694 1915 1692 1914 1689 1912 1687 1910 1684 1907 1683 1904 1681 1901 1681 1898 1682 1895 1683 1894 1685 1892 1687 1892 
1689 1892 1690 1892 1691 1893 1693 1894 1694 1896 1696 1898 1693 1887 1692 1884 1690 1883 1688 1883 1688 1882 1700 1882 1700 1883 1698 1883 1697 1884 
1696 1885 1697 1886 1697 1887 1704 1914 1700 1914 35 _pl _cp 1686 1898 _m
_sp 1686 1898 1687 1895 1689 1894 1691 1894 1692 1896 1694 1897 1695 1900 1697 1903 1698 1906 1699 1908 1699 1910 1698 1912 1696 1913 1694 1912 1691 1911 
1689 1908 1687 1905 1686 1902 1686 1899 1686 1899 20 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1825 _m
_sp 2250 1825 2250 2075 2247 2075 3 _pl _pf _np _s _s 1852 2072 _m
_sp 2242 2072 2242 2075 1852 2075 3 _pl _pf _np _s _s 1852 1825 _m
_sp 1855 1825 1855 2075 1852 2075 3 _pl _pf _np _s _s 2239 1825 _m
_sp 2242 1825 2242 2075 2239 2075 3 _pl _pf _np 
_s 0 g 246 382 1856 1825 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 8021 _m
(-6.25)_S 67 _t
(E-3)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1822 _m
_sp 555 1822 555 1825 308 1825 3 _pl _pf _np _s _s 300 1616 _m
_sp 303 1616 303 1825 300 1825 3 _pl _pf _np _s _s 308 1616 _m
_sp 311 1616 311 1825 308 1825 3 _pl _pf _np 
_s 0 g 205 243 312 1616 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1549 6866 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 92 387 1716 _cw 
_s 403 1775 _m
_sp 403 1775 397 1751 396 1749 395 1747 394 1746 393 1746 393 1746 392 1745 402 1745 403 1746 401 1746 400 1747 399 1748 399 1749 399 1750 
400 1750 400 1752 405 1771 408 1745 409 1745 427 1772 421 1751 420 1749 419 1747 418 1746 417 1746 417 1746 417 1745 429 1745 429 1746 
428 1746 427 1747 426 1749 426 1749 426 1750 427 1752 432 1772 433 1774 433 1776 434 1777 435 1777 436 1777 436 1778 428 1778 412 1754 
409 1778 400 1778 400 1777 400 1777 402 1776 50 _pl _cp 
0 g _f _s _s 
0 g 447 1744 _m
_sp 447 1744 446 1742 445 1740 444 1738 443 1735 442 1733 440 1732 439 1731 438 1731 438 1731 438 1731 438 1732 438 1733 441 1744 436 1743 
436 1743 437 1743 438 1743 438 1742 438 1741 437 1740 436 1734 436 1733 435 1732 435 1732 435 1731 436 1730 437 1729 439 1729 441 1731 
442 1732 442 1733 443 1734 444 1736 444 1733 443 1732 443 1730 444 1729 445 1729 446 1729 447 1730 449 1731 450 1733 449 1733 449 1733 
448 1731 447 1731 446 1730 446 1731 446 1731 446 1732 446 1732 446 1733 447 1734 447 1736 448 1738 449 1742 449 1744 58 _pl _cp 
0 g _f _s _s 
0 g 458 1733 _m
_sp 458 1733 457 1735 457 1737 457 1738 457 1740 456 1742 456 1744 452 1743 451 1743 452 1743 454 1742 454 1741 455 1738 455 1735 455 1732 
455 1729 456 1729 463 1740 464 1729 465 1729 467 1731 468 1733 470 1735 471 1737 472 1740 473 1742 472 1743 471 1744 470 1744 470 1743 
470 1742 470 1742 471 1741 471 1740 471 1740 471 1739 470 1737 468 1735 467 1733 466 1732 465 1744 464 1744 42 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
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_s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2096 1020 _m
_sp 2096 1020 2097 1018 2099 1017 2101 1018 2102 1020 2101 1022 2099 1023 2097 1022 8 _pl _cp _f _s _s grestore _s grestore gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 2140 1020 _m
_sp 2140 1020 2141 1018 2143 1017 2145 1018 2146 1020 2145 1022 2143 1023 2141 1022 8 _pl _cp _f _s _s grestore _s grestore 7795 4007 _m
(+0.377)_S 8358 4007 _m
8409 4007 _m
(L)_S 8532 4007 _m
7883 3302 _m
gsave 4 4 scale 16 _sr 
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_s 1975 914 _m
_sp 1975 914 1975 913 1999 913 2002 922 2000 922 1999 920 1998 918 1996 917 1994 916 1991 915 1988 915 1982 915 2005 945 2005 946 1982 946 
1980 938 1981 938 1982 940 1983 942 1985 943 1986 943 1989 944 1992 944 1998 944 24 _pl _cp 
0 g _f _s _s 
0 g 2016 912 _m
_sp 2016 912 2015 910 2014 908 2013 906 2012 903 2011 901 2009 900 2008 899 2007 899 2007 899 2007 899 2007 900 2007 901 2010 912 2005 911 
2005 911 2006 911 2007 911 2007 910 2007 909 2006 908 2005 902 2005 901 2004 900 2004 900 2004 899 2005 898 2006 897 2008 897 2010 899 
2011 900 2011 901 2012 902 2013 904 2013 901 2012 900 2012 898 2013 897 2014 897 2015 897 2016 898 2018 899 2019 901 2018 901 2018 901 
2017 899 2016 899 2015 898 2015 899 2015 899 2015 900 2015 900 2015 901 2016 902 2016 904 2017 906 2018 910 2018 912 58 _pl _cp 
0 g _f _s _s 
0 g 2046 912 _m
_sp 2046 912 2045 910 2044 908 2043 906 2042 903 2041 901 2039 900 2038 899 2037 899 2037 899 2037 899 2037 900 2037 901 2040 912 2035 911 
2035 911 2036 911 2037 911 2037 910 2037 909 2036 908 2035 902 2035 901 2034 900 2034 900 2034 899 2035 898 2036 897 2038 897 2040 899 
2041 900 2041 901 2042 902 2043 904 2043 901 2042 900 2042 898 2043 897 2044 897 2045 897 2046 898 2048 899 2049 901 2048 901 2048 901 
2047 899 2046 899 2045 898 2045 899 2045 899 2045 900 2045 900 2045 901 2046 902 2046 904 2047 906 2048 910 2048 912 58 _pl _cp 
0 g _f _s _s 
0 g 2094 909 _m
_sp 2094 909 2095 912 2089 911 2089 911 2090 911 2091 911 2091 910 2091 909 2091 908 2087 894 2086 892 2085 891 2085 891 2085 891 2091 891 
2091 891 2090 891 2090 892 2089 892 2089 893 2089 893 2090 894 2091 897 2092 897 2093 897 2095 897 2096 898 2098 899 2099 900 2100 902 
2102 904 2103 906 2103 908 2102 911 2099 912 2098 912 2096 911 2095 910 38 _pl _cp 2091 900 _m
_sp 2091 900 2091 899 2091 899 2092 898 2093 898 2095 898 2096 899 2097 901 2099 904 2100 906 2100 908 2099 910 2098 911 2097 910 2095 909 
2094 908 2094 907 2093 905 2092 903 19 _pl _cp 
0 g _f _s _s 
0 g 2104 902 _m
_sp 2104 902 2104 897 2104 897 2105 897 2105 897 2105 897 2105 897 2106 897 2107 897 2108 897 2109 897 2111 897 2113 898 2114 899 2115 901 
2115 902 2114 903 2113 904 2112 906 2110 908 2109 910 2110 911 2111 911 2114 910 2115 907 2116 907 2117 912 2116 912 2116 912 2115 912 
2114 912 2113 912 2112 912 2111 912 2108 911 2107 909 2107 908 2107 906 2108 905 2110 903 2112 902 2112 900 2111 899 2109 898 2106 899 
2105 902 46 _pl _cp 
0 g _f _s _s 
0 g 2027 922 _m
_sp 2027 922 2027 889 2028 889 2028 922 4 _pl _cp 
0 g _f _s _s 
0 g 2057 922 _m
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0 g 2081 916 _m
_sp 2081 916 2079 918 2077 919 2075 920 2073 919 2072 917 2072 916 2073 915 2075 913 2076 912 2073 911 2072 910 2070 907 2070 904 2071 901 
2072 899 2074 898 2076 897 2079 898 2081 899 2082 901 2083 904 2083 906 2083 907 2082 908 2081 910 2080 911 2078 912 2076 914 2075 915 
2074 916 2074 917 2074 918 2075 918 2076 917 2078 916 2079 914 37 _pl _cp 2080 904 _m
_sp 2080 904 2080 902 2079 900 2078 899 2076 898 2075 899 2074 900 2073 902 2073 904 2073 907 2074 909 2075 910 2076 910 2078 910 2079 909 
2080 907 16 _pl _cp 
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_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 555 811 555 814 308 814 3 _pl _pf _np _s _s 300 517 _m
_sp 303 517 303 814 300 814 3 _pl _pf _np _s _s 308 517 _m
_sp 311 517 311 814 308 814 3 _pl _pf _np 
_s 0 g 293 243 312 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1507 2820 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
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_s 392 764 _m
_sp 392 764 386 740 385 738 384 736 383 735 382 735 382 735 381 734 391 734 392 735 390 735 389 736 388 737 388 738 388 739 
389 739 389 741 394 760 397 734 398 734 416 761 410 740 409 738 408 736 407 735 406 735 406 735 406 734 418 734 418 735 
417 735 416 736 415 738 415 738 415 739 416 741 421 761 422 763 422 765 423 766 424 766 425 766 425 767 417 767 401 743 
398 767 389 767 389 766 389 766 391 765 50 _pl _cp 
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0 g 436 731 _m
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431 720 433 722 431 715 430 713 429 712 428 712 428 712 436 712 436 712 435 712 434 713 434 713 434 714 434 715 439 733 
436 733 31 _pl _cp 427 722 _m
_sp 427 722 428 720 429 720 431 721 433 724 434 726 434 727 435 729 435 730 435 731 433 732 432 732 430 730 429 728 428 726 
427 724 427 722 427 722 18 _pl _cp 
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461 720 463 722 461 715 460 713 459 712 458 712 458 712 466 712 466 712 465 712 464 713 464 713 464 714 464 715 469 733 
466 733 31 _pl _cp 457 722 _m
_sp 457 722 458 720 459 720 461 721 463 724 464 726 464 727 465 729 465 730 465 731 463 732 462 732 460 730 459 728 458 726 
457 724 457 722 457 722 18 _pl _cp 
0 g _f _s _s 
0 g 447 743 _m
_sp 447 743 447 710 448 710 448 743 4 _pl _cp 
0 g _f _s _s 
0 g 477 743 _m
_sp 477 743 477 710 478 710 478 743 4 _pl _cp 
0 g _f _s 
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_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 811 805 814 554 814 3 _pl _pf _np _s _s 554 517 _m
_sp 557 517 557 814 554 814 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 1853 811 1853 814 804 814 3 _pl _pf _np _s _s 804 517 _m
_sp 807 517 807 814 804 814 3 _pl _pf _np 
_s 0 g 293 1045 808 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 2977 _m
(Drag)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(lateral)_S 67 _t
(body)_S 67 _t
(axis)_S 67 _t
(due)_S 67 _t
(to)_S 3333 2627 _m
(signed)_S 67 _t
(square)_S 67 _t
(of)_S 67 _t
(existing)_S 67 _t
(pitch)_S 67 _t
/Times-BoldItalicR 600 _ff
(q)_S /Times-RomanR 600 _ff
67 _t
3333 2277 _m
(corresponding)_S 67 _t
(to)_S 67 _t
(turbulent)_S 67 _t
(flow)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 517 _m
_sp 2250 517 2250 814 2247 814 3 _pl _pf _np _s _s 1852 811 _m
_sp 2242 811 2242 814 1852 814 3 _pl _pf _np _s _s 1852 517 _m
_sp 1855 517 1855 814 1852 814 3 _pl _pf _np _s _s 2239 517 _m
_sp 2242 517 2242 814 2239 814 3 _pl _pf _np 
_s 0 g 293 382 1856 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7853 2977 _m
(-7.0)_S 67 _t
(E-3)_S 7856 2628 _m
(estimate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 513 _m
_sp 555 513 555 516 300 516 3 _pl _pf _np _s _s 300 513 _m
_sp 303 513 303 518 300 518 3 _pl _pf _np _s _s 308 513 _m
_sp 311 513 311 518 308 518 3 _pl _pf _np 
_s 0 g 1 243 312 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 513 _m
_sp 805 513 805 516 554 516 3 _pl _pf _np _s _s 554 513 _m
_sp 557 513 557 518 554 518 3 _pl _pf _np 
_s 0 g 1 247 558 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 513 _m
_sp 1853 513 1853 516 804 516 3 _pl _pf _np _s _s 804 513 _m
_sp 807 513 807 518 804 518 3 _pl _pf _np 
_s 0 g 1 1045 808 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 513 _m
_sp 2250 513 2250 516 1852 516 3 _pl _pf _np _s _s 2247 513 _m
_sp 2250 513 2250 518 2247 518 3 _pl _pf _np _s _s 1852 513 _m
_sp 1855 513 1855 518 1852 518 3 _pl _pf _np _s _s 2239 513 _m
_sp 2242 513 2242 518 2239 518 3 _pl _pf _np 
_s 0 g 1 382 1856 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(138)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2800 _m
_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2445 _m
_sp 303 2445 303 2801 300 2801 3 _pl _pf _np _s _s 308 2445 _m
_sp 311 2445 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 352 243 312 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1591 10768 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
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_s 413 2751 _m
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410 2726 410 2728 415 2747 418 2721 419 2721 437 2748 431 2727 430 2725 429 2723 428 2722 427 2722 427 2722 427 2721 439 2721 439 2722 
438 2722 437 2723 436 2725 436 2725 436 2726 437 2728 442 2748 443 2750 443 2752 444 2753 445 2753 446 2753 446 2754 438 2754 422 2730 
419 2754 410 2754 410 2753 410 2753 412 2752 50 _pl _cp 
0 g _f _s _s 
0 g 458 2718 _m
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453 2707 455 2709 453 2702 452 2700 451 2699 450 2699 450 2699 458 2699 458 2699 457 2699 456 2700 456 2700 456 2701 456 2702 461 2720 
458 2720 31 _pl _cp 449 2709 _m
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449 2711 449 2709 449 2709 18 _pl _cp 
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_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 2798 805 2801 554 2801 3 _pl _pf _np _s _s 554 2445 _m
_sp 557 2445 557 2801 554 2801 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np _s _s 804 2445 _m
_sp 807 2445 807 2801 804 2801 3 _pl _pf _np 
_s 0 g 352 1045 808 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10925 _m
(Drag)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(lateral)_S 67 _t
(body)_S 67 _t
(axis)_S 67 _t
(due)_S 67 _t
(to)_S 3333 10575 _m
(existing)_S 67 _t
(pitch)_S 67 _t
/Times-BoldItalicR 600 _ff
(q)_S /Times-RomanR 600 _ff
67 _t
(corresponding)_S 67 _t
(to)_S 67 _t
(laminar)_S 67 _t
(flow,)_S 3333 10068 _m
(approximately)_S 67 _t
(equals)_S 67 _t
5133 9948 _m
5586 10068 _m
67 _t
(at)_S 67 _t
5865 10008 _m
gsave 4 4 scale 16 _sr 
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_s 1299 2546 _m
_sp 1299 2546 1293 2522 1292 2520 1291 2518 1290 2517 1289 2517 1289 2517 1288 2516 1298 2516 1299 2517 1297 2517 1296 2518 1295 2519 1295 2520 1295 2521 
1296 2521 1296 2523 1301 2542 1304 2516 1305 2516 1323 2543 1317 2522 1316 2520 1315 2518 1314 2517 1313 2517 1313 2517 1313 2516 1325 2516 1325 2517 
1324 2517 1323 2518 1322 2520 1322 2520 1322 2521 1323 2523 1328 2543 1329 2545 1329 2547 1330 2548 1331 2548 1332 2548 1332 2549 1324 2549 1308 2525 
1305 2549 1296 2549 1296 2548 1296 2548 1298 2547 50 _pl _cp 
0 g _f _s _s 
0 g 1343 2513 _m
_sp 1343 2513 1342 2515 1340 2515 1339 2515 1337 2514 1336 2513 1334 2512 1333 2510 1332 2508 1331 2506 1331 2504 1332 2501 1334 2500 1335 2500 1336 2500 
1338 2502 1340 2504 1338 2497 1337 2495 1336 2494 1335 2494 1335 2494 1343 2494 1343 2494 1342 2494 1341 2495 1341 2495 1341 2496 1341 2497 1346 2515 
1343 2515 31 _pl _cp 1334 2504 _m
_sp 1334 2504 1335 2502 1336 2502 1338 2503 1340 2506 1341 2508 1341 2509 1342 2511 1342 2512 1342 2513 1340 2514 1339 2514 1337 2512 1336 2510 1335 2508 
1334 2506 1334 2504 1334 2504 18 _pl _cp 
0 g _f _s _s 
0 g 1373 2513 _m
_sp 1373 2513 1372 2515 1370 2515 1369 2515 1367 2514 1366 2513 1364 2512 1363 2510 1362 2508 1361 2506 1361 2504 1362 2501 1364 2500 1365 2500 1366 2500 
1368 2502 1370 2504 1368 2497 1367 2495 1366 2494 1365 2494 1365 2494 1373 2494 1373 2494 1372 2494 1371 2495 1371 2495 1371 2496 1371 2497 1376 2515 
1373 2515 31 _pl _cp 1364 2504 _m
_sp 1364 2504 1365 2502 1366 2502 1368 2503 1370 2506 1371 2508 1371 2509 1372 2511 1372 2512 1372 2513 1370 2514 1369 2514 1367 2512 1366 2510 1365 2508 
1364 2506 1364 2504 1364 2504 18 _pl _cp 
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0 g 1354 2525 _m
_sp 1354 2525 1354 2492 1355 2492 1355 2525 4 _pl _cp 
0 g _f _s _s 
0 g 1384 2525 _m
_sp 1384 2525 1384 2492 1385 2492 1385 2525 4 _pl _cp 
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_s grestore gsave 4 4 scale 16 _sr 
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_s 1477 2548 _m
_sp 1477 2548 1477 2547 1479 2548 1480 2548 1481 2548 1482 2547 1482 2546 1482 2525 1482 2523 1482 2521 1480 2520 1478 2520 1477 2520 1477 2519 1491 2519 
1491 2520 1490 2520 1488 2520 1487 2521 1487 2523 1487 2525 1487 2553 22 _pl _cp 
0 g _f _s _s 
0 g 1531 2552 _m
_sp 1531 2552 1520 2511 1524 2511 1535 2552 4 _pl _cp 
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0 g 1537 2519 _m
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1549 2531 1548 2532 1545 2533 1543 2534 1541 2535 1540 2536 1540 2537 1541 2539 1544 2540 1547 2540 1549 2539 1550 2537 1551 2534 1552 2534 1552 2541 
1551 2541 1551 2541 1550 2541 1550 2541 1549 2541 1547 2542 1546 2542 1544 2542 1541 2541 1539 2540 1538 2538 1537 2536 1537 2534 1538 2532 1540 2531 
1542 2529 1546 2527 1549 2525 1550 2523 1550 2522 1549 2521 1547 2520 1545 2520 1543 2521 1540 2522 1539 2524 1538 2527 1537 2527 58 _pl _cp 
0 g _f _s _s 
0 g 1560 2533 _m
_sp 1560 2533 1575 2533 1574 2537 1573 2539 1570 2541 1566 2542 1562 2541 1559 2539 1557 2535 1556 2530 1557 2525 1559 2522 1562 2520 1566 2519 1569 2519 
1572 2521 1574 2523 1576 2527 1575 2527 1574 2525 1572 2523 1570 2522 1568 2521 1565 2522 1562 2524 1561 2528 1560 2532 1560 2532 28 _pl _cp 1570 2534 _m
_sp 1570 2534 1570 2537 1569 2539 1567 2540 1565 2540 1563 2540 1561 2539 1560 2537 1560 2534 9 _pl _cp 
0 g _f _s _s 
0 g 1597 2527 _m
_sp 1597 2527 1595 2525 1594 2523 1592 2522 1590 2522 1587 2523 1585 2525 1583 2528 1582 2532 1583 2535 1584 2538 1586 2539 1589 2540 1591 2540 1592 2537 
1593 2535 1595 2534 1596 2535 1597 2537 1596 2539 1595 2540 1593 2542 1590 2542 1586 2541 1583 2540 1580 2537 1579 2534 1578 2530 1579 2525 1581 2522 
1584 2520 1588 2519 1590 2519 1592 2519 1593 2520 1595 2521 1596 2522 1596 2523 1597 2524 1598 2526 40 _pl _cp 
0 g _f _s _s 
0 g 1499 2548 _m
_sp 1499 2548 1500 2545 1501 2543 1503 2542 1506 2541 1509 2542 1511 2543 1512 2545 1513 2548 1512 2550 1511 2552 1509 2553 1506 2554 1503 2553 1501 2552 
1500 2550 16 _pl _cp 1501 2548 _m
_sp 1501 2548 1501 2549 1502 2551 1504 2552 1506 2552 1508 2552 1510 2551 1511 2549 1511 2548 1511 2546 1510 2544 1508 2543 1506 2543 1504 2543 1502 2544 
1501 2546 16 _pl _cp 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 2250 2445 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 1852 2445 _m
_sp 1855 2445 1855 2801 1852 2801 3 _pl _pf _np _s _s 2239 2445 _m
_sp 2242 2445 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 352 382 1856 2445 _cw 

_s 0 g 0 0 0 0 _cw 
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gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 136 272 1911 2631 _cw 
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_sp 1927 2717 1921 2694 1920 2692 1919 2690 1918 2689 1917 2689 1917 2689 1916 2688 1926 2688 1927 2689 1925 2689 1924 2690 1923 2691 1923 2692 1923 2692 
1924 2693 1924 2694 1929 2714 1932 2688 1933 2688 1951 2715 1945 2694 1944 2692 1943 2690 1942 2689 1941 2689 1941 2689 1941 2688 1953 2688 1953 2689 
1952 2689 1951 2690 1950 2691 1950 2692 1950 2692 1951 2694 1956 2714 1957 2716 1957 2718 1958 2719 1959 2719 1960 2719 1960 2721 1952 2721 1936 2696 
1933 2721 1924 2721 1924 2719 1924 2719 1926 2719 50 _pl _cp 
0 g _f _s _s 
0 g 1971 2685 _m
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1966 2674 1968 2676 1966 2669 1965 2667 1964 2666 1963 2666 1963 2665 1971 2665 1971 2666 1970 2666 1969 2666 1969 2667 1969 2668 1969 2669 1974 2686 
1971 2686 31 _pl _cp 1962 2676 _m
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1962 2678 1962 2676 1962 2676 18 _pl _cp 
0 g _f _s _s 
0 g 2001 2685 _m
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1996 2674 1998 2676 1996 2669 1995 2667 1994 2666 1993 2666 1993 2665 2001 2665 2001 2666 2000 2666 1999 2666 1999 2667 1999 2668 1999 2669 2004 2686 
2001 2686 31 _pl _cp 1992 2676 _m
_sp 1992 2676 1993 2674 1994 2673 1996 2674 1998 2677 1999 2679 1999 2681 2000 2682 2000 2684 2000 2685 1998 2686 1997 2685 1995 2684 1994 2682 1993 2680 
1992 2678 1992 2676 1992 2676 18 _pl _cp 
0 g _f _s _s 
0 g 1982 2697 _m
_sp 1982 2697 1982 2664 1983 2664 1983 2697 4 _pl _cp 
0 g _f _s _s 
0 g 2012 2697 _m
_sp 2012 2697 2012 2664 2013 2664 2013 2697 4 _pl _cp 
0 g _f _s _s 
0 g 2132 2677 _m
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2133 2679 16 _pl _cp 2134 2677 _m
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2134 2675 16 _pl _cp 
0 g _f _s _s 
0 g 2034 2696 _m
_sp 2034 2696 2031 2696 2031 2708 2031 2713 2031 2717 2031 2721 2031 2726 2032 2730 2033 2733 2034 2737 2035 2740 2036 2743 2038 2746 2041 2750 2044 2755 
2045 2755 2042 2750 2040 2745 2038 2742 2037 2738 2036 2735 2035 2732 2035 2728 2034 2723 2034 2719 2034 2715 2034 2711 2034 2707 28 _pl _cp 
0 g _f _s _s 
0 g 2034 2696 _m
_sp 2034 2696 2031 2696 2031 2682 2031 2677 2031 2673 2031 2668 2031 2664 2032 2660 2033 2656 2034 2653 2035 2650 2036 2647 2038 2643 2041 2639 2044 2635 
2045 2635 2042 2640 2040 2645 2038 2648 2037 2651 2036 2655 2035 2658 2035 2662 2034 2666 2034 2671 2034 2675 2034 2679 2034 2683 28 _pl _cp 
0 g _f _s _s 
0 g 2172 2696 _m
_sp 2172 2696 2175 2696 2175 2708 2175 2713 2175 2717 2175 2721 2174 2726 2174 2730 2173 2733 2172 2737 2171 2740 2170 2743 2168 2746 2165 2750 2162 2755 
2161 2755 2164 2750 2166 2745 2168 2742 2169 2738 2170 2735 2171 2732 2171 2728 2172 2723 2172 2719 2172 2715 2172 2711 2172 2707 28 _pl _cp 
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2161 2635 2164 2640 2166 2645 2168 2648 2169 2651 2170 2655 2171 2658 2171 2662 2172 2666 2172 2671 2172 2675 2172 2679 2172 2683 28 _pl _cp 
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_sp 2049 2700 2049 2698 2155 2698 2155 2700 4 _pl _cp 
0 g _f _s _s 
0 g 2109 2734 _m
_sp 2109 2734 2115 2734 2115 2737 2100 2737 2097 2737 2096 2737 2095 2736 2094 2735 2092 2734 2091 2732 2092 2731 2093 2732 2095 2733 2096 2734 2097 2734 
2098 2734 2098 2734 2098 2727 2098 2725 2097 2723 2097 2722 2096 2720 2095 2719 2095 2717 2095 2716 2097 2715 2098 2716 2099 2717 2100 2720 2100 2724 
2100 2727 2100 2734 2106 2734 2106 2723 2106 2719 2107 2717 2109 2715 2111 2715 2112 2716 2113 2717 2114 2719 2114 2722 2112 2722 2112 2720 2110 2719 
2109 2720 2109 2723 47 _pl _cp 
0 g _f _s _s 
0 g 2060 2677 _m
_sp 2060 2677 2060 2676 2062 2677 2063 2677 2064 2677 2065 2676 2065 2675 2065 2654 2065 2652 2065 2650 2063 2649 2061 2649 2060 2649 2060 2648 2074 2648 
2074 2649 2073 2649 2071 2649 2070 2650 2070 2652 2070 2654 2070 2682 22 _pl _cp 
0 g _f _s _s 
0 g 2088 2665 _m
_sp 2088 2665 2086 2663 2084 2661 2082 2659 2082 2656 2083 2653 2085 2650 2088 2649 2092 2648 2096 2649 2099 2650 2101 2653 2102 2656 2102 2658 2101 2659 
2101 2661 2100 2662 2099 2663 2097 2664 2096 2665 2094 2667 2096 2668 2097 2669 2098 2670 2099 2671 2100 2673 2101 2675 2100 2678 2098 2680 2096 2681 
2092 2682 2088 2681 2085 2680 2083 2677 2082 2674 2083 2671 2084 2669 2086 2667 38 _pl _cp 2090 2663 _m
_sp 2090 2663 2088 2661 2087 2660 2086 2658 2086 2656 2087 2653 2088 2651 2090 2650 2092 2649 2094 2649 2096 2650 2097 2652 2097 2654 2097 2656 2096 2658 
2094 2660 2092 2662 2091 2663 18 _pl _cp 2092 2668 _m
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2090 2670 16 _pl _cp 
0 g _f _s _s 
0 g 2105 2664 _m
_sp 2105 2664 2105 2662 2106 2660 2106 2657 2107 2655 2108 2654 2109 2653 2109 2651 2110 2650 2112 2649 2113 2648 2115 2648 2117 2648 2121 2649 2124 2651 
2126 2654 2127 2659 2128 2665 2127 2670 2126 2675 2124 2679 2121 2681 2117 2682 2113 2681 2110 2679 2107 2675 2105 2670 27 _pl _cp 2110 2665 _m
_sp 2110 2665 2110 2659 2111 2655 2113 2652 2115 2650 2117 2650 2119 2650 2120 2651 2121 2653 2122 2656 2123 2660 2123 2665 2123 2670 2122 2674 2121 2677 
2119 2679 2117 2680 2114 2679 2112 2677 2111 2674 2110 2670 21 _pl _cp 
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_s grestore 7856 10111 _m
(estimate)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 2443 555 2446 308 2446 3 _pl _pf _np _s _s 300 2324 _m
_sp 303 2324 303 2446 300 2446 3 _pl _pf _np _s _s 308 2324 _m
_sp 311 2324 311 2446 308 2446 3 _pl _pf _np 
_s 0 g 118 243 312 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2443 _m
_sp 805 2443 805 2446 554 2446 3 _pl _pf _np 
_s 0 g 118 251 554 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2443 _m
_sp 1853 2443 1853 2446 804 2446 3 _pl _pf _np 
_s 0 g 118 1049 804 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 2250 2324 2250 2446 2247 2446 3 _pl _pf _np _s _s 1852 2443 _m
_sp 2242 2443 2242 2446 1852 2446 3 _pl _pf _np _s _s 2239 2324 _m
_sp 2242 2324 2242 2446 2239 2446 3 _pl _pf _np 
_s 0 g 118 386 1852 2324 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4050 9503 _m
/Times-BoldItalicR 600 _ff
(Yaw)_S 67 _t
(moment)_S 67 _t
(coefficients)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2321 _m
_sp 555 2321 555 2324 308 2324 3 _pl _pf _np _s _s 300 2074 _m
_sp 303 2074 303 2324 300 2324 3 _pl _pf _np _s _s 308 2074 _m
_sp 311 2074 311 2324 308 2324 3 _pl _pf _np 
_s 0 g 246 243 312 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1614 8862 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 59 403 2215 _cw 
_s 418 2273 _m
_sp 418 2273 413 2250 412 2248 411 2246 410 2245 409 2245 408 2245 408 2244 418 2244 418 2245 417 2245 415 2246 415 2248 415 2248 415 2250 
420 2271 432 2244 433 2244 433 2244 433 2245 433 2246 434 2247 434 2248 435 2251 440 2271 441 2273 442 2275 443 2276 444 2276 444 2276 
445 2277 435 2277 435 2276 436 2276 438 2275 438 2274 438 2273 438 2272 437 2271 433 2252 422 2277 415 2277 415 2276 416 2276 417 2275 
45 _pl _cp 
0 g _f _s _s 
0 g 442 2242 _m
_sp 442 2242 442 2242 442 2242 442 2242 444 2241 445 2240 446 2238 446 2236 446 2235 446 2233 446 2230 447 2228 447 2228 448 2228 448 2229 
450 2231 452 2233 453 2234 454 2236 455 2237 455 2238 456 2240 457 2241 456 2242 455 2243 454 2243 453 2242 453 2241 454 2240 455 2240 
455 2239 455 2238 454 2237 453 2236 452 2235 451 2233 449 2231 449 2232 449 2235 449 2236 448 2238 448 2239 448 2241 447 2243 44 _pl _cp 
0 g _f _s _s 
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_sp 450 2248 451 2247 452 2246 453 2247 453 2248 453 2249 452 2250 451 2249 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2321 _m
_sp 805 2321 805 2324 554 2324 3 _pl _pf _np _s _s 554 2074 _m
_sp 557 2074 557 2324 554 2324 3 _pl _pf _np 
_s 0 g 246 247 558 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2321 _m
_sp 1853 2321 1853 2324 804 2324 3 _pl _pf _np _s _s 804 2074 _m
_sp 807 2074 807 2324 804 2324 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 3333 9019 _m
(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(vertical)_S 67 _t
(body)_S 67 _t
(axis)_S 3333 8561 _m
(due)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(sway)_S 67 _t
(\()_S 6346 8501 _m
6486 8561 _m
(\))_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 35 1586 2125 _cw 
_s 1604 2172 _m
_sp 1604 2172 1605 2170 1607 2169 1608 2170 1609 2172 1608 2174 1607 2175 1605 2174 8 _pl _cp 
0 g _f _s _s 
0 g 1592 2163 _m
_sp 1592 2163 1592 2163 1592 2163 1593 2163 1595 2162 1596 2160 1597 2159 1597 2157 1597 2156 1598 2154 1598 2152 1599 2149 1599 2146 1599 2142 1600 2142 
1601 2143 1601 2143 1603 2145 1604 2146 1606 2148 1607 2150 1608 2152 1610 2153 1611 2155 1612 2156 1613 2158 1613 2159 1614 2161 1614 2162 1613 2164 
1611 2165 1610 2164 1609 2163 1609 2162 1610 2161 1611 2160 1611 2159 1611 2157 1610 2155 1609 2154 1607 2152 1606 2150 1605 2149 1604 2148 1603 2147 
1603 2149 1602 2152 1602 2155 1602 2157 1601 2159 1600 2161 1600 2163 1600 2164 1600 2165 54 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2074 _m
_sp 2250 2074 2250 2324 2247 2324 3 _pl _pf _np _s _s 1852 2321 _m
_sp 2242 2321 2242 2324 1852 2324 3 _pl _pf _np _s _s 1852 2074 _m
_sp 1855 2074 1855 2324 1852 2324 3 _pl _pf _np _s _s 2239 2074 _m
_sp 2242 2074 2242 2324 2239 2324 3 _pl _pf _np 
_s 0 g 246 382 1856 2074 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 9019 _m
(-1.78)_S 67 _t
(E-3)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2072 _m
_sp 555 2072 555 2075 308 2075 3 _pl _pf _np _s _s 300 1825 _m
_sp 303 1825 303 2075 300 2075 3 _pl _pf _np _s _s 308 1825 _m
_sp 311 1825 311 2075 308 2075 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1618 7864 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 58 404 1966 _cw 
_s 419 2024 _m
_sp 419 2024 414 2001 413 1999 412 1997 411 1996 410 1996 409 1996 409 1995 419 1995 419 1996 418 1996 416 1997 416 1999 416 1999 416 2001 
421 2022 433 1995 434 1995 434 1995 434 1996 434 1997 435 1998 435 1999 436 2002 441 2022 442 2024 443 2026 444 2027 445 2027 445 2027 
446 2028 436 2028 436 2027 437 2027 439 2026 439 2025 439 2024 439 2023 438 2022 434 2003 423 2028 416 2028 416 2027 417 2027 418 2026 
45 _pl _cp 
0 g _f _s _s 
0 g 444 1979 _m
_sp 444 1979 446 1979 447 1982 448 1984 448 1985 449 1986 450 1988 450 1989 451 1990 452 1991 453 1992 453 1992 453 1991 454 1991 454 1990 
455 1991 456 1992 455 1993 454 1994 453 1994 451 1993 451 1991 449 1989 449 1989 449 1988 450 1994 445 1993 445 1993 446 1993 447 1993 
447 1992 447 1991 447 1990 33 _pl _cp 
0 g _f _s _s 
0 g 450 1999 _m
_sp 450 1999 451 1998 452 1997 453 1998 454 1999 453 2000 452 2001 451 2000 8 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2072 _m
_sp 805 2072 805 2075 554 2075 3 _pl _pf _np _s _s 554 1825 _m
_sp 557 1825 557 2075 554 2075 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2072 _m
_sp 1853 2072 1853 2075 804 2075 3 _pl _pf _np _s _s 804 1825 _m
_sp 807 1825 807 2075 804 2075 3 _pl _pf _np 
_s 0 g 246 1045 808 1825 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 8021 _m
(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(vertical)_S 67 _t
(body)_S 67 _t
(axis)_S 3333 7563 _m
(due)_S 67 _t
(to)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(yaw)_S 67 _t
(\()_S 6268 7503 _m
6408 7563 _m
(\))_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 64 34 1567 1875 _cw 
_s 1584 1922 _m
_sp 1584 1922 1585 1920 1586 1919 1588 1920 1589 1922 1588 1924 1586 1925 1585 1924 8 _pl _cp 
0 g _f _s _s 
0 g 1574 1892 _m
_sp 1574 1892 1578 1892 1579 1897 1580 1900 1581 1902 1582 1904 1583 1905 1583 1907 1584 1908 1586 1910 1587 1911 1588 1911 1588 1910 1589 1910 1590 1909 
1591 1910 1592 1912 1591 1914 1590 1915 1588 1914 1586 1912 1584 1911 1582 1908 1582 1907 1581 1906 1584 1915 1576 1914 1576 1913 1577 1913 1578 1912 
1579 1911 1579 1910 1578 1909 33 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1825 _m
_sp 2250 1825 2250 2075 2247 2075 3 _pl _pf _np _s _s 1852 2072 _m
_sp 2242 2072 2242 2075 1852 2075 3 _pl _pf _np _s _s 1852 1825 _m
_sp 1855 1825 1855 2075 1852 2075 3 _pl _pf _np _s _s 2239 1825 _m
_sp 2242 1825 2242 2075 2239 2075 3 _pl _pf _np 
_s 0 g 246 382 1856 1825 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7853 8021 _m
(-4.7)_S 67 _t
(E-4)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 1822 _m
_sp 555 1822 555 1825 308 1825 3 _pl _pf _np _s _s 300 1616 _m
_sp 303 1616 303 1825 300 1825 3 _pl _pf _np _s _s 308 1616 _m
_sp 311 1616 311 1825 308 1825 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1581 6866 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 76 395 1716 _cw 
_s 410 1774 _m
_sp 410 1774 405 1751 404 1749 403 1747 402 1746 401 1746 400 1746 400 1745 410 1745 410 1746 409 1746 407 1747 407 1749 407 1749 407 1751 
412 1772 424 1745 425 1745 425 1745 425 1746 425 1747 426 1748 426 1749 427 1752 432 1772 433 1774 434 1776 435 1777 436 1777 436 1777 
437 1778 427 1778 427 1777 428 1777 430 1776 430 1775 430 1774 430 1773 429 1772 425 1753 414 1778 407 1778 407 1777 408 1777 409 1776 
45 _pl _cp 
0 g _f _s _s 
0 g 446 1744 _m
_sp 446 1744 446 1742 445 1740 444 1739 444 1738 443 1736 442 1735 440 1732 438 1731 438 1731 437 1731 437 1732 438 1733 441 1744 436 1743 
435 1743 436 1743 437 1743 437 1742 437 1741 437 1740 435 1734 435 1733 435 1732 435 1732 435 1731 435 1730 436 1729 438 1729 440 1731 
441 1732 442 1733 443 1734 444 1736 443 1733 443 1732 443 1730 443 1729 445 1729 447 1730 449 1733 449 1733 448 1733 447 1731 446 1731 
446 1730 446 1731 445 1731 445 1732 446 1732 446 1733 446 1734 447 1736 447 1738 448 1742 449 1744 56 _pl _cp 
0 g _f _s _s 
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459 1732 461 1734 462 1735 463 1737 464 1738 464 1739 465 1741 465 1742 465 1743 463 1744 462 1744 462 1743 462 1742 463 1741 463 1741 
463 1740 463 1739 462 1738 462 1737 461 1736 460 1734 458 1732 458 1733 457 1736 457 1737 457 1739 457 1740 456 1742 456 1744 44 _pl _cp 
0 g _f _s 
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_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 1822 805 1825 554 1825 3 _pl _pf _np _s _s 554 1616 _m
_sp 557 1616 557 1825 554 1825 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 1822 _m
_sp 1853 1822 1853 1825 804 1825 3 _pl _pf _np _s _s 804 1616 _m
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_s 0 g 0 0 0 0 _cw 
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(Fluid)_S 67 _t
(inertia)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(vertical)_S 67 _t
(body)_S 67 _t
(axis)_S 3333 6673 _m
(due)_S 67 _t
(to)_S 67 _t
(existing)_S 67 _t
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/Times-BoldItalicR 600 _ff
(v)_S /Times-RomanR 600 _ff
67 _t
(and)_S 67 _t
(surge)_S 67 _t
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 1616 _m
_sp 2250 1616 2250 1825 2247 1825 3 _pl _pf _np _s _s 1852 1822 _m
_sp 2242 1822 2242 1825 1852 1825 3 _pl _pf _np _s _s 1852 1616 _m
_sp 1855 1616 1855 1825 1852 1825 3 _pl _pf _np _s _s 2239 1616 _m
_sp 2242 1616 2242 1825 2239 1825 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 8064 7023 _m
(0.0)_S gsave 4 4 scale 16 _sr _s 
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_sp 555 1613 555 1616 308 1616 3 _pl _pf _np _s _s 300 1407 _m
_sp 303 1407 303 1616 300 1616 3 _pl _pf _np _s _s 308 1407 _m
_sp 311 1407 311 1616 308 1616 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore 1584 6030 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 74 396 1507 _cw 
_s 411 1565 _m
_sp 411 1565 406 1542 405 1540 404 1538 403 1537 402 1537 401 1537 401 1536 411 1536 411 1537 410 1537 408 1538 408 1540 408 1540 408 1542 
413 1563 425 1536 426 1536 426 1536 426 1537 426 1538 427 1539 427 1540 428 1543 433 1563 434 1565 435 1567 436 1568 437 1568 437 1568 
438 1569 428 1569 428 1568 429 1568 431 1567 431 1566 431 1565 431 1564 430 1563 426 1544 415 1569 408 1569 408 1568 409 1568 410 1567 
45 _pl _cp 
0 g _f _s _s 
0 g 447 1535 _m
_sp 447 1535 447 1533 446 1531 445 1530 445 1529 444 1527 443 1526 441 1523 439 1522 439 1522 438 1522 438 1523 439 1524 442 1535 437 1534 
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442 1523 443 1524 444 1525 445 1527 444 1524 444 1523 444 1521 444 1520 446 1520 448 1521 450 1524 450 1524 449 1524 448 1522 447 1522 
447 1521 447 1522 446 1522 446 1523 447 1523 447 1524 447 1525 448 1527 448 1529 449 1533 450 1535 56 _pl _cp 
0 g _f _s _s 
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464 1534 463 1535 462 1535 460 1534 459 1532 458 1530 458 1530 457 1529 459 1535 454 1534 453 1534 455 1534 456 1534 456 1533 456 1532 
455 1531 31 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1613 _m
_sp 805 1613 805 1616 554 1616 3 _pl _pf _np _s _s 554 1407 _m
_sp 557 1407 557 1616 554 1616 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 1853 1613 1853 1616 804 1616 3 _pl _pf _np _s _s 804 1407 _m
_sp 807 1407 807 1616 804 1616 3 _pl _pf _np 
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0 g 424 718 _m
_sp 424 718 426 718 427 721 428 723 428 724 429 725 430 727 430 728 431 729 432 730 433 731 433 731 433 730 434 730 434 729 
435 730 436 731 435 732 434 733 433 733 431 732 431 730 429 728 429 728 429 727 430 733 425 732 425 732 426 732 427 732 
427 731 427 730 427 729 33 _pl _cp 
0 g _f _s _s 
0 g 450 718 _m
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462 730 462 731 461 732 460 733 459 733 458 732 457 730 456 728 455 728 455 727 456 733 451 732 451 732 452 732 453 732 
453 731 453 730 453 729 33 _pl _cp 
0 g _f _s _s 
0 g 443 743 _m
_sp 443 743 443 710 444 710 444 743 4 _pl _cp 
0 g _f _s _s 
0 g 469 743 _m
_sp 469 743 469 710 470 710 470 743 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 811 _m
_sp 805 811 805 814 554 814 3 _pl _pf _np _s _s 554 517 _m
_sp 557 517 557 814 554 814 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 811 _m
_sp 1853 811 1853 814 804 814 3 _pl _pf _np _s _s 804 517 _m
_sp 807 517 807 814 804 814 3 _pl _pf _np 
_s 0 g 293 1045 808 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 2977 _m
(Drag)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(vertical)_S 67 _t
(body)_S 67 _t
(axis)_S 67 _t
(due)_S 67 _t
(to)_S 3333 2627 _m
(signed)_S 67 _t
(square)_S 67 _t
(of)_S 67 _t
(existing)_S 67 _t
(yaw)_S 67 _t
/Times-BoldItalicR 600 _ff
(r)_S /Times-RomanR 600 _ff
3333 2277 _m
(corresponding)_S 67 _t
(to)_S 67 _t
(turbulent)_S 67 _t
(flow)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 517 _m
_sp 2250 517 2250 814 2247 814 3 _pl _pf _np _s _s 1852 811 _m
_sp 2242 811 2242 814 1852 814 3 _pl _pf _np _s _s 1852 517 _m
_sp 1855 517 1855 814 1852 814 3 _pl _pf _np _s _s 2239 517 _m
_sp 2242 517 2242 814 2239 814 3 _pl _pf _np 
_s 0 g 293 382 1856 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7803 2977 _m
(-5.48)_S 67 _t
(E-3)_S 7856 2628 _m
(estimate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 513 _m
_sp 555 513 555 516 300 516 3 _pl _pf _np _s _s 300 513 _m
_sp 303 513 303 518 300 518 3 _pl _pf _np _s _s 308 513 _m
_sp 311 513 311 518 308 518 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
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_sp 805 513 805 516 554 516 3 _pl _pf _np _s _s 554 513 _m
_sp 557 513 557 518 554 518 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 513 _m
_sp 1853 513 1853 516 804 516 3 _pl _pf _np _s _s 804 513 _m
_sp 807 513 807 518 804 518 3 _pl _pf _np 
_s 0 g 1 1045 808 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 513 _m
_sp 2250 513 2250 516 1852 516 3 _pl _pf _np _s _s 2247 513 _m
_sp 2250 513 2250 518 2247 518 3 _pl _pf _np _s _s 1852 513 _m
_sp 1855 513 1855 518 1852 518 3 _pl _pf _np _s _s 2239 513 _m
_sp 2242 513 2242 518 2239 518 3 _pl _pf _np 
_s 0 g 1 382 1856 517 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 4950 1288 _m
(139)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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gsave 4 4 scale 16 _sr _s 
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_sp 555 2800 555 2803 308 2803 3 _pl _pf _np _s _s 300 2996 _m
_sp 555 2996 555 2999 300 2999 3 _pl _pf _np _s _s 300 2800 _m
_sp 303 2800 303 2999 300 2999 3 _pl _pf _np _s _s 308 2808 _m
_sp 555 2808 555 2811 308 2811 3 _pl _pf _np _s _s 308 2988 _m
_sp 555 2988 555 2991 308 2991 3 _pl _pf _np _s _s 308 2808 _m
_sp 311 2808 311 2991 308 2991 3 _pl _pf _np 
_s 0 g 175 243 312 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1733 11716 _m
/Times-BoldR 480 _ff
1360 11427 _m
(Coefficient)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2800 _m
_sp 805 2800 805 2803 554 2803 3 _pl _pf _np _s _s 554 2996 _m
_sp 805 2996 805 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 557 2808 557 2991 554 2991 3 _pl _pf _np _s _s 554 2996 _m
_sp 557 2996 557 2999 554 2999 3 _pl _pf _np _s _s 554 2808 _m
_sp 805 2808 805 2811 554 2811 3 _pl _pf _np _s _s 554 2988 _m
_sp 805 2988 805 2991 554 2991 3 _pl _pf _np 
_s 0 g 175 247 558 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 2526 11427 _m
(Name)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2800 _m
_sp 1853 2800 1853 2803 804 2803 3 _pl _pf _np _s _s 804 2996 _m
_sp 1853 2996 1853 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 807 2808 807 2991 804 2991 3 _pl _pf _np _s _s 804 2996 _m
_sp 807 2996 807 2999 804 2999 3 _pl _pf _np _s _s 804 2808 _m
_sp 1853 2808 1853 2811 804 2811 3 _pl _pf _np _s _s 804 2988 _m
_sp 1853 2988 1853 2991 804 2991 3 _pl _pf _np 
_s 0 g 175 1045 808 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 11427 _m
(Description)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 2800 _m
_sp 2242 2800 2242 2803 1852 2803 3 _pl _pf _np _s _s 2247 2800 _m
_sp 2250 2800 2250 2999 2247 2999 3 _pl _pf _np _s _s 1852 2996 _m
_sp 2250 2996 2250 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 1855 2808 1855 2991 1852 2991 3 _pl _pf _np _s _s 1852 2996 _m
_sp 1855 2996 1855 2999 1852 2999 3 _pl _pf _np _s _s 1852 2808 _m
_sp 2242 2808 2242 2811 1852 2811 3 _pl _pf _np _s _s 2239 2808 _m
_sp 2242 2808 2242 2991 2239 2991 3 _pl _pf _np _s _s 1852 2988 _m
_sp 2242 2988 2242 2991 1852 2991 3 _pl _pf _np 
_s 0 g 175 382 1856 2812 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7860 11716 _m
(Value)_S 53 _t
(for)_S 7749 11427 _m
(NPS)_S 53 _t
(AUV)_S 53 _t
(II)_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 308 2798 _m
_sp 555 2798 555 2801 308 2801 3 _pl _pf _np _s _s 300 2445 _m
_sp 303 2445 303 2801 300 2801 3 _pl _pf _np _s _s 308 2445 _m
_sp 311 2445 311 2801 308 2801 3 _pl _pf _np 
_s 0 g 352 243 312 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1616 10768 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 58 404 2692 _cw 
_s 419 2750 _m
_sp 419 2750 414 2727 413 2725 412 2723 411 2722 410 2722 409 2722 409 2721 419 2721 419 2722 418 2722 416 2723 416 2725 416 2725 416 2727 
421 2748 433 2721 434 2721 434 2721 434 2722 434 2723 435 2724 435 2725 436 2728 441 2748 442 2750 443 2752 444 2753 445 2753 445 2753 
446 2754 436 2754 436 2753 437 2753 439 2752 439 2751 439 2750 439 2749 438 2748 434 2729 423 2754 416 2754 416 2753 417 2753 418 2752 
45 _pl _cp 
0 g _f _s _s 
0 g 445 2705 _m
_sp 445 2705 447 2705 448 2708 449 2710 449 2711 450 2712 451 2714 451 2715 452 2716 453 2717 454 2718 454 2718 454 2717 455 2717 455 2716 
456 2717 457 2718 456 2719 455 2720 454 2720 452 2719 452 2717 450 2715 450 2715 450 2714 451 2720 446 2719 446 2719 447 2719 448 2719 
448 2718 448 2717 448 2716 33 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 2798 _m
_sp 805 2798 805 2801 554 2801 3 _pl _pf _np _s _s 554 2445 _m
_sp 557 2445 557 2801 554 2801 3 _pl _pf _np 
_s 0 g 352 247 558 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 804 2798 _m
_sp 1853 2798 1853 2801 804 2801 3 _pl _pf _np _s _s 804 2445 _m
_sp 807 2445 807 2801 804 2801 3 _pl _pf _np 
_s 0 g 352 1045 808 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 3333 10925 _m
(Drag)_S 67 _t
(moment)_S 67 _t
(about)_S 67 _t
(vertical)_S 67 _t
(body)_S 67 _t
(axis)_S 67 _t
(due)_S 67 _t
(to)_S 3333 10575 _m
(existing)_S 67 _t
(yaw)_S 67 _t
/Times-BoldItalicR 600 _ff
(r)_S /Times-RomanR 600 _ff
67 _t
(corresponding)_S 67 _t
(to)_S 67 _t
(laminar)_S 67 _t
(flow,)_S 3333 10068 _m
(approximately)_S 67 _t
(equals)_S 67 _t
5133 9948 _m
5522 10068 _m
67 _t
(at)_S 67 _t
5801 10008 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 97 1283 2487 _cw 
_s 1298 2545 _m
_sp 1298 2545 1293 2522 1292 2520 1291 2518 1290 2517 1289 2517 1288 2517 1288 2516 1298 2516 1298 2517 1297 2517 1295 2518 1295 2520 1295 2520 1295 2522 
1300 2543 1312 2516 1313 2516 1313 2516 1313 2517 1313 2518 1314 2519 1314 2520 1315 2523 1320 2543 1321 2545 1322 2547 1323 2548 1324 2548 1324 2548 
1325 2549 1315 2549 1315 2548 1316 2548 1318 2547 1318 2546 1318 2545 1318 2544 1317 2543 1313 2524 1302 2549 1295 2549 1295 2548 1296 2548 1297 2547 
45 _pl _cp 
0 g _f _s _s 
0 g 1323 2500 _m
_sp 1323 2500 1325 2500 1326 2503 1327 2505 1327 2506 1328 2507 1329 2509 1329 2510 1330 2511 1331 2512 1332 2513 1332 2513 1332 2512 1333 2512 1333 2511 
1334 2512 1335 2513 1334 2514 1333 2515 1332 2515 1330 2514 1330 2512 1328 2510 1328 2510 1328 2509 1329 2515 1324 2514 1324 2514 1325 2514 1326 2514 
1326 2513 1326 2512 1326 2511 33 _pl _cp 
0 g _f _s _s 
0 g 1349 2500 _m
_sp 1349 2500 1352 2500 1352 2503 1353 2505 1353 2506 1354 2507 1355 2509 1355 2510 1356 2511 1357 2512 1358 2513 1358 2513 1358 2512 1359 2512 1360 2511 
1361 2512 1361 2513 1360 2514 1359 2515 1358 2515 1357 2514 1356 2512 1355 2510 1354 2510 1354 2509 1355 2515 1350 2514 1350 2514 1351 2514 1352 2514 
1352 2513 1352 2512 1352 2511 33 _pl _cp 
0 g _f _s _s 
0 g 1342 2525 _m
_sp 1342 2525 1342 2492 1343 2492 1343 2525 4 _pl _cp 
0 g _f _s _s 
0 g 1368 2525 _m
_sp 1368 2525 1368 2492 1369 2492 1369 2525 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 139 1450 2502 _cw 
_s 1461 2548 _m
_sp 1461 2548 1461 2547 1463 2548 1464 2548 1465 2548 1466 2547 1466 2546 1466 2525 1466 2523 1466 2521 1464 2520 1462 2520 1461 2520 1461 2519 1475 2519 
1475 2520 1474 2520 1472 2520 1471 2521 1471 2523 1471 2525 1471 2553 22 _pl _cp 
0 g _f _s _s 
0 g 1515 2552 _m
_sp 1515 2552 1504 2511 1508 2511 1519 2552 4 _pl _cp 
0 g _f _s _s 
0 g 1521 2519 _m
_sp 1521 2519 1522 2519 1522 2519 1523 2519 1524 2519 1525 2519 1528 2519 1530 2519 1533 2519 1536 2521 1537 2522 1538 2525 1537 2527 1536 2529 1535 2530 
1533 2531 1532 2532 1529 2533 1527 2534 1525 2535 1524 2536 1524 2537 1525 2539 1528 2540 1531 2540 1533 2539 1534 2537 1535 2534 1536 2534 1536 2541 
1535 2541 1535 2541 1534 2541 1534 2541 1533 2541 1531 2542 1530 2542 1528 2542 1525 2541 1523 2540 1522 2538 1521 2536 1521 2534 1522 2532 1524 2531 
1526 2529 1530 2527 1533 2525 1534 2523 1534 2522 1533 2521 1531 2520 1529 2520 1527 2521 1524 2522 1523 2524 1522 2527 1521 2527 58 _pl _cp 
0 g _f _s _s 
0 g 1544 2533 _m
_sp 1544 2533 1559 2533 1558 2537 1557 2539 1554 2541 1550 2542 1546 2541 1543 2539 1541 2535 1540 2530 1541 2525 1543 2522 1546 2520 1550 2519 1553 2519 
1556 2521 1558 2523 1560 2527 1559 2527 1558 2525 1556 2523 1554 2522 1552 2521 1549 2522 1546 2524 1545 2528 1544 2532 1544 2532 28 _pl _cp 1554 2534 _m
_sp 1554 2534 1554 2537 1553 2539 1551 2540 1549 2540 1547 2540 1545 2539 1544 2537 1544 2534 9 _pl _cp 
0 g _f _s _s 
0 g 1581 2527 _m
_sp 1581 2527 1579 2525 1578 2523 1576 2522 1574 2522 1571 2523 1569 2525 1567 2528 1566 2532 1567 2535 1568 2538 1570 2539 1573 2540 1575 2540 1576 2537 
1577 2535 1579 2534 1580 2535 1581 2537 1580 2539 1579 2540 1577 2542 1574 2542 1570 2541 1567 2540 1564 2537 1563 2534 1562 2530 1563 2525 1565 2522 
1568 2520 1572 2519 1574 2519 1576 2519 1577 2520 1579 2521 1580 2522 1580 2523 1581 2524 1582 2526 40 _pl _cp 
0 g _f _s _s 
0 g 1483 2548 _m
_sp 1483 2548 1484 2545 1485 2543 1487 2542 1490 2541 1493 2542 1495 2543 1496 2545 1497 2548 1496 2550 1495 2552 1493 2553 1490 2554 1487 2553 1485 2552 
1484 2550 16 _pl _cp 1485 2548 _m
_sp 1485 2548 1485 2549 1486 2551 1488 2552 1490 2552 1492 2552 1494 2551 1495 2549 1495 2548 1495 2546 1494 2544 1492 2543 1490 2543 1488 2543 1486 2544 
1485 2546 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 2247 2445 _m
_sp 2250 2445 2250 2801 2247 2801 3 _pl _pf _np _s _s 1852 2798 _m
_sp 2242 2798 2242 2801 1852 2801 3 _pl _pf _np _s _s 1852 2445 _m
_sp 1855 2445 1855 2801 1852 2801 3 _pl _pf _np _s _s 2239 2445 _m
_sp 2242 2445 2242 2801 2239 2801 3 _pl _pf _np 
_s 0 g 352 382 1856 2445 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7676 10527 _m
gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 136 256 1919 2631 _cw 
_s 1934 2717 _m
_sp 1934 2717 1929 2694 1928 2692 1927 2690 1926 2689 1925 2689 1924 2689 1924 2688 1934 2688 1934 2689 1933 2689 1931 2690 1931 2691 1931 2692 1931 2694 
1936 2714 1948 2687 1949 2687 1949 2688 1949 2689 1949 2689 1950 2690 1950 2692 1951 2695 1956 2714 1957 2716 1958 2718 1959 2719 1960 2719 1960 2719 
1961 2721 1951 2721 1951 2719 1952 2719 1954 2719 1954 2717 1954 2717 1954 2716 1953 2714 1949 2696 1938 2721 1931 2721 1931 2719 1932 2719 1933 2719 
45 _pl _cp 
0 g _f _s _s 
0 g 1959 2672 _m
_sp 1959 2672 1961 2672 1962 2675 1963 2677 1963 2678 1965 2680 1966 2682 1967 2684 1968 2684 1968 2684 1968 2684 1969 2683 1969 2683 1970 2684 1971 2685 
1970 2686 1969 2687 1968 2686 1966 2685 1966 2684 1964 2682 1964 2682 1964 2681 1965 2687 1960 2686 1960 2685 1961 2685 1962 2685 1962 2685 1962 2684 
1962 2683 31 _pl _cp 
0 g _f _s _s 
0 g 1985 2672 _m
_sp 1985 2672 1988 2672 1988 2675 1989 2677 1989 2678 1991 2680 1992 2682 1993 2684 1994 2684 1994 2684 1994 2684 1995 2683 1996 2683 1997 2684 1997 2685 
1996 2686 1995 2687 1994 2686 1993 2685 1992 2684 1991 2682 1990 2682 1990 2681 1991 2687 1986 2686 1986 2685 1987 2685 1988 2685 1988 2685 1988 2684 
1988 2683 31 _pl _cp 
0 g _f _s _s 
0 g 1978 2697 _m
_sp 1978 2697 1978 2664 1979 2664 1979 2697 4 _pl _cp 
0 g _f _s _s 
0 g 2004 2697 _m
_sp 2004 2697 2004 2664 2005 2664 2005 2697 4 _pl _cp 
0 g _f _s _s 
0 g 2124 2677 _m
_sp 2124 2677 2125 2674 2126 2672 2128 2671 2131 2670 2134 2671 2136 2672 2137 2674 2138 2677 2137 2679 2136 2681 2134 2682 2131 2683 2128 2682 2126 2681 
2125 2679 16 _pl _cp 2126 2677 _m
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2126 2675 16 _pl _cp 
0 g _f _s _s 
0 g 2026 2696 _m
_sp 2026 2696 2023 2696 2023 2708 2023 2713 2023 2717 2023 2721 2023 2726 2024 2730 2025 2733 2026 2737 2027 2740 2028 2743 2030 2746 2033 2750 2036 2755 
2037 2755 2034 2750 2032 2745 2030 2742 2029 2738 2028 2735 2027 2732 2027 2728 2026 2723 2026 2719 2026 2715 2026 2711 2026 2707 28 _pl _cp 
0 g _f _s _s 
0 g 2026 2696 _m
_sp 2026 2696 2023 2696 2023 2682 2023 2677 2023 2673 2023 2668 2023 2664 2024 2660 2025 2656 2026 2653 2027 2650 2028 2647 2030 2643 2033 2639 2036 2635 
2037 2635 2034 2640 2032 2645 2030 2648 2029 2651 2028 2655 2027 2658 2027 2662 2026 2666 2026 2671 2026 2675 2026 2679 2026 2683 28 _pl _cp 
0 g _f _s _s 
0 g 2164 2696 _m
_sp 2164 2696 2167 2696 2167 2708 2167 2713 2167 2717 2167 2721 2166 2726 2166 2730 2165 2733 2164 2737 2163 2740 2162 2743 2160 2746 2157 2750 2154 2755 
2153 2755 2156 2750 2158 2745 2160 2742 2161 2738 2162 2735 2163 2732 2163 2728 2164 2723 2164 2719 2164 2715 2164 2711 2164 2707 28 _pl _cp 
0 g _f _s _s 
0 g 2164 2696 _m
_sp 2164 2696 2167 2696 2167 2682 2167 2677 2167 2673 2167 2668 2166 2664 2166 2660 2165 2656 2164 2653 2163 2650 2162 2647 2160 2643 2157 2639 2154 2635 
2153 2635 2156 2640 2158 2645 2160 2648 2161 2651 2162 2655 2163 2658 2163 2662 2164 2666 2164 2671 2164 2675 2164 2679 2164 2683 28 _pl _cp 
0 g _f _s _s 
0 g 2041 2700 _m
_sp 2041 2700 2041 2698 2147 2698 2147 2700 4 _pl _cp 
0 g _f _s _s 
0 g 2101 2734 _m
_sp 2101 2734 2107 2734 2107 2737 2092 2737 2089 2737 2088 2737 2087 2736 2086 2735 2084 2734 2083 2732 2084 2731 2085 2732 2087 2733 2088 2734 2089 2734 
2090 2734 2090 2734 2090 2727 2090 2725 2089 2723 2089 2722 2088 2720 2087 2719 2087 2717 2087 2716 2089 2715 2090 2716 2091 2717 2092 2720 2092 2724 
2092 2727 2092 2734 2098 2734 2098 2723 2098 2719 2099 2717 2101 2715 2103 2715 2104 2716 2105 2717 2106 2719 2106 2722 2104 2722 2104 2720 2102 2719 
2101 2720 2101 2723 47 _pl _cp 
0 g _f _s _s 
0 g 2052 2677 _m
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2066 2649 2065 2649 2063 2649 2062 2650 2062 2652 2062 2654 2062 2682 22 _pl _cp 
0 g _f _s _s 
0 g 2080 2665 _m
_sp 2080 2665 2078 2663 2076 2661 2074 2659 2074 2656 2075 2653 2077 2650 2080 2649 2084 2648 2088 2649 2091 2650 2093 2653 2094 2656 2094 2658 2093 2659 
2093 2661 2092 2662 2091 2663 2089 2664 2088 2665 2086 2667 2088 2668 2089 2669 2090 2670 2091 2671 2092 2673 2093 2675 2092 2678 2090 2680 2088 2681 
2084 2682 2080 2681 2077 2680 2075 2677 2074 2674 2075 2671 2076 2669 2078 2667 38 _pl _cp 2082 2663 _m
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2086 2660 2084 2662 2083 2663 18 _pl _cp 2084 2668 _m
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2082 2670 16 _pl _cp 
0 g _f _s _s 
0 g 2097 2664 _m
_sp 2097 2664 2097 2662 2098 2660 2098 2657 2099 2655 2100 2654 2101 2653 2101 2651 2102 2650 2104 2649 2105 2648 2107 2648 2109 2648 2113 2649 2116 2651 
2118 2654 2119 2659 2120 2665 2119 2670 2118 2675 2116 2679 2113 2681 2109 2682 2105 2681 2102 2679 2099 2675 2097 2670 27 _pl _cp 2102 2665 _m
_sp 2102 2665 2102 2659 2103 2655 2105 2652 2107 2650 2109 2650 2111 2650 2112 2651 2113 2653 2114 2656 2115 2660 2115 2665 2115 2670 2114 2674 2113 2677 
2111 2679 2109 2680 2106 2679 2104 2677 2103 2674 2102 2670 21 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 7856 10111 _m
(estimate)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 300 1632 _m
_sp 555 1632 555 1635 300 1635 3 _pl _pf _np _s _s 308 2443 _m
_sp 555 2443 555 2446 308 2446 3 _pl _pf _np _s _s 300 1632 _m
_sp 303 1632 303 2446 300 2446 3 _pl _pf _np _s _s 308 1640 _m
_sp 555 1640 555 1643 308 1643 3 _pl _pf _np _s _s 308 1640 _m
_sp 311 1640 311 2446 308 2446 3 _pl _pf _np 
_s 0 g 798 243 312 1644 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 1515 9347 _m
/Times-BoldItalicR 600 _ff
gsave 4 4 scale 16 _sr 
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420 2398 410 2398 410 2397 411 2397 413 2396 413 2395 413 2394 413 2393 412 2392 408 2373 397 2398 390 2398 390 2397 391 2397 392 2396 
45 _pl _cp 
0 g _f _s _s 
0 g 424 2361 _m
_sp 424 2361 425 2364 420 2363 419 2363 421 2363 422 2363 422 2362 422 2361 421 2360 418 2346 417 2344 416 2343 415 2343 415 2343 422 2343 
422 2343 421 2343 420 2344 420 2344 420 2345 420 2345 420 2346 421 2349 422 2349 423 2349 425 2349 427 2350 428 2351 430 2352 431 2354 
432 2356 433 2358 433 2360 432 2363 430 2364 429 2364 427 2363 426 2362 38 _pl _cp 422 2352 _m
_sp 422 2352 422 2351 422 2351 422 2350 423 2350 425 2350 427 2351 428 2353 429 2356 430 2358 430 2360 430 2362 428 2363 427 2362 426 2361 
425 2360 424 2359 424 2357 423 2355 19 _pl _cp 
0 g _f _s _s 
0 g 435 2349 _m
_sp 435 2349 438 2349 439 2352 440 2354 440 2355 441 2358 442 2360 443 2361 444 2362 445 2362 445 2361 446 2361 446 2360 447 2361 448 2362 
447 2363 446 2364 445 2364 443 2363 442 2361 441 2359 441 2359 440 2358 442 2364 437 2363 436 2363 438 2363 439 2363 439 2362 439 2361 
438 2360 31 _pl _cp 
0 g _f _s _s 
0 g 448 2354 _m
_sp 448 2354 448 2352 449 2350 451 2349 453 2349 455 2349 457 2350 458 2351 460 2352 461 2354 462 2356 463 2357 463 2359 463 2361 462 2363 
460 2364 458 2364 456 2364 454 2363 453 2362 451 2361 450 2359 449 2358 448 2356 448 2354 448 2354 26 _pl _cp 451 2353 _m
_sp 451 2353 452 2351 454 2350 456 2351 458 2353 459 2355 459 2357 460 2358 460 2360 459 2362 457 2363 455 2362 453 2359 452 2358 452 2356 
451 2355 451 2353 451 2353 18 _pl _cp 
0 g _f _s _s 
0 g 471 2361 _m
_sp 471 2361 472 2364 466 2363 466 2363 467 2363 468 2363 468 2362 468 2361 468 2360 464 2346 463 2344 462 2343 462 2343 462 2343 468 2343 
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479 2356 480 2358 480 2360 479 2363 476 2364 475 2364 473 2363 472 2362 38 _pl _cp 468 2352 _m
_sp 468 2352 468 2351 468 2351 469 2350 470 2350 472 2350 473 2351 474 2353 476 2356 477 2358 477 2360 476 2362 475 2363 474 2362 472 2361 
471 2360 471 2359 470 2357 469 2355 19 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 554 1632 _m
_sp 805 1632 805 1635 554 1635 3 _pl _pf _np _s _s 554 2443 _m
_sp 805 2443 805 2446 554 2446 3 _pl _pf _np _s _s 554 1640 _m
_sp 557 1640 557 2446 554 2446 3 _pl _pf _np _s _s 554 1640 _m
_sp 805 1640 805 1643 554 1643 3 _pl _pf _np 
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_s 0 g 0 0 0 0 _cw 
_s grestore /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr _s 
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_sp 1853 1632 1853 1635 804 1635 3 _pl _pf _np _s _s 804 2443 _m
_sp 1853 2443 1853 2446 804 2446 3 _pl _pf _np _s _s 804 1640 _m
_sp 807 1640 807 2446 804 2446 3 _pl _pf _np _s _s 804 1640 _m
_sp 1853 1640 1853 1643 804 1643 3 _pl _pf _np 
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(Propeller)_S 67 _t
(yaw)_S 67 _t
(moment)_S 67 _t
(for)_S 67 _t
(NPS)_S 67 _t
(AUV)_S 67 _t
(II)_S 67 _t
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(normally)_S 67 _t
(zero)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(twin)_S 67 _t
(propellers)_S 67 _t
(that)_S 67 _t
(are)_S 3333 8806 _m
(identically)_S 67 _t
(paired,)_S 67 _t
(offsetting)_S 67 _t
(and)_S 3333 8300 _m
(counterrotating.)_S 134 _t
(However)_S 67 _t
5539 8180 _m
5975 8264 _m
67 _t
(yaw)_S 67 _t
(moments)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 75 109 1384 2045 _cw 
_s 1399 2103 _m
_sp 1399 2103 1394 2080 1393 2078 1392 2076 1391 2075 1390 2075 1389 2075 1389 2074 1399 2074 1399 2075 1398 2075 1396 2076 1396 2078 1396 2078 1396 2080 
1401 2101 1413 2074 1414 2074 1414 2074 1414 2075 1414 2076 1415 2077 1415 2078 1416 2081 1421 2101 1422 2103 1423 2105 1424 2106 1425 2106 1425 2106 
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45 _pl _cp 
0 g _f _s _s 
0 g 1430 2070 _m
_sp 1430 2070 1431 2073 1426 2072 1425 2072 1427 2072 1428 2072 1428 2071 1428 2070 1427 2069 1424 2055 1423 2053 1422 2052 1421 2052 1421 2052 1428 2052 
1428 2052 1427 2052 1426 2053 1426 2053 1426 2054 1426 2054 1426 2055 1427 2058 1428 2058 1429 2058 1431 2058 1433 2059 1434 2060 1436 2061 1437 2063 
1438 2065 1439 2067 1439 2069 1438 2072 1436 2073 1435 2073 1433 2072 1432 2071 38 _pl _cp 1428 2061 _m
_sp 1428 2061 1428 2060 1428 2060 1428 2059 1429 2059 1431 2059 1433 2060 1434 2062 1435 2065 1436 2067 1436 2069 1436 2071 1434 2072 1433 2071 1432 2070 
1431 2069 1430 2068 1430 2066 1429 2064 19 _pl _cp 
0 g _f _s _s 
0 g 1441 2058 _m
_sp 1441 2058 1444 2058 1445 2061 1446 2063 1446 2064 1447 2067 1448 2069 1449 2070 1450 2071 1451 2071 1451 2070 1452 2070 1452 2069 1453 2070 1454 2071 
1453 2072 1452 2073 1451 2073 1449 2072 1448 2070 1447 2068 1447 2068 1446 2067 1448 2073 1443 2072 1442 2072 1444 2072 1445 2072 1445 2071 1445 2070 
1444 2069 31 _pl _cp 
0 g _f _s _s 
0 g 1454 2063 _m
_sp 1454 2063 1454 2061 1455 2059 1457 2058 1459 2058 1461 2058 1463 2059 1464 2060 1466 2061 1467 2063 1468 2065 1469 2066 1469 2068 1469 2070 1468 2072 
1466 2073 1464 2073 1462 2073 1460 2072 1459 2071 1457 2070 1456 2068 1455 2067 1454 2065 1454 2063 1454 2063 26 _pl _cp 1457 2062 _m
_sp 1457 2062 1458 2060 1460 2059 1462 2060 1464 2062 1465 2064 1465 2066 1466 2067 1466 2069 1465 2071 1463 2072 1461 2071 1459 2068 1458 2067 1458 2065 
1457 2064 1457 2062 1457 2062 18 _pl _cp 
0 g _f _s _s 
0 g 1477 2070 _m
_sp 1477 2070 1478 2073 1472 2072 1472 2072 1473 2072 1474 2072 1474 2071 1474 2070 1474 2069 1470 2055 1469 2053 1468 2052 1468 2052 1468 2052 1474 2052 
1474 2052 1473 2052 1473 2053 1472 2053 1472 2054 1472 2054 1473 2055 1474 2058 1475 2058 1476 2058 1478 2058 1479 2059 1481 2060 1482 2061 1483 2063 
1485 2065 1486 2067 1486 2069 1485 2072 1482 2073 1481 2073 1479 2072 1478 2071 38 _pl _cp 1474 2061 _m
_sp 1474 2061 1474 2060 1474 2060 1475 2059 1476 2059 1478 2059 1479 2060 1480 2062 1482 2065 1483 2067 1483 2069 1482 2071 1481 2072 1480 2071 1478 2070 
1477 2069 1477 2068 1476 2066 1475 2064 19 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 3333 7836 _m
(are)_S 67 _t
(not)_S 67 _t
(zero)_S 67 _t
(if)_S 67 _t
(paired)_S 67 _t
(propeller)_S 67 _t
(rpm)_S 67 _t
(values)_S 3333 7487 _m
(differ.)_S 134 _t
(Actual)_S 67 _t
(moments)_S 67 _t
(equal)_S gsave 4 4 scale 16 _sr gsave 0 0 0 _c _s 1022 1802 _m
_sp 1022 1802 1022 1800 1024 1799 1026 1800 1028 1802 1028 1804 1026 1805 1023 1804 8 _pl _cp _f _s _s 1023 1802 _m
_sp 1023 1802 1023 1800 1025 1799 1027 1800 1029 1802 1029 1804 1027 1805 1024 1804 8 _pl _cp _f _s _s grestore _s grestore 3333 7137 _m
/Times-BoldR 600 _ff
(\()_S /Times-BoldItalicR 600 _ff
(F)_S /Times-BoldItalicR 360 _ff
3533 7092 _m
(propeller)_S 3980 7092 _m
/Times-BoldItalicR 600 _ff
3980 7137 _m
67 _t
4047 7137 _m
4098 7137 _m
67 _t
(y)_S /Times-BoldItalicR 360 _ff
4254 7092 _m
(propeller)_S 4701 7092 _m
/Times-BoldR 600 _ff
4701 7137 _m
(\))_S /Times-RomanR 600 _ff
67 _t
(for)_S 67 _t
(each)_S 67 _t
(propeller,)_S 67 _t
(now)_S 3333 6787 _m
(included)_S 67 _t
(in)_S 67 _t
(yaw)_S 67 _t
(equation)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
/Times-BoldR 600 _ff
(\(6.53\))_S /Times-RomanR 600 _ff
(.)_S gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 1852 1632 _m
_sp 2250 1632 2250 1635 1852 1635 3 _pl _pf _np _s _s 2247 1632 _m
_sp 2250 1632 2250 2446 2247 2446 3 _pl _pf _np _s _s 1852 2443 _m
_sp 2242 2443 2242 2446 1852 2446 3 _pl _pf _np _s _s 1852 1640 _m
_sp 1855 1640 1855 2446 1852 2446 3 _pl _pf _np _s _s 1852 1640 _m
_sp 2242 1640 2242 1643 1852 1643 3 _pl _pf _np _s _s 2239 1640 _m
_sp 2242 1640 2242 2446 2239 2446 3 _pl _pf _np 
_s 0 g 798 382 1856 1644 _cw 

_s 0 g 0 0 0 0 _cw 
_s grestore 7764 9504 _m
(Not)_S 67 _t
(used.)_S 67 _t
7550 9155 _m
(Previous)_S 67 _t
(values)_S 7644 8806 _m
(are)_S 67 _t
(no)_S 67 _t
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(applicable.)_S 4950 1288 _m
(140)_S _ep
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0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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/Times-BoldR 600 _ff
(8.)_S 2400 11735 _m
(Modifications)_S 67 _t
(to)_S 67 _t
(Previous)_S 67 _t
(Dynamics)_S 67 _t
(Equations)_S 67 _t
(of)_S 67 _t
(Motion)_S /Times-RomanR 600 _ff
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(Given)_S 67 _t
(these)_S 67 _t
(nomenclature)_S 67 _t
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(next)_S 67 _t
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(dynamics)_S 67 _t
(equations)_S 67 _t
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(motion)_S 67 _t
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(body-acceleration-related)_S 67 _t
(terms)_S 67 _t
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(left-hand)_S 67 _t
(sides,)_S 67 _t
(and)_S 67 _t
(group)_S 67 _t
(velocity-related)_S 67 _t
(terms)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(right-hand)_S 67 _t
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(algebraic)_S 67 _t
(transformations)_S 67 _t
(are)_S 67 _t
(similar)_S 67 _t
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(each)_S 67 _t
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(the)_S 67 _t
(six)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion.)_S 67 _t
1500 9990 _m
(However)_S 67 _t
(the)_S 67 _t
(surge)_S 67 _t
(equation)_S 67 _t
(requires)_S 67 _t
(a)_S 67 _t
(number)_S 67 _t
(of)_S 67 _t
(important)_S 67 _t
(modifications)_S 67 _t
(and)_S 67 _t
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(derived)_S 67 _t
(in)_S 67 _t
(detail.)_S 134 _t
(The)_S 67 _t
(surge)_S 67 _t
(equation)_S 67 _t
(describes)_S 67 _t
(the)_S 67 _t
(relationships)_S 67 _t
(between)_S 67 _t
(all)_S 67 _t
(forces)_S 1500 9292 _m
(affecting)_S 67 _t
(the)_S 67 _t
(linear)_S 67 _t
(body)_S 67 _t
(acceleration)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(along)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(longitudinal)_S 67 _t
(axis.)_S 67 _t
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(The)_S 67 _t
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(surge)_S 67 _t
(motion)_S 67 _t
(equation)_S 67 _t
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(\(Healey)_S 67 _t
(93,)_S 67 _t
(appendix\))_S 67 _t
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(as)_S 67 _t
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/Times-BoldR 600 _ff
(Previous)_S 67 _t
(Surge)_S 67 _t
(Equation)_S 67 _t
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(Motion)_S /Times-RomanR 600 _ff
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/Times-BoldR 600 _ff
(\(6.39\))_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr 
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_s 496 1843 _m
_sp 496 1843 500 1843 502 1848 502 1850 503 1851 504 1853 505 1855 505 1856 506 1858 508 1860 509 1862 511 1863 512 1863 513 1863 513 1862 
513 1860 512 1858 511 1853 508 1843 512 1843 514 1849 515 1852 516 1854 517 1856 518 1858 519 1860 521 1862 522 1863 523 1863 524 1863 
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529 1849 528 1848 527 1846 525 1845 525 1846 524 1846 524 1846 524 1846 525 1848 525 1849 527 1857 528 1859 528 1861 528 1862 528 1863 
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514 1866 513 1866 512 1865 510 1864 509 1863 508 1861 507 1860 505 1858 504 1856 507 1866 498 1865 498 1864 500 1864 501 1863 501 1862 
501 1861 501 1860 92 _pl _cp 
0 g _f _s _s 
0 g 589 1865 _m
_sp 589 1865 588 1863 587 1860 586 1858 585 1856 584 1854 583 1852 581 1849 579 1848 578 1846 576 1846 576 1846 576 1847 576 1848 576 1849 
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576 1843 577 1844 579 1845 580 1846 581 1847 582 1849 583 1851 585 1854 584 1849 584 1847 584 1845 585 1844 587 1843 588 1843 589 1844 
591 1846 593 1849 592 1849 592 1849 590 1847 589 1846 588 1845 588 1846 588 1846 588 1847 588 1848 588 1850 589 1851 589 1853 590 1855 
590 1856 590 1857 592 1862 593 1865 64 _pl _cp 
0 g _f _s _s 
0 g 670 1865 _m
_sp 670 1865 669 1864 670 1864 670 1864 672 1863 674 1862 674 1860 675 1859 675 1857 675 1856 676 1853 676 1850 676 1847 676 1843 677 1843 
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680 1856 679 1858 679 1860 678 1862 678 1864 677 1865 677 1866 52 _pl _cp 
0 g _f _s _s 
0 g 693 1843 _m
_sp 693 1843 697 1843 698 1848 699 1851 700 1853 701 1855 702 1856 702 1858 703 1859 705 1861 706 1862 706 1862 707 1861 708 1861 709 1860 
710 1861 711 1863 710 1865 709 1866 707 1865 705 1864 704 1863 703 1862 702 1861 701 1859 701 1858 700 1857 703 1866 695 1865 694 1864 
696 1864 697 1863 698 1862 698 1861 697 1860 35 _pl _cp 
0 g _f _s _s 
0 g 795 1850 _m
_sp 795 1850 795 1853 795 1855 794 1857 794 1859 793 1862 793 1864 793 1865 792 1866 786 1864 786 1864 787 1864 789 1863 789 1862 790 1858 
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809 1849 807 1848 805 1865 805 1866 49 _pl _cp 
0 g _f _s _s 
0 g 837 1863 _m
_sp 837 1863 835 1865 833 1866 831 1866 829 1865 826 1863 824 1861 822 1858 820 1855 819 1852 819 1849 819 1846 820 1845 822 1843 824 1843 
826 1843 827 1843 829 1844 830 1845 832 1847 833 1849 830 1838 829 1835 827 1835 826 1835 825 1834 837 1834 837 1835 835 1835 834 1835 
834 1836 834 1837 834 1838 842 1865 838 1865 35 _pl _cp 823 1849 _m
_sp 823 1849 825 1847 826 1846 828 1846 830 1847 831 1849 833 1852 834 1854 835 1857 836 1859 836 1861 835 1863 833 1864 831 1864 829 1862 
827 1859 825 1856 824 1853 823 1850 823 1850 20 _pl _cp 
0 g _f _s _s 
0 g 927 1854 _m
_sp 927 1854 925 1853 923 1849 922 1847 920 1846 920 1846 919 1846 918 1847 917 1847 917 1846 916 1845 917 1844 918 1843 920 1843 921 1844 
922 1845 922 1846 923 1847 925 1848 926 1850 927 1852 927 1852 927 1851 928 1848 929 1846 930 1844 930 1843 931 1843 933 1843 934 1844 
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928 1863 928 1865 927 1866 926 1866 925 1866 923 1865 920 1864 920 1863 922 1864 923 1864 923 1864 924 1864 925 1862 925 1860 926 1857 
75 _pl _cp 
0 g _f _s _s 
0 g 963 1850 _m
_sp 963 1850 962 1849 961 1849 961 1849 960 1849 960 1849 959 1849 957 1850 955 1850 951 1849 947 1847 945 1844 943 1840 942 1836 943 1832 
945 1830 948 1828 952 1827 954 1827 955 1827 957 1828 959 1829 961 1834 961 1835 961 1836 961 1836 961 1837 962 1837 964 1837 964 1837 
964 1837 964 1838 955 1838 955 1837 955 1837 957 1837 957 1836 957 1836 957 1835 956 1832 955 1829 952 1828 949 1829 948 1830 946 1832 
946 1835 947 1840 949 1844 951 1847 955 1848 957 1848 959 1847 960 1845 961 1843 962 1843 964 1850 56 _pl _cp 
0 g _f _s _s 
0 g 1006 1863 _m
_sp 1006 1863 1004 1865 1002 1866 1000 1866 998 1865 995 1863 993 1861 990 1858 989 1855 987 1852 987 1849 988 1846 989 1845 991 1843 993 1843 
995 1843 996 1843 997 1844 999 1845 1000 1847 1002 1849 999 1838 998 1835 996 1835 994 1835 994 1834 1006 1834 1006 1835 1004 1835 1003 1835 
1002 1836 1003 1837 1003 1838 1010 1865 1006 1865 35 _pl _cp 992 1849 _m
_sp 992 1849 993 1847 995 1846 997 1846 998 1847 1000 1849 1001 1852 1003 1854 1004 1857 1005 1859 1005 1861 1004 1863 1002 1864 1000 1864 997 1862 
995 1859 993 1856 992 1853 992 1850 992 1850 20 _pl _cp 
0 g _f _s _s 
0 g 1066 1843 _m
_sp 1066 1843 1070 1843 1072 1848 1073 1851 1073 1853 1074 1855 1075 1856 1076 1858 1077 1859 1079 1861 1080 1862 1080 1862 1080 1861 1081 1861 1082 1860 
1084 1861 1085 1863 1084 1865 1082 1866 1080 1865 1078 1864 1077 1863 1077 1862 1076 1861 1075 1859 1075 1858 1074 1857 1076 1866 1068 1865 1068 1864 
1070 1864 1071 1863 1071 1862 1071 1861 1071 1860 35 _pl _cp 
0 g _f _s _s 
0 g 1199 1865 _m
_sp 1199 1865 1199 1864 1200 1864 1201 1864 1203 1863 1204 1860 1205 1858 1206 1855 1207 1853 1207 1850 1208 1848 1208 1847 1208 1845 1208 1843 1207 1841 
1206 1839 1204 1837 1202 1836 1202 1836 1201 1836 1201 1837 1201 1837 1200 1837 1199 1837 1198 1837 1197 1835 1198 1834 1200 1833 1202 1833 1203 1834 
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1211 1848 1211 1849 1210 1853 1210 1856 1209 1859 1208 1861 1207 1865 1206 1866 68 _pl _cp 
0 g _f _s _s 
0 g 1244 1850 _m
_sp 1244 1850 1243 1849 1242 1849 1242 1849 1242 1849 1241 1849 1240 1849 1238 1850 1236 1850 1232 1849 1228 1847 1225 1844 1224 1840 1223 1836 1224 1832 
1226 1830 1229 1828 1233 1827 1235 1827 1236 1827 1238 1828 1240 1829 1242 1834 1242 1835 1242 1836 1242 1836 1243 1837 1243 1837 1245 1837 1245 1837 
1245 1837 1245 1838 1236 1838 1236 1837 1236 1837 1238 1837 1239 1836 1239 1836 1238 1835 1238 1832 1237 1830 1236 1829 1235 1828 1233 1828 1230 1829 
1229 1830 1227 1832 1227 1835 1228 1840 1230 1844 1232 1847 1236 1848 1238 1848 1240 1847 1242 1845 1242 1843 1243 1843 1245 1850 58 _pl _cp 
0 g _f _s _s 
0 g 1278 1861 _m
_sp 1278 1861 1279 1866 1271 1865 1270 1864 1272 1864 1273 1863 1274 1862 1274 1861 1273 1860 1268 1838 1267 1835 1265 1835 1264 1835 1264 1834 1274 1834 
1274 1835 1273 1835 1272 1835 1271 1836 1271 1837 1271 1837 1272 1838 1273 1843 1275 1843 1276 1843 1278 1843 1281 1844 1284 1845 1286 1847 1288 1850 
1290 1853 1291 1856 1291 1860 1291 1863 1290 1865 1288 1866 1286 1866 1284 1866 1282 1865 1280 1863 40 _pl _cp 1274 1848 _m
_sp 1274 1848 1274 1847 1274 1846 1275 1845 1276 1844 1277 1844 1279 1845 1280 1846 1281 1847 1283 1850 1285 1853 1286 1857 1287 1860 1286 1863 1284 1864 
1282 1863 1280 1862 1279 1860 1278 1858 1276 1856 1275 1853 21 _pl _cp 
0 g _f _s _s 
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1926 1522 1927 1524 1926 1526 1925 1527 1923 1526 1921 1525 1920 1524 1919 1523 1918 1522 1917 1520 1917 1519 1916 1518 1919 1527 1911 1526 1910 1525 
1912 1525 1913 1524 1914 1523 1914 1522 1913 1521 35 _pl _cp 
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780 1382 783 1390 782 1391 781 1389 779 1387 778 1386 776 1386 775 1385 773 1385 772 1384 770 1384 770 1384 770 1384 768 1384 766 1385 
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863 1388 864 1387 864 1386 864 1385 864 1384 862 1383 861 1383 861 1382 872 1382 873 1383 872 1383 870 1384 868 1387 868 1388 864 1400 
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900 1369 902 1371 903 1372 904 1374 905 1375 905 1376 906 1378 906 1379 906 1380 904 1381 903 1381 903 1380 903 1379 904 1378 904 1378 
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921 1383 922 1383 923 1385 925 1386 926 1388 928 1390 929 1392 930 1393 932 1395 932 1396 933 1398 934 1399 934 1401 934 1402 933 1404 
931 1405 930 1404 929 1403 929 1402 930 1401 931 1400 931 1399 931 1397 930 1395 929 1394 927 1392 926 1390 925 1389 924 1388 923 1387 
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1005 1388 1006 1387 1006 1386 1006 1385 1006 1384 1004 1383 1003 1383 1003 1382 1014 1382 1015 1383 1014 1383 1012 1384 1010 1387 1010 1388 1006 1400 
1007 1402 1008 1403 1009 1405 1010 1406 1011 1407 1013 1409 1014 1410 1015 1411 1017 1413 1018 1414 1019 1415 1010 1415 1010 1414 1010 1414 1011 1414 
1012 1413 1012 1412 1011 1411 1010 1410 1009 1409 1005 1402 1002 1409 1002 1411 1001 1412 1001 1412 1002 1413 1003 1414 1004 1414 1004 1415 993 1415 
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1023 1366 1024 1366 1030 1377 1032 1366 1032 1366 1034 1368 1036 1370 1037 1372 1039 1374 1040 1377 1041 1379 1040 1380 1039 1381 1038 1381 1038 1380 
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1045 1366 1046 1366 1053 1377 1054 1366 1055 1366 1057 1368 1058 1370 1060 1372 1061 1374 1062 1377 1063 1379 1062 1380 1061 1381 1060 1381 1060 1380 
1060 1379 1060 1379 1061 1378 1061 1377 1061 1377 1061 1376 1060 1374 1058 1372 1057 1370 1056 1369 1055 1381 1054 1381 42 _pl _cp 
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1075 1393 1075 1390 1075 1386 1076 1382 1076 1382 1086 1398 1088 1382 1089 1382 1092 1385 1094 1388 1097 1391 1099 1394 1100 1397 1101 1399 1102 1400 
1102 1402 1101 1404 1099 1405 1098 1404 1097 1403 1097 1402 1098 1401 1099 1400 1099 1399 1099 1398 1099 1397 1098 1396 1097 1394 1096 1393 1095 1391 
1093 1388 1091 1387 1089 1404 1089 1405 49 _pl _cp 
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1173 1388 1174 1387 1174 1386 1174 1385 1174 1384 1172 1383 1171 1383 1171 1382 1182 1382 1183 1383 1182 1383 1180 1384 1178 1387 1178 1388 1174 1400 
1175 1402 1176 1403 1177 1405 1178 1406 1179 1407 1181 1409 1182 1410 1183 1411 1185 1413 1186 1414 1187 1415 1178 1415 1178 1414 1178 1414 1179 1414 
1180 1413 1180 1412 1179 1411 1178 1410 1177 1409 1173 1402 1170 1409 1170 1411 1169 1412 1169 1412 1170 1413 1171 1414 1172 1414 1172 1415 1161 1415 
1161 1414 1161 1414 1162 1414 1164 1413 1165 1411 1166 1409 66 _pl _cp 
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1239 1380 1238 1381 1237 1381 1235 1380 1234 1378 1233 1376 1233 1376 1232 1375 1234 1381 1229 1380 1228 1380 1230 1380 1231 1380 1231 1379 1231 1378 
1230 1377 31 _pl _cp 
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1256 1405 1248 1404 1248 1403 1249 1403 1250 1402 1250 1401 1250 1400 1250 1399 1247 1389 1247 1388 1247 1387 1247 1386 1247 1384 1248 1383 1249 1382 
1251 1382 1252 1383 1254 1384 1255 1385 1256 1386 1257 1388 1258 1390 1260 1393 1259 1388 1259 1386 1259 1384 1260 1382 1262 1382 1263 1382 1264 1383 
1266 1385 1268 1388 1267 1388 1267 1387 1265 1386 1264 1384 1263 1384 1263 1384 1263 1385 1263 1386 1263 1387 1263 1388 1264 1390 1264 1392 1265 1393 
1265 1395 1265 1396 1267 1401 1268 1404 64 _pl _cp 
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1279 1383 1280 1383 1282 1385 1283 1386 1285 1388 1286 1390 1287 1392 1289 1393 1290 1395 1291 1396 1292 1398 1292 1399 1293 1401 1293 1402 1292 1404 
1290 1405 1288 1404 1287 1403 1288 1402 1289 1401 1290 1400 1290 1399 1289 1397 1288 1395 1287 1394 1286 1392 1285 1390 1284 1389 1282 1388 1281 1387 
1281 1389 1281 1392 1281 1395 1280 1397 1280 1399 1279 1401 1279 1403 1278 1404 1278 1405 54 _pl _cp 
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1336 1378 1336 1379 1335 1380 1334 1381 1333 1381 1332 1380 1331 1378 1330 1376 1329 1376 1329 1375 1330 1381 1325 1380 1325 1380 1326 1380 1327 1380 
1327 1379 1327 1378 1327 1377 33 _pl _cp 
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1399 1405 1391 1404 1391 1403 1392 1403 1393 1402 1393 1401 1393 1400 1393 1399 1390 1389 1390 1388 1390 1387 1390 1386 1390 1384 1391 1383 1392 1382 
1394 1382 1395 1383 1397 1384 1398 1385 1399 1386 1400 1388 1401 1390 1403 1393 1402 1388 1402 1386 1402 1384 1403 1382 1405 1382 1406 1382 1407 1383 
1409 1385 1411 1388 1410 1388 1410 1387 1408 1386 1407 1384 1406 1384 1406 1384 1406 1385 1406 1386 1406 1387 1406 1388 1407 1390 1407 1392 1408 1393 
1408 1395 1408 1396 1410 1401 1411 1404 64 _pl _cp 
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1419 1393 1419 1390 1420 1386 1420 1382 1421 1382 1431 1398 1433 1382 1433 1382 1436 1385 1439 1388 1441 1391 1443 1394 1444 1397 1445 1399 1446 1400 
1446 1402 1445 1404 1444 1405 1442 1404 1441 1403 1442 1402 1442 1401 1444 1400 1444 1399 1444 1398 1443 1397 1442 1396 1441 1394 1440 1393 1439 1391 
1437 1388 1436 1387 1434 1404 1433 1405 49 _pl _cp 
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1486 1388 1487 1387 1487 1386 1487 1385 1487 1384 1486 1383 1484 1383 1484 1382 1496 1382 1496 1383 1495 1383 1493 1384 1492 1387 1491 1388 1487 1400 
1488 1402 1489 1403 1490 1405 1491 1406 1492 1407 1494 1409 1495 1410 1496 1411 1498 1413 1500 1414 1500 1415 1491 1415 1491 1414 1491 1414 1493 1414 
1493 1413 1493 1412 1492 1411 1491 1410 1491 1409 1486 1402 1484 1409 1483 1411 1483 1412 1482 1412 1483 1413 1484 1414 1485 1414 1486 1415 1474 1415 
1474 1414 1475 1414 1476 1414 1477 1413 1478 1411 1479 1409 66 _pl _cp 
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1503 1366 1504 1366 1511 1377 1512 1366 1513 1366 1515 1368 1516 1370 1518 1372 1519 1374 1520 1377 1521 1379 1520 1380 1519 1381 1518 1381 1518 1380 
1518 1379 1518 1379 1519 1378 1519 1377 1519 1377 1519 1376 1518 1374 1516 1372 1515 1370 1514 1369 1513 1381 1512 1381 42 _pl _cp 
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1552 1371 1552 1372 1551 1373 1549 1375 1548 1377 1547 1379 1548 1380 1549 1380 1551 1379 1553 1376 1554 1376 1554 1381 1554 1381 1553 1381 1553 1381 
1552 1381 1551 1381 1550 1381 1549 1381 1547 1381 1545 1380 1544 1379 1544 1378 1544 1377 1545 1375 1546 1374 1548 1372 1549 1371 1550 1369 1549 1368 
1547 1367 1544 1368 1543 1371 48 _pl _cp 
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1596 1371 1596 1372 1595 1373 1593 1375 1591 1377 1591 1379 1592 1380 1593 1380 1595 1379 1597 1376 1597 1376 1598 1381 1598 1381 1597 1381 1596 1381 
1596 1381 1595 1381 1594 1381 1593 1381 1591 1381 1589 1380 1588 1379 1588 1378 1588 1377 1589 1375 1590 1374 1591 1372 1593 1371 1593 1369 1592 1368 
1591 1367 1589 1367 1588 1368 1587 1369 1586 1371 50 _pl _cp 
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1646 1388 1647 1387 1647 1386 1647 1385 1647 1384 1646 1383 1644 1383 1644 1382 1656 1382 1656 1383 1655 1383 1653 1384 1652 1387 1651 1388 1647 1400 
1648 1402 1649 1403 1650 1405 1651 1406 1652 1407 1654 1409 1655 1410 1656 1411 1658 1413 1660 1414 1660 1415 1651 1415 1651 1414 1651 1414 1653 1414 
1653 1413 1653 1412 1652 1411 1651 1410 1651 1409 1646 1402 1644 1409 1643 1411 1643 1412 1642 1412 1643 1413 1644 1414 1645 1414 1646 1415 1634 1415 
1634 1414 1635 1414 1636 1414 1637 1413 1638 1411 1639 1409 66 _pl _cp 
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1663 1366 1664 1366 1671 1377 1672 1366 1673 1366 1675 1368 1676 1370 1678 1372 1679 1374 1680 1377 1681 1379 1680 1380 1679 1381 1678 1381 1678 1380 
1678 1379 1678 1379 1679 1378 1679 1377 1679 1377 1679 1376 1678 1374 1676 1372 1675 1370 1674 1369 1673 1381 1672 1381 42 _pl _cp 
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1705 1366 1707 1366 1709 1366 1711 1367 1712 1368 1714 1369 1716 1371 1717 1373 1718 1375 1718 1377 1717 1380 1714 1381 1713 1381 1712 1381 1710 1379 
30 _pl _cp 1706 1368 _m
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1706 1372 1706 1370 1706 1369 18 _pl _cp 
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1779 1366 1781 1366 1783 1366 1785 1367 1786 1368 1788 1369 1789 1371 1790 1373 1791 1375 1791 1377 1790 1380 1788 1381 1787 1381 1786 1381 1784 1379 
30 _pl _cp 1779 1368 _m
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1780 1372 1780 1370 1779 1369 18 _pl _cp 
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1803 1371 1802 1372 1801 1373 1800 1375 1798 1377 1797 1379 1798 1380 1799 1380 1802 1379 1803 1376 1804 1376 1805 1381 1804 1381 1804 1381 1803 1381 
1802 1381 1801 1381 1800 1381 1799 1381 1796 1380 1795 1378 1795 1377 1795 1375 1796 1374 1798 1372 1800 1371 1800 1369 1799 1368 1797 1367 1794 1368 
1793 1371 46 _pl _cp 
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1853 1388 1854 1387 1854 1386 1854 1385 1853 1384 1852 1383 1851 1383 1850 1382 1862 1382 1863 1383 1862 1383 1860 1384 1858 1387 1858 1388 1853 1400 
1854 1402 1856 1403 1857 1405 1858 1406 1859 1407 1860 1409 1861 1410 1862 1411 1864 1413 1866 1414 1867 1415 1858 1415 1857 1414 1858 1414 1859 1414 
1860 1413 1859 1412 1858 1411 1858 1410 1857 1409 1852 1402 1850 1409 1849 1411 1849 1412 1849 1412 1849 1413 1851 1414 1852 1414 1852 1415 1841 1415 
1840 1414 1841 1414 1842 1414 1843 1413 1844 1411 1845 1409 66 _pl _cp 
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1870 1366 1870 1366 1877 1377 1878 1366 1879 1366 1881 1368 1883 1370 1884 1372 1886 1374 1887 1377 1887 1379 1887 1380 1886 1381 1885 1381 1884 1380 
1884 1379 1885 1379 1886 1378 1886 1377 1886 1377 1885 1376 1884 1374 1883 1372 1881 1370 1881 1369 1879 1381 1879 1381 42 _pl _cp 
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1912 1366 1914 1366 1916 1366 1918 1367 1919 1368 1921 1369 1922 1371 1923 1373 1924 1375 1924 1377 1923 1380 1921 1381 1920 1381 1919 1381 1917 1379 
30 _pl _cp 1912 1368 _m
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1913 1372 1913 1370 1912 1369 18 _pl _cp 
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1985 1366 1987 1366 1989 1366 1991 1367 1992 1368 1994 1369 1996 1371 1997 1373 1998 1375 1998 1377 1997 1380 1994 1381 1993 1381 1992 1381 1990 1379 
30 _pl _cp 1986 1368 _m
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1986 1372 1986 1370 1986 1369 18 _pl _cp 
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2003 1360 2002 1360 2001 1361 2001 1361 2001 1362 2001 1362 2001 1363 2002 1366 2003 1366 2004 1366 2006 1366 2007 1367 2009 1368 2010 1369 2012 1371 
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2005 1377 2005 1376 2004 1374 2004 1372 19 _pl _cp 
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1401 1283 1393 1281 1393 1280 1394 1280 1395 1280 1396 1279 1396 1278 1395 1276 1393 1267 1392 1266 1392 1264 1392 1263 1392 1262 1393 1260 1394 1259 
1396 1259 1397 1260 1399 1261 1400 1262 1401 1263 1402 1265 1404 1267 1406 1270 1405 1266 1404 1264 1404 1262 1405 1260 1407 1259 1408 1259 1410 1261 
1412 1262 1414 1265 1413 1266 1412 1265 1410 1263 1409 1262 1408 1262 1408 1262 1408 1263 1408 1264 1408 1265 1409 1266 1409 1267 1409 1269 1410 1271 
1410 1272 1410 1274 1412 1279 1413 1282 64 _pl _cp 
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725 1799 723 1798 721 1797 720 1796 719 1794 717 1792 717 1790 717 1788 717 1786 717 1784 25 _pl _cp 732 1787 _m
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732 1791 16 _pl _cp 
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733 1677 731 1676 729 1675 728 1674 727 1672 725 1670 725 1668 725 1665 725 1664 725 1662 25 _pl _cp 740 1665 _m
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740 1669 16 _pl _cp 
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1077 1490 1079 1489 1082 1488 1085 1489 1087 1490 1088 1493 1089 1496 1089 1498 1088 1499 1087 1501 1084 1503 1082 1505 1080 1506 1080 1507 1080 1508 
1080 1509 1080 1509 1082 1508 1084 1507 1085 1506 35 _pl _cp 1086 1495 _m
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1086 1498 16 _pl _cp 
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1113 1523 1111 1520 1110 1515 1111 1511 1113 1507 1116 1505 1120 1504 1124 1505 1128 1507 1130 1511 1131 1515 1131 1518 1130 1520 1129 1522 1128 1523 
1126 1525 1124 1527 1122 1528 1120 1530 1119 1531 1118 1532 1117 1533 1117 1534 1117 1535 1118 1535 1119 1535 1120 1534 1121 1533 1123 1532 1125 1530 
45 _pl _cp 1126 1515 _m
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1126 1519 16 _pl _cp 
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1232 1490 1234 1489 1236 1488 1239 1489 1241 1490 1242 1493 1243 1496 1243 1498 1243 1499 1241 1501 1239 1503 1236 1505 1235 1506 1234 1507 1234 1508 
1234 1509 1235 1509 1236 1508 1238 1507 1240 1506 35 _pl _cp 1240 1495 _m
_sp 1240 1495 1240 1493 1239 1491 1238 1490 1237 1489 1235 1490 1234 1491 1233 1493 1233 1495 1233 1498 1234 1500 1235 1501 1237 1501 1238 1501 1239 1500 
1240 1498 16 _pl _cp 
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1298 1523 1296 1520 1295 1515 1296 1511 1298 1507 1301 1505 1305 1504 1309 1505 1312 1507 1314 1511 1315 1515 1315 1518 1314 1520 1313 1522 1312 1523 
1310 1525 1308 1527 1306 1528 1304 1530 1303 1531 1302 1532 1301 1533 1301 1534 1302 1535 1302 1535 1303 1535 1304 1534 1306 1533 1307 1532 1309 1530 
45 _pl _cp 1311 1515 _m
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1311 1519 16 _pl _cp 
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1437 1490 1439 1489 1441 1488 1444 1489 1446 1490 1447 1493 1448 1496 1448 1498 1448 1499 1447 1500 1446 1501 1445 1502 1443 1503 1441 1505 1440 1506 
1439 1507 1439 1508 1439 1509 1440 1509 1441 1508 1443 1507 1444 1506 37 _pl _cp 1445 1495 _m
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1445 1498 16 _pl _cp 
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1502 1523 1500 1520 1499 1515 1500 1511 1502 1507 1505 1505 1509 1504 1513 1505 1517 1507 1519 1511 1520 1515 1520 1518 1519 1520 1518 1522 1517 1523 
1515 1525 1513 1527 1511 1528 1509 1530 1508 1531 1507 1532 1506 1533 1506 1534 1506 1535 1507 1535 1508 1535 1509 1534 1510 1533 1512 1532 1514 1530 
45 _pl _cp 1515 1515 _m
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1515 1519 16 _pl _cp 
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1634 1490 1636 1489 1638 1488 1641 1489 1643 1490 1644 1493 1645 1496 1645 1498 1645 1499 1643 1501 1641 1503 1638 1505 1637 1506 1636 1507 1636 1508 
1636 1509 1637 1509 1638 1508 1640 1507 1642 1506 35 _pl _cp 1642 1495 _m
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1642 1498 16 _pl _cp 
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1717 1515 1718 1511 1720 1507 1723 1505 1727 1504 1731 1505 1734 1507 1736 1511 1737 1515 1737 1518 1736 1520 1735 1522 1734 1523 1732 1525 1730 1527 
1728 1528 1727 1530 1725 1531 1724 1532 1724 1533 1723 1534 1724 1535 1725 1535 1726 1535 1727 1534 1728 1533 1730 1532 1732 1530 43 _pl _cp 1733 1515 _m
_sp 1733 1515 1732 1511 1731 1509 1729 1507 1727 1506 1724 1507 1723 1509 1721 1511 1721 1515 1721 1519 1723 1522 1724 1523 1727 1524 1730 1523 1732 1522 
1733 1519 16 _pl _cp 
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_sp 1866 1507 1865 1509 1863 1510 1860 1511 1858 1510 1857 1508 1857 1507 1858 1506 1860 1504 1862 1503 1859 1502 1857 1501 1855 1498 1855 1495 1856 1492 
1857 1490 1859 1489 1861 1488 1864 1489 1866 1490 1867 1493 1868 1496 1868 1498 1868 1499 1866 1501 1864 1503 1861 1505 1860 1506 1859 1507 1859 1508 
1859 1509 1860 1509 1861 1508 1863 1507 1865 1506 35 _pl _cp 1865 1495 _m
_sp 1865 1495 1865 1493 1864 1491 1863 1490 1862 1489 1860 1490 1859 1491 1858 1493 1858 1495 1858 1498 1859 1500 1860 1501 1862 1501 1863 1501 1864 1500 
1865 1498 16 _pl _cp 
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1934 1523 1932 1520 1931 1515 1932 1511 1934 1507 1937 1505 1941 1504 1945 1505 1948 1507 1950 1511 1951 1515 1951 1518 1951 1520 1950 1522 1949 1523 
1947 1525 1944 1527 1942 1528 1941 1530 1940 1531 1939 1532 1938 1533 1937 1534 1938 1535 1939 1535 1940 1535 1941 1534 1942 1533 1944 1532 1946 1530 
45 _pl _cp 1947 1515 _m
_sp 1947 1515 1947 1511 1946 1509 1944 1507 1941 1506 1939 1507 1937 1509 1936 1511 1936 1515 1936 1519 1937 1522 1939 1523 1941 1524 1944 1523 1946 1522 
1947 1519 16 _pl _cp 
0 g _f _s _s 
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_sp 725 1400 729 1400 729 1413 730 1411 732 1410 733 1410 735 1410 739 1411 742 1413 744 1416 745 1421 744 1425 742 1429 739 1431 735 1432 
733 1432 731 1431 729 1430 728 1429 727 1427 725 1425 725 1423 725 1421 725 1420 725 1418 25 _pl _cp 740 1421 _m
_sp 740 1421 740 1417 739 1414 737 1413 734 1412 732 1413 730 1414 729 1417 729 1421 729 1425 731 1428 732 1429 735 1430 737 1429 739 1428 
740 1425 16 _pl _cp 
0 g _f _s _s 
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1211 1368 1213 1367 1215 1366 1218 1367 1220 1368 1221 1370 1222 1373 1222 1375 1222 1376 1221 1377 1220 1379 1219 1380 1218 1381 1215 1383 1214 1384 
1213 1385 1213 1386 1213 1387 1214 1387 1215 1386 1217 1385 1219 1383 37 _pl _cp 1219 1373 _m
_sp 1219 1373 1219 1371 1218 1369 1217 1368 1216 1367 1214 1368 1213 1369 1212 1371 1212 1373 1212 1376 1213 1378 1214 1379 1216 1379 1217 1379 1218 1378 
1219 1376 16 _pl _cp 
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1300 1401 1298 1397 1297 1392 1298 1388 1300 1385 1303 1383 1307 1382 1311 1383 1314 1385 1316 1389 1317 1393 1317 1396 1316 1398 1315 1400 1314 1401 
1312 1403 1310 1405 1308 1406 1306 1407 1305 1408 1304 1409 1303 1411 1303 1412 1304 1413 1304 1413 1305 1413 1306 1412 1308 1411 1309 1410 1311 1408 
45 _pl _cp 1313 1393 _m
_sp 1313 1393 1312 1389 1311 1386 1309 1385 1307 1384 1304 1385 1303 1386 1301 1389 1301 1393 1301 1397 1303 1399 1304 1401 1307 1402 1310 1401 1312 1400 
1313 1397 16 _pl _cp 
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1526 1368 1528 1367 1531 1366 1534 1367 1536 1368 1537 1370 1538 1373 1538 1375 1537 1376 1536 1377 1535 1379 1534 1380 1533 1381 1531 1383 1529 1384 
1529 1385 1528 1386 1529 1387 1529 1387 1531 1386 1532 1385 1534 1383 37 _pl _cp 1535 1373 _m
_sp 1535 1373 1535 1371 1534 1369 1532 1368 1531 1367 1529 1368 1528 1369 1527 1371 1527 1373 1527 1376 1528 1378 1529 1379 1531 1379 1532 1379 1534 1378 
1535 1376 16 _pl _cp 
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1562 1401 1560 1397 1559 1392 1560 1388 1562 1385 1565 1383 1569 1382 1573 1383 1576 1385 1578 1389 1579 1393 1579 1396 1579 1398 1578 1400 1577 1401 
1575 1403 1572 1405 1570 1406 1569 1407 1568 1408 1567 1409 1566 1411 1565 1412 1566 1413 1567 1413 1568 1413 1569 1412 1570 1411 1572 1410 1574 1408 
45 _pl _cp 1575 1393 _m
_sp 1575 1393 1575 1389 1574 1386 1572 1385 1569 1384 1567 1385 1565 1386 1564 1389 1564 1393 1564 1397 1565 1399 1567 1401 1569 1402 1572 1401 1574 1400 
1575 1397 16 _pl _cp 
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1686 1368 1688 1367 1691 1366 1694 1367 1696 1368 1697 1370 1698 1373 1698 1375 1697 1376 1696 1377 1695 1379 1694 1380 1693 1381 1691 1383 1689 1384 
1689 1385 1688 1386 1689 1387 1689 1387 1691 1386 1692 1385 1694 1383 37 _pl _cp 1695 1373 _m
_sp 1695 1373 1695 1371 1694 1369 1692 1368 1691 1367 1689 1368 1688 1369 1687 1371 1687 1373 1687 1376 1688 1378 1689 1379 1691 1379 1692 1379 1694 1378 
1695 1376 16 _pl _cp 
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1749 1392 1750 1388 1752 1385 1755 1383 1759 1382 1763 1383 1766 1385 1768 1389 1769 1393 1769 1396 1768 1398 1767 1400 1766 1401 1764 1403 1762 1405 
1760 1406 1759 1407 1757 1408 1756 1409 1756 1411 1755 1412 1756 1413 1757 1413 1758 1413 1759 1412 1760 1411 1762 1410 1764 1408 43 _pl _cp 1765 1393 _m
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1765 1397 16 _pl _cp 
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1893 1368 1895 1367 1897 1366 1900 1367 1902 1368 1903 1370 1904 1373 1904 1375 1904 1376 1903 1377 1902 1379 1901 1380 1899 1381 1897 1383 1896 1384 
1895 1385 1895 1386 1895 1387 1896 1387 1897 1386 1899 1385 1900 1383 37 _pl _cp 1901 1373 _m
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1901 1376 16 _pl _cp 
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1959 1402 1957 1399 1955 1396 1955 1392 1956 1388 1958 1385 1961 1383 1965 1382 1969 1383 1973 1385 1975 1389 1976 1393 1976 1396 1975 1398 1974 1400 
1973 1401 1971 1403 1969 1405 1967 1406 1965 1407 1964 1408 1963 1409 1962 1411 1962 1412 1962 1413 1963 1413 1964 1413 1965 1412 1966 1411 1968 1410 
1970 1408 46 _pl _cp 1971 1393 _m
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1971 1397 16 _pl _cp 
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1496 1246 1498 1245 1501 1244 1504 1245 1506 1246 1507 1248 1508 1251 1508 1253 1507 1254 1506 1255 1505 1257 1504 1258 1503 1259 1501 1261 1499 1262 
1499 1263 1498 1263 1499 1264 1499 1264 1501 1264 1502 1262 1504 1261 37 _pl _cp 1505 1251 _m
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1505 1254 16 _pl _cp 
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1530 1246 1532 1245 1534 1244 1537 1245 1539 1246 1540 1248 1541 1251 1541 1253 1541 1254 1540 1255 1539 1257 1538 1258 1536 1259 1534 1261 1533 1262 
1532 1263 1532 1263 1532 1264 1533 1264 1534 1264 1536 1262 1537 1261 37 _pl _cp 1538 1251 _m
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1538 1254 16 _pl _cp 
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1566 1279 1564 1275 1563 1270 1564 1266 1566 1263 1569 1261 1573 1260 1577 1261 1580 1263 1582 1266 1583 1271 1583 1273 1582 1275 1581 1277 1580 1279 
1578 1281 1576 1283 1574 1284 1572 1285 1571 1286 1570 1287 1569 1288 1569 1289 1570 1290 1570 1291 1571 1291 1572 1290 1574 1289 1575 1288 1577 1286 
45 _pl _cp 1579 1270 _m
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1579 1274 16 _pl _cp 
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1671 1246 1673 1245 1676 1244 1679 1245 1681 1246 1682 1248 1683 1251 1683 1253 1682 1254 1681 1255 1680 1257 1679 1258 1678 1259 1676 1261 1674 1262 
1674 1263 1673 1263 1674 1264 1674 1264 1676 1264 1677 1262 1679 1261 37 _pl _cp 1680 1251 _m
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1680 1254 16 _pl _cp 
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1708 1246 1710 1245 1713 1244 1716 1245 1718 1246 1719 1248 1720 1251 1720 1253 1719 1254 1719 1255 1718 1257 1717 1258 1715 1259 1713 1261 1711 1262 
1711 1263 1711 1263 1711 1264 1711 1264 1713 1264 1715 1262 1716 1261 37 _pl _cp 1717 1251 _m
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1717 1254 16 _pl _cp 
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1774 1279 1772 1275 1771 1270 1772 1266 1774 1263 1777 1261 1781 1260 1785 1261 1788 1263 1790 1266 1791 1271 1791 1273 1791 1275 1790 1277 1789 1279 
1787 1281 1784 1283 1782 1284 1781 1285 1780 1286 1779 1287 1778 1288 1777 1289 1778 1290 1779 1291 1780 1291 1781 1290 1782 1289 1784 1288 1786 1286 
45 _pl _cp 1787 1270 _m
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1787 1274 16 _pl _cp 
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1802 1249 1804 1248 1807 1247 1810 1248 1812 1249 1813 1251 1814 1254 1814 1256 1813 1257 1813 1258 1812 1260 1811 1261 1809 1262 1807 1264 1805 1265 
1805 1266 1805 1267 1805 1268 1805 1268 1807 1267 1809 1266 1810 1264 37 _pl _cp 1811 1254 _m
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1811 1257 16 _pl _cp 
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1900 1246 1902 1245 1905 1244 1908 1245 1910 1246 1911 1248 1912 1251 1912 1253 1911 1254 1910 1255 1909 1257 1908 1258 1907 1259 1905 1261 1903 1262 
1903 1263 1902 1263 1903 1264 1903 1264 1905 1264 1906 1262 1908 1261 37 _pl _cp 1909 1251 _m
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1909 1254 16 _pl _cp 
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1934 1246 1936 1245 1938 1244 1941 1245 1943 1246 1944 1248 1945 1251 1945 1253 1945 1254 1944 1255 1943 1257 1942 1258 1940 1259 1938 1261 1937 1262 
1936 1263 1936 1263 1936 1264 1937 1264 1938 1264 1940 1262 1941 1261 37 _pl _cp 1942 1251 _m
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1942 1254 16 _pl _cp 
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1970 1279 1968 1275 1967 1270 1968 1266 1970 1263 1973 1261 1977 1260 1981 1261 1984 1263 1986 1266 1987 1271 1987 1273 1986 1275 1985 1277 1984 1279 
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45 _pl _cp 1983 1270 _m
_sp 1983 1270 1982 1267 1981 1264 1979 1263 1977 1262 1974 1263 1973 1264 1971 1267 1971 1271 1971 1275 1973 1277 1974 1279 1977 1280 1980 1279 1982 1277 
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933 1183 16 _pl _cp 
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733 1133 731 1132 729 1131 728 1130 727 1128 725 1126 725 1124 725 1122 725 1120 725 1118 25 _pl _cp 740 1121 _m
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740 1125 16 _pl _cp 
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883 1086 883 1086 883 1087 884 1087 885 1087 887 1085 888 1084 37 _pl _cp 889 1074 _m
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889 1077 16 _pl _cp 
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995 1109 46 _pl _cp 996 1093 _m
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996 1097 16 _pl _cp 
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_sp 1039 1095 1026 1095 1027 1098 1029 1101 1032 1102 1035 1103 1037 1103 1039 1102 1040 1104 1038 1105 1035 1105 1031 1104 1027 1103 1024 1100 1023 1097 
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1037 1085 1036 1085 1034 1085 1031 1086 1028 1087 1027 1090 1026 1093 1039 1093 38 _pl _cp 
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0 g 1068 1083 _m
_sp 1068 1083 1072 1083 1072 1098 1074 1100 1075 1101 1077 1102 1078 1102 1080 1102 1081 1100 1082 1098 1082 1094 1082 1073 1086 1073 1086 1094 1086 1097 
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1064 1099 1064 1098 1066 1098 1066 1099 1066 1099 1066 1101 1067 1102 1068 1101 1068 1100 1068 1098 40 _pl _cp 
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0 g 1200 1101 _m
_sp 1200 1101 1204 1101 1204 1113 1206 1112 1207 1111 1209 1110 1210 1110 1214 1111 1217 1113 1219 1117 1220 1121 1219 1126 1217 1130 1214 1132 1210 1133 
1208 1133 1206 1132 1205 1131 1203 1130 1202 1128 1201 1126 1200 1124 1200 1122 1200 1120 1200 1118 25 _pl _cp 1216 1121 _m
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1216 1125 16 _pl _cp 
0 g _f _s _s 
0 g 1388 1086 _m
_sp 1388 1086 1386 1087 1384 1089 1382 1090 1380 1089 1379 1086 1379 1085 1380 1084 1381 1082 1383 1081 1380 1080 1378 1079 1377 1077 1376 1074 1377 1071 
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1381 1086 1380 1086 1381 1087 1381 1087 1383 1087 1384 1085 1386 1084 37 _pl _cp 1387 1074 _m
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1387 1077 16 _pl _cp 
0 g _f _s _s 
0 g 1503 1112 _m
_sp 1503 1112 1501 1114 1499 1115 1497 1116 1496 1117 1495 1117 1493 1117 1491 1116 1490 1114 1490 1112 1490 1110 1492 1109 1493 1107 1496 1105 1492 1104 
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45 _pl _cp 1502 1093 _m
_sp 1502 1093 1502 1090 1501 1087 1499 1086 1496 1085 1494 1086 1492 1087 1491 1090 1491 1094 1491 1098 1492 1100 1494 1102 1496 1103 1499 1102 1501 1100 
1502 1097 16 _pl _cp 
0 g _f _s _s 
0 g 1617 1086 _m
_sp 1617 1086 1615 1087 1613 1089 1611 1090 1609 1089 1608 1086 1608 1085 1609 1084 1611 1082 1612 1081 1609 1080 1608 1079 1606 1077 1606 1074 1607 1071 
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1610 1086 1610 1086 1610 1087 1611 1087 1612 1087 1614 1085 1615 1084 37 _pl _cp 1616 1074 _m
_sp 1616 1074 1616 1071 1615 1070 1614 1068 1612 1068 1611 1068 1610 1070 1609 1071 1609 1074 1609 1077 1610 1079 1611 1080 1612 1080 1614 1080 1615 1079 
1616 1077 16 _pl _cp 
0 g _f _s _s 
0 g 1651 1086 _m
_sp 1651 1086 1649 1087 1647 1089 1645 1090 1643 1089 1642 1086 1642 1085 1643 1084 1644 1082 1646 1081 1643 1080 1641 1079 1640 1077 1639 1074 1640 1071 
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1644 1086 1643 1086 1644 1087 1644 1087 1646 1087 1647 1085 1649 1084 37 _pl _cp 1650 1074 _m
_sp 1650 1074 1650 1071 1649 1070 1647 1068 1646 1068 1644 1068 1643 1070 1642 1071 1642 1074 1642 1077 1643 1079 1644 1080 1646 1080 1647 1080 1649 1079 
1650 1077 16 _pl _cp 
0 g _f _s _s 
0 g 1756 1112 _m
_sp 1756 1112 1754 1114 1752 1115 1750 1116 1749 1117 1748 1117 1746 1117 1744 1116 1743 1114 1743 1112 1743 1110 1745 1109 1746 1107 1749 1105 1745 1104 
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1755 1104 1752 1106 1750 1107 1749 1108 1748 1109 1747 1110 1746 1111 1745 1112 1746 1113 1747 1114 1748 1114 1749 1113 1750 1112 1752 1111 1754 1109 
45 _pl _cp 1755 1093 _m
_sp 1755 1093 1755 1090 1754 1087 1752 1086 1749 1085 1747 1086 1745 1087 1744 1090 1744 1094 1744 1098 1745 1100 1747 1102 1749 1103 1752 1102 1754 1100 
1755 1097 16 _pl _cp 
0 g _f _s _s 
0 g 1836 1095 _m
_sp 1836 1095 1823 1095 1824 1098 1826 1101 1829 1102 1832 1103 1835 1103 1837 1102 1838 1104 1837 1105 1835 1105 1834 1105 1832 1105 1827 1104 1824 1103 
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1837 1087 1836 1086 1834 1085 1833 1085 1831 1085 1828 1086 1826 1087 1824 1090 1823 1093 1836 1093 40 _pl _cp 
0 g _f _s _s 
0 g 1866 1083 _m
_sp 1866 1083 1870 1083 1870 1098 1871 1100 1872 1101 1874 1102 1875 1102 1877 1102 1878 1100 1879 1098 1879 1094 1879 1073 1883 1073 1883 1094 1883 1097 
1883 1099 1882 1102 1880 1104 1878 1105 1876 1105 1875 1105 1873 1104 1872 1103 1870 1101 1869 1103 1868 1104 1867 1105 1865 1105 1864 1105 1862 1104 
1861 1102 1861 1099 1861 1099 1861 1098 1863 1098 1863 1099 1863 1099 1863 1101 1864 1102 1865 1101 1866 1100 1866 1098 42 _pl _cp 
0 g _f _s _s 
0 g 725 979 _m
_sp 725 979 729 979 729 991 730 990 732 989 733 988 735 988 739 989 742 991 744 995 745 999 744 1004 742 1008 739 1010 735 1011 
733 1011 731 1010 729 1009 728 1008 727 1006 725 1004 725 1002 725 999 725 998 725 996 25 _pl _cp 740 999 _m
_sp 740 999 740 995 739 993 737 991 734 990 732 991 730 993 729 995 729 999 729 1003 731 1006 732 1007 735 1008 737 1007 739 1006 
740 1003 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 2400 3004 _m
(The)_S 67 _t
(\(Healey)_S 67 _t
(93\))_S 67 _t
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(the)_S 67 _t
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(U.S.)_S 67 _t
(Navy)_S 67 _t
(Swimmer)_S 67 _t
(Delivery)_S 67 _t
(Vehicle)_S 67 _t
(hull)_S 67 _t
(number)_S 67 _t
(9)_S 67 _t
(\(SDV-9\))_S 67 _t
(equations)_S 67 _t
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(\(Smith)_S 67 _t
(78,)_S 67 _t
(declassified\),)_S 67 _t
(which)_S 67 _t
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67 _t
(\()_S /Symbol 600 _ff
(h)_S /Times-BoldR 600 _ff
(\))_S /Times-RomanR 600 _ff
67 _t
(term)_S 67 _t
(in)_S 67 _t
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(\(6.39\))_S 67 _t
(approximates)_S 67 _t
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(141)_S _ep
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0 13200 10200 _ornt 
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(propulsion)_S 67 _t
(response)_S 67 _t
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(tank)_S 67 _t
(testing.)_S 134 _t
(Tow)_S 67 _t
(tank)_S 67 _t
(testing)_S 67 _t
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(vehicles.)_S 134 _t
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/Symbol 600 _ff
(d)_S /Times-BoldItalicR 360 _ff
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(b/2)_S 4876 11461 _m
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67 _t
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(to)_S 67 _t
(an)_S 67 _t
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(control)_S 1500 11157 _m
(arrangement)_S 67 _t
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(the)_S 67 _t
(SDV-9)_S 67 _t
(that)_S 67 _t
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(control)_S 67 _t
(of)_S 67 _t
(port)_S 67 _t
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(bow)_S 67 _t
(planes)_S 67 _t
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(surfaces)_S 67 _t
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(\()_S /Symbol 600 _ff
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(the)_S 67 _t
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(vehicle)_S 67 _t
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(prop)_S 2760 6923 _m
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67 _t
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(equation)_S 67 _t
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(X)_S /Times-BoldItalicR 360 _ff
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(prop)_S 3133 6223 _m
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1065 1039 1065 1039 1066 1039 1068 1038 1069 1036 1070 1034 66 _pl _cp 
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_sp 1097 1003 1098 1006 1093 1005 1092 1005 1094 1005 1095 1005 1095 1004 1095 1003 1094 1002 1091 988 1090 986 1089 985 1088 985 1088 985 1095 985 
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1098 1002 1097 1001 1097 999 1096 997 19 _pl _cp 
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1111 1002 31 _pl _cp 
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_sp 1121 996 1121 994 1122 992 1124 991 1126 991 1128 991 1130 992 1131 993 1133 994 1134 996 1135 998 1136 999 1136 1001 1136 1003 1135 1005 
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551 2948 550 2947 549 2944 18 _pl _cp 
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0 g 561 2940 _m
_sp 561 2940 561 2937 562 2935 563 2934 564 2932 566 2931 567 2930 570 2931 572 2933 574 2936 574 2940 574 2944 573 2947 571 2949 568 2950 
565 2949 563 2947 562 2944 18 _pl _cp 564 2941 _m
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566 2948 565 2947 564 2944 18 _pl _cp 
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557 2965 557 2966 557 2966 557 2967 556 2967 555 2967 555 2966 556 2965 557 2964 559 2965 560 2966 561 2967 562 2969 563 2971 564 2974 
566 2981 569 2981 569 2983 566 2983 566 2983 567 2985 567 2987 569 2988 570 2989 570 2989 570 2988 570 2988 570 2988 570 2988 570 2988 
570 2988 570 2987 571 2986 572 2987 572 2988 571 2989 570 2990 568 2989 566 2988 565 2987 565 2986 564 2984 563 2983 561 2983 561 2981 
60 _pl _cp 
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592 2943 591 2944 590 2943 589 2942 588 2941 587 2940 587 2939 586 2939 588 2944 583 2943 583 2942 584 2942 585 2942 585 2942 585 2941 
585 2940 31 _pl _cp 
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596 2926 595 2926 595 2926 594 2926 594 2927 594 2927 595 2928 595 2931 596 2930 597 2930 599 2930 600 2931 602 2932 603 2933 604 2935 
605 2937 606 2938 606 2940 605 2943 603 2944 602 2944 601 2943 599 2942 38 _pl _cp 596 2933 _m
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598 2939 597 2936 17 _pl _cp 
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623 2930 625 2931 627 2934 626 2934 626 2933 625 2932 624 2932 624 2932 624 2932 624 2932 624 2932 624 2933 624 2934 625 2939 626 2941 
626 2942 625 2943 624 2944 623 2943 621 2942 620 2940 619 2938 619 2941 619 2942 619 2943 618 2944 617 2943 615 2942 614 2940 612 2938 
613 2944 609 2943 609 2942 610 2942 610 2942 610 2942 610 2941 610 2940 68 _pl _cp 
0 g _f _s 
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(ratio.)_S 2400 10902 _m
(Combining)_S 67 _t
(\(6.40\))_S 67 _t
(with)_S 67 _t
(\(6.41\))_S 67 _t
(and)_S 67 _t
(expanding)_S 67 _t
(the)_S 67 _t
(last)_S 67 _t
(complete)_S 67 _t
(term)_S 1500 10553 _m
(contained)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(\(Healey)_S 67 _t
(93\))_S 67 _t
(surge)_S 67 _t
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(\(6.39\):)_S gsave 4 4 scale 16 _sr 
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0 g 1144 2168 _m
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_sp 1349 2168 1352 2168 1352 2180 1352 2185 1352 2189 1352 2193 1351 2198 1351 2202 1350 2205 1349 2209 1348 2212 1346 2215 1344 2219 1342 2222 1338 2227 
1338 2227 1341 2222 1343 2217 1345 2214 1346 2210 1347 2207 1348 2204 1348 2200 1349 2195 1349 2191 1349 2187 1349 2183 1349 2179 28 _pl _cp 
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_sp 1492 2172 1492 2170 1524 2170 1524 2172 4 _pl _cp 
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_sp 1537 2172 1537 2170 1609 2170 1609 2172 4 _pl _cp 
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0 g 945 1998 _m
_sp 945 1998 945 1996 983 1996 983 1998 4 _pl _cp 
0 g _f _s _s 
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_sp 1132 2013 1130 2013 1130 2074 1139 2074 1139 2072 1132 2072 6 _pl _cp 
0 g _f _s _s 
0 g 1132 1994 _m
_sp 1132 1994 1130 1994 1130 2016 1132 2016 4 _pl _cp 
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0 g 1130 1997 _m
_sp 1130 1997 1132 1997 1132 1934 1139 1934 1139 1932 1130 1932 6 _pl _cp 
0 g _f _s _s 
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_sp 1661 2013 1663 2013 1663 2074 1654 2074 1654 2072 1661 2072 6 _pl _cp 
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_sp 1144 1994 1141 1994 1141 2006 1141 2011 1141 2015 1141 2019 1142 2024 1142 2028 1143 2031 1144 2035 1145 2038 1146 2041 1148 2045 1151 2048 1154 2053 
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0 g _f _s _s 
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1155 1933 1152 1938 1150 1943 1148 1946 1147 1949 1146 1953 1145 1956 1145 1960 1144 1964 1144 1969 1144 1973 1144 1977 1144 1981 28 _pl _cp 
0 g _f _s _s 
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655 2538 653 2537 651 2536 650 2535 649 2533 647 2531 647 2529 647 2527 647 2526 647 2524 25 _pl _cp 662 2527 _m
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662 2531 16 _pl _cp 
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965 2538 963 2537 962 2536 960 2535 959 2533 958 2531 957 2529 957 2527 957 2526 957 2524 25 _pl _cp 973 2527 _m
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973 2531 16 _pl _cp 
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1238 2507 1238 2504 1238 2504 1238 2504 1240 2504 1240 2504 1240 2504 1241 2506 1242 2507 1243 2506 1243 2505 1243 2504 42 _pl _cp 
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1313 2502 1313 2504 1313 2505 1312 2507 1311 2509 1309 2510 1307 2510 1305 2510 1303 2509 1302 2508 1300 2506 1298 2509 1296 2510 1294 2510 1292 2509 
1291 2507 1291 2504 1291 2504 1291 2504 1293 2504 1293 2504 1293 2504 1294 2506 1295 2507 1296 2506 1296 2505 1296 2504 42 _pl _cp 
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965 2384 963 2383 962 2382 960 2381 959 2379 958 2377 957 2375 957 2373 957 2371 957 2369 25 _pl _cp 973 2372 _m
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973 2376 16 _pl _cp 
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973 2202 16 _pl _cp 
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965 2036 963 2035 962 2034 960 2033 959 2031 958 2029 957 2027 957 2025 957 2023 957 2021 25 _pl _cp 973 2024 _m
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973 2028 16 _pl _cp 
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653 2482 651 2481 650 2480 648 2479 647 2478 646 2476 645 2475 645 2472 646 2472 647 2474 648 2476 650 2477 653 2478 656 2477 658 2476 
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662 2453 660 2453 47 _pl _cp 
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714 2527 713 2526 713 2525 712 2523 713 2523 714 2525 715 2526 716 2527 718 2527 721 2526 722 2523 722 2521 721 2519 720 2516 718 2514 
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762 2526 761 2523 761 2523 762 2525 763 2526 765 2527 766 2527 768 2527 770 2526 771 2524 771 2523 771 2521 770 2519 768 2516 766 2514 
763 2511 760 2508 760 2508 773 2508 775 2512 775 2512 774 2512 774 2511 773 2511 772 2510 771 2510 41 _pl _cp 
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964 2482 962 2481 960 2480 958 2479 957 2478 956 2476 956 2475 955 2472 956 2472 957 2474 958 2476 961 2477 963 2478 966 2477 968 2476 
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972 2453 970 2453 47 _pl _cp 
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1024 2526 1023 2523 1023 2523 1024 2525 1025 2526 1027 2527 1028 2527 1030 2527 1032 2526 1033 2524 1033 2523 1033 2521 1032 2519 1030 2516 1028 2514 
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1230 2481 1233 2479 1234 2480 1232 2482 1230 2484 1229 2485 1228 2487 1227 2488 1227 2489 1226 2491 1226 2494 1226 2497 1226 2500 1226 2503 1226 2506 
1226 2509 1227 2511 1227 2512 1228 2514 1229 2515 1230 2516 1231 2517 1232 2519 1233 2520 1234 2521 40 _pl _cp 
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972 2298 970 2298 47 _pl _cp 
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1024 2372 1023 2369 1023 2369 1024 2371 1025 2372 1027 2373 1028 2373 1030 2373 1032 2372 1033 2370 1033 2368 1033 2366 1032 2364 1030 2362 1028 2360 
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1269 2366 1267 2366 47 _pl _cp 
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60 _pl _cp 
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60 _pl _cp 
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1229 2151 1227 2152 1224 2151 1222 2150 1221 2146 1220 2142 21 _pl _cp 
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1060 2491 1062 2494 1061 2494 1060 2493 1059 2492 1058 2490 1057 2490 1057 2490 1056 2491 1056 2492 1057 2493 1057 2494 1057 2496 1058 2498 1058 2499 
1059 2501 1059 2502 1060 2507 1061 2510 64 _pl _cp 
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1105 2491 1107 2494 1106 2494 1105 2493 1104 2492 1103 2490 1102 2490 1102 2490 1101 2491 1101 2492 1102 2493 1102 2494 1102 2496 1103 2498 1103 2499 
1104 2501 1104 2502 1105 2507 1106 2510 64 _pl _cp 
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1160 2521 1160 2521 1159 2521 1158 2521 1156 2521 1154 2522 1153 2522 1151 2522 1147 2521 1143 2520 1139 2517 1136 2514 1133 2510 1132 2505 1131 2501 
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1186 2488 1185 2484 1184 2481 1184 2477 1184 2477 20 _pl _cp 
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1104 2346 1104 2348 1105 2353 1106 2356 64 _pl _cp 
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1170 2332 1169 2331 1167 2330 1166 2328 1164 2326 1163 2324 1163 2322 1164 2319 1167 2318 1169 2318 1172 2320 1172 2321 42 _pl _cp 1166 2321 _m
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1168 2327 1167 2325 1166 2324 1166 2322 1166 2322 20 _pl _cp 
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1186 2333 1185 2330 1184 2327 1184 2323 1184 2323 20 _pl _cp 
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1283 2354 1283 2354 1283 2355 1282 2356 1281 2357 1280 2356 1279 2354 1280 2352 1283 2351 1284 2351 1286 2352 1287 2353 1288 2354 1289 2356 1290 2358 
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1305 2394 1305 2394 1305 2394 1305 2393 1305 2393 1305 2392 1305 2391 1306 2390 1308 2391 1309 2393 1308 2395 1305 2396 1303 2396 1301 2395 1300 2394 
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1343 2312 1344 2314 1343 2316 1342 2317 1340 2316 1338 2314 1336 2313 1334 2310 1334 2309 1333 2308 1336 2317 1328 2316 1328 2315 1329 2315 1330 2314 
1331 2313 1331 2312 1330 2311 33 _pl _cp 
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1367 2304 1368 2307 1368 2310 1367 2313 1366 2315 1364 2316 1362 2317 1360 2317 1358 2316 1356 2314 40 _pl _cp 1350 2298 _m
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1358 2314 1356 2312 1355 2311 1354 2309 1353 2307 1352 2304 21 _pl _cp 
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1387 2311 1386 2309 1384 2303 1382 2294 1386 2294 1387 2300 1388 2303 1389 2305 1391 2307 1392 2309 1393 2311 1395 2313 1396 2314 1397 2314 1398 2314 
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90 _pl _cp 
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1450 2307 1451 2308 1452 2313 1453 2316 64 _pl _cp 
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1595 2366 1595 2366 1595 2368 1599 2382 1603 2382 1604 2384 1599 2384 1601 2389 1600 2389 1598 2387 1596 2385 1594 2384 1591 2383 1591 2382 29 _pl _cp 
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1631 2312 1632 2314 1631 2316 1630 2317 1628 2316 1626 2314 1624 2313 1622 2310 1622 2309 1621 2308 1624 2317 1616 2316 1616 2315 1617 2315 1618 2314 
1619 2313 1619 2312 1618 2311 33 _pl _cp 
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1675 2311 1674 2309 1672 2303 1670 2294 1674 2294 1675 2300 1676 2303 1677 2305 1679 2307 1680 2309 1681 2311 1683 2313 1684 2314 1685 2314 1686 2314 
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90 _pl _cp 
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1078 2153 1077 2151 1076 2150 1076 2148 1076 2148 20 _pl _cp 
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1209 2180 1209 2180 1209 2181 1208 2182 1207 2183 1206 2182 1205 2180 1206 2178 1209 2177 1210 2177 1212 2178 1213 2179 1214 2180 1215 2182 1216 2184 
1218 2187 1219 2191 1220 2195 1224 2208 1229 2208 1230 2210 1224 2210 1224 2211 1225 2213 1226 2215 1226 2216 1227 2217 1229 2219 1230 2220 1231 2220 
1231 2220 1231 2220 1231 2220 1231 2219 1231 2219 1231 2218 1231 2217 1232 2216 1234 2217 1235 2219 1234 2221 1231 2222 1229 2222 1227 2221 1226 2220 
1224 2219 1223 2217 1222 2215 1221 2213 1220 2210 1215 2210 1215 2208 67 _pl _cp 
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1233 2192 1233 2192 1233 2194 1237 2208 1241 2208 1242 2210 1237 2210 1239 2215 1238 2215 1236 2213 1234 2211 1232 2210 1229 2209 1229 2208 29 _pl _cp 
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_sp 1280 2138 1281 2143 1273 2142 1273 2141 1275 2141 1276 2140 1276 2139 1276 2138 1276 2137 1270 2115 1269 2112 1267 2111 1266 2111 1266 2110 1276 2110 
1276 2111 1275 2111 1274 2112 1273 2113 1273 2113 1273 2114 1274 2115 1275 2120 1277 2120 1279 2120 1281 2120 1284 2121 1286 2122 1288 2124 1291 2127 
1293 2130 1294 2133 1294 2136 1293 2139 1292 2141 1290 2142 1288 2143 1286 2143 1284 2142 1282 2140 40 _pl _cp 1276 2124 _m
_sp 1276 2124 1276 2124 1276 2123 1277 2122 1278 2121 1280 2121 1281 2122 1283 2123 1284 2124 1286 2127 1288 2130 1289 2133 1289 2137 1288 2139 1286 2140 
1284 2140 1282 2138 1281 2137 1280 2135 1279 2133 1278 2130 21 _pl _cp 
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1313 2137 1312 2135 1310 2129 1308 2120 1312 2120 1313 2126 1314 2129 1315 2131 1317 2133 1318 2135 1319 2137 1321 2139 1322 2140 1323 2140 1324 2140 
1324 2139 1324 2138 1324 2137 1323 2135 1321 2129 1321 2127 1321 2125 1320 2123 1320 2122 1321 2121 1323 2120 1324 2120 1326 2121 1327 2123 1329 2125 
1328 2126 1328 2125 1326 2123 1325 2122 1324 2122 1324 2123 1324 2123 1324 2123 1324 2125 1325 2126 1327 2134 1328 2137 1328 2139 1327 2142 1325 2143 
1324 2143 1323 2142 1321 2141 1320 2140 1319 2139 1318 2137 1316 2136 1315 2133 1316 2136 1316 2138 1317 2139 1317 2140 1316 2142 1314 2143 1313 2143 
1311 2142 1310 2141 1308 2139 1307 2138 1306 2136 1305 2135 1304 2133 1306 2143 1298 2142 1298 2141 1300 2141 1301 2140 1301 2139 1301 2138 1301 2137 
90 _pl _cp 
0 g _f _s _s 
0 g 1394 2160 _m
_sp 1394 2160 1398 2160 1400 2166 1401 2169 1402 2171 1403 2172 1404 2174 1404 2175 1405 2176 1406 2177 1408 2179 1409 2180 1410 2180 1411 2179 1411 2178 
1411 2178 1411 2177 1411 2175 1408 2166 1408 2164 1407 2162 1408 2160 1410 2159 1412 2159 1413 2161 1415 2162 1417 2165 1416 2166 1414 2163 1412 2162 
1412 2162 1412 2163 1412 2163 1412 2164 1412 2166 1415 2175 1415 2177 1415 2179 1414 2182 1412 2183 1410 2182 1408 2180 1407 2179 1405 2178 1404 2176 
1402 2173 1402 2173 1401 2172 1404 2183 1396 2181 1396 2180 1398 2180 1399 2180 1399 2179 1399 2178 1399 2176 56 _pl _cp 
0 g _f _s _s 
0 g 1439 2160 _m
_sp 1439 2160 1443 2160 1445 2166 1446 2169 1447 2171 1448 2172 1449 2174 1449 2175 1450 2176 1451 2177 1453 2179 1454 2180 1455 2180 1456 2179 1456 2178 
1456 2178 1456 2177 1456 2175 1453 2166 1453 2164 1452 2162 1453 2160 1455 2159 1457 2159 1458 2161 1460 2162 1462 2165 1461 2166 1459 2163 1457 2162 
1457 2162 1457 2163 1457 2163 1457 2164 1457 2166 1460 2175 1460 2177 1460 2179 1459 2182 1457 2183 1455 2182 1453 2180 1452 2179 1450 2178 1449 2176 
1447 2173 1447 2173 1446 2172 1449 2183 1441 2181 1441 2180 1443 2180 1444 2180 1444 2179 1444 2178 1444 2176 56 _pl _cp 
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1503 2192 1504 2193 1508 2210 1501 2209 1500 2208 1502 2208 1503 2208 1503 2207 1503 2206 1503 2204 1500 2194 1500 2193 1500 2192 1499 2191 1499 2190 
1500 2188 1502 2187 1504 2187 1505 2188 1507 2189 1508 2190 1509 2191 1510 2193 1511 2195 1513 2198 1512 2194 1512 2192 1511 2190 1512 2188 1514 2187 
1516 2187 1517 2188 1519 2190 1521 2193 1520 2194 1519 2193 1518 2191 1517 2190 1516 2190 1516 2190 1515 2190 1515 2191 1516 2192 1516 2194 1516 2195 
1517 2197 1517 2199 1518 2200 1518 2201 1519 2207 1520 2210 66 _pl _cp 
0 g _f _s _s 
0 g 1516 2142 _m
_sp 1516 2142 1516 2140 1515 2137 1514 2135 1513 2133 1512 2131 1511 2129 1509 2126 1507 2124 1506 2123 1504 2122 1504 2123 1503 2123 1503 2125 1504 2126 
1508 2143 1501 2142 1500 2141 1502 2141 1503 2140 1503 2139 1503 2138 1503 2137 1500 2127 1500 2126 1500 2125 1499 2124 1499 2122 1500 2121 1502 2120 
1504 2120 1505 2121 1507 2122 1508 2123 1509 2124 1510 2126 1511 2128 1513 2131 1512 2126 1512 2124 1511 2122 1512 2120 1514 2120 1516 2120 1517 2121 
1519 2123 1521 2126 1520 2126 1519 2125 1518 2124 1517 2122 1516 2122 1516 2122 1515 2123 1515 2124 1516 2125 1516 2126 1516 2128 1517 2130 1517 2131 
1518 2133 1518 2134 1519 2139 1520 2142 64 _pl _cp 
0 g _f _s _s 
0 g 1581 2210 _m
_sp 1581 2210 1581 2208 1581 2207 1580 2205 1580 2204 1579 2202 1578 2200 1577 2198 1576 2196 1574 2193 1572 2192 1571 2190 1569 2190 1569 2190 1568 2191 
1568 2192 1569 2193 1573 2210 1566 2209 1565 2208 1567 2208 1568 2208 1568 2207 1568 2206 1568 2204 1565 2194 1565 2193 1565 2192 1564 2191 1564 2190 
1565 2188 1567 2187 1569 2187 1570 2188 1572 2189 1573 2190 1574 2191 1575 2193 1576 2195 1578 2198 1577 2194 1577 2192 1576 2190 1577 2188 1579 2187 
1581 2187 1582 2188 1584 2190 1586 2193 1585 2194 1584 2193 1583 2191 1582 2190 1581 2190 1581 2190 1580 2190 1580 2191 1581 2192 1581 2194 1581 2195 
1582 2197 1582 2199 1583 2200 1583 2201 1584 2207 1585 2210 66 _pl _cp 
0 g _f _s _s 
0 g 1581 2142 _m
_sp 1581 2142 1581 2140 1580 2137 1579 2135 1578 2133 1577 2131 1576 2129 1574 2126 1572 2124 1571 2123 1569 2122 1569 2123 1568 2123 1568 2125 1569 2126 
1573 2143 1566 2142 1565 2141 1567 2141 1568 2140 1568 2139 1568 2138 1568 2137 1565 2127 1565 2126 1565 2125 1564 2124 1564 2122 1565 2121 1567 2120 
1569 2120 1570 2121 1572 2122 1573 2123 1574 2124 1575 2126 1576 2128 1578 2131 1577 2126 1577 2124 1576 2122 1577 2120 1579 2120 1581 2120 1582 2121 
1584 2123 1586 2126 1585 2126 1584 2125 1583 2124 1582 2122 1581 2122 1581 2122 1580 2123 1580 2124 1581 2125 1581 2126 1581 2128 1582 2130 1582 2131 
1583 2133 1583 2134 1584 2139 1585 2142 64 _pl _cp 
0 g _f _s _s 
0 g 1706 2182 _m
_sp 1706 2182 1705 2179 1704 2177 1703 2174 1702 2173 1701 2171 1700 2169 1698 2166 1696 2164 1695 2163 1693 2162 1693 2163 1693 2163 1693 2164 1693 2165 
1698 2183 1690 2181 1690 2180 1691 2180 1692 2180 1692 2179 1692 2178 1692 2176 1689 2167 1689 2166 1689 2164 1689 2163 1689 2162 1690 2160 1691 2159 
1693 2159 1694 2160 1696 2161 1697 2162 1698 2163 1699 2165 1700 2167 1702 2170 1701 2166 1701 2164 1701 2162 1702 2160 1704 2159 1705 2159 1706 2161 
1708 2162 1710 2165 1709 2166 1709 2165 1707 2163 1706 2162 1705 2162 1705 2162 1705 2163 1705 2164 1705 2165 1705 2166 1706 2167 1706 2169 1707 2171 
1707 2172 1707 2174 1709 2179 1710 2182 64 _pl _cp 
0 g _f _s _s 
0 g 1751 2182 _m
_sp 1751 2182 1750 2179 1749 2177 1748 2174 1747 2173 1746 2171 1745 2169 1743 2166 1741 2164 1740 2163 1738 2162 1738 2163 1738 2163 1738 2164 1738 2165 
1743 2183 1735 2181 1735 2180 1736 2180 1737 2180 1737 2179 1737 2178 1737 2176 1734 2167 1734 2166 1734 2164 1734 2163 1734 2162 1735 2160 1736 2159 
1738 2159 1739 2160 1741 2161 1742 2162 1743 2163 1744 2165 1745 2167 1747 2170 1746 2166 1746 2164 1746 2162 1747 2160 1749 2159 1750 2159 1751 2161 
1753 2162 1755 2165 1754 2166 1754 2165 1752 2163 1751 2162 1750 2162 1750 2162 1750 2163 1750 2164 1750 2165 1750 2166 1751 2167 1751 2169 1752 2171 
1752 2172 1752 2174 1754 2179 1755 2182 64 _pl _cp 
0 g _f _s _s 
0 g 996 2017 _m
_sp 996 2017 997 2017 998 2017 999 2015 999 2015 999 2014 999 2013 998 2012 993 1992 992 1990 991 1988 990 1987 989 1987 989 1987 988 1986 
1012 1986 1015 1994 1014 1995 1013 1993 1011 1991 1010 1990 1008 1989 1007 1989 1005 1989 1004 1988 1002 1988 1002 1988 1002 1988 1000 1988 999 1989 
998 1990 998 1991 998 1993 1004 2012 1005 2014 1005 2016 1006 2017 1008 2017 1008 2017 1008 2019 996 2019 41 _pl _cp 
0 g _f _s _s 
0 g 1067 1994 _m
_sp 1067 1994 1064 1991 1062 1989 1059 1988 1056 1988 1054 1988 1052 1989 1051 1989 1050 1990 1049 1992 1048 1994 1047 1996 1047 1998 1048 2003 1049 2007 
1051 2011 1054 2014 1058 2016 1061 2017 1063 2017 1065 2017 1066 2016 1067 2015 1068 2014 1068 2013 1069 2011 1069 2009 1070 2009 1072 2019 1071 2019 
1070 2019 1070 2018 1069 2018 1068 2019 1066 2019 1064 2019 1063 2019 1061 2019 1057 2018 1053 2017 1049 2015 1046 2011 1043 2008 1042 2003 1041 1999 
1041 1996 1042 1993 1044 1991 1045 1989 1047 1988 1049 1986 1052 1985 1055 1985 1058 1986 1060 1986 1062 1987 1064 1989 1066 1991 1068 1993 59 _pl _cp 
0 g _f _s _s 
0 g 1083 1973 _m
_sp 1083 1973 1083 1973 1083 1972 1083 1971 1083 1970 1084 1970 1085 1970 1086 1970 1087 1971 1089 1973 1088 1974 1088 1973 1086 1971 1086 1971 1086 1972 
1085 1972 1085 1973 1086 1974 1091 1993 1085 1992 1085 1991 1086 1991 1087 1991 1087 1990 1087 1990 1087 1989 1086 1983 1085 1985 1083 1985 1082 1985 
1080 1984 1079 1983 1077 1982 1076 1980 1074 1978 1073 1976 1073 1974 1074 1971 1077 1970 1079 1970 1082 1972 1082 1973 42 _pl _cp 1076 1973 _m
_sp 1076 1973 1077 1972 1078 1971 1079 1971 1081 1972 1082 1973 1083 1975 1083 1976 1084 1977 1085 1980 1085 1982 1084 1983 1083 1984 1081 1983 1079 1980 
1078 1979 1077 1977 1076 1976 1076 1974 1076 1974 20 _pl _cp 
0 g _f _s _s 
0 g 1091 1976 _m
_sp 1091 1976 1091 1973 1092 1972 1094 1970 1096 1970 1099 1971 1102 1973 1105 1976 1106 1980 1107 1984 1106 1987 1105 1990 1103 1991 1101 1992 1098 1991 
1095 1989 1093 1986 1092 1982 1091 1977 1091 1977 20 _pl _cp 1094 1975 _m
_sp 1094 1975 1095 1972 1097 1971 1099 1972 1101 1974 1102 1977 1103 1980 1104 1983 1104 1986 1104 1988 1103 1990 1102 1991 1101 1991 1099 1990 1097 1988 
1096 1985 1095 1982 1094 1979 1094 1975 1094 1975 20 _pl _cp 
0 g _f _s _s 
0 g 1219 2034 _m
_sp 1219 2034 1219 2031 1217 2023 1215 2015 1214 2012 1213 2009 1212 2007 1211 2006 1210 2005 1209 2005 1209 2005 1209 2005 1209 2005 1209 2005 1209 2006 
1209 2006 1209 2006 1209 2007 1208 2008 1207 2009 1206 2008 1205 2006 1206 2004 1209 2003 1210 2003 1212 2004 1213 2005 1214 2006 1215 2008 1216 2010 
1218 2013 1219 2017 1220 2021 1224 2034 1229 2034 1230 2036 1224 2036 1224 2037 1225 2039 1226 2041 1226 2042 1227 2043 1229 2045 1230 2046 1231 2046 
1231 2046 1231 2046 1231 2046 1231 2045 1231 2045 1231 2044 1231 2043 1232 2042 1234 2043 1235 2045 1234 2047 1231 2048 1229 2048 1227 2047 1226 2046 
1224 2045 1223 2043 1222 2041 1221 2039 1220 2036 1215 2036 1215 2034 67 _pl _cp 
0 g _f _s _s 
0 g 1233 2034 _m
_sp 1233 2034 1229 2020 1229 2017 1228 2016 1229 2014 1231 2013 1233 2014 1235 2015 1237 2017 1238 2019 1237 2020 1235 2017 1233 2016 1233 2016 1232 2017 
1233 2018 1233 2018 1233 2020 1237 2034 1241 2034 1242 2036 1237 2036 1239 2041 1238 2041 1236 2039 1234 2037 1232 2036 1229 2035 1229 2034 29 _pl _cp 
0 g _f _s _s 
0 g 1252 1946 _m
_sp 1252 1946 1256 1946 1257 1951 1258 1954 1259 1956 1260 1958 1261 1959 1261 1961 1262 1962 1264 1964 1265 1965 1266 1965 1266 1964 1267 1964 1268 1963 
1269 1964 1270 1966 1269 1968 1268 1969 1266 1968 1264 1966 1262 1965 1260 1962 1260 1961 1259 1960 1262 1969 1254 1968 1254 1967 1255 1967 1256 1966 
1257 1965 1257 1964 1256 1963 33 _pl _cp 
0 g _f _s _s 
0 g 1280 1964 _m
_sp 1280 1964 1281 1969 1273 1968 1273 1967 1275 1967 1276 1966 1276 1965 1276 1964 1276 1963 1270 1941 1269 1938 1267 1937 1266 1937 1266 1936 1276 1936 
1276 1937 1275 1937 1274 1938 1273 1939 1273 1939 1273 1940 1274 1941 1275 1946 1277 1946 1279 1946 1281 1946 1284 1947 1286 1948 1288 1950 1291 1953 
1293 1956 1294 1959 1294 1962 1293 1965 1292 1967 1290 1968 1288 1969 1286 1969 1284 1968 1282 1966 40 _pl _cp 1276 1950 _m
_sp 1276 1950 1276 1950 1276 1949 1277 1948 1278 1947 1280 1947 1281 1948 1283 1949 1284 1950 1286 1953 1288 1956 1289 1959 1289 1963 1288 1965 1286 1966 
1284 1966 1282 1964 1281 1963 1280 1961 1279 1959 1278 1956 21 _pl _cp 
0 g _f _s _s 
0 g 1296 1946 _m
_sp 1296 1946 1300 1946 1301 1950 1302 1952 1302 1954 1303 1956 1304 1958 1305 1959 1306 1961 1308 1963 1309 1965 1310 1966 1311 1966 1312 1966 1313 1965 
1313 1963 1312 1961 1310 1955 1308 1946 1312 1946 1313 1952 1314 1955 1315 1957 1317 1959 1318 1961 1319 1963 1321 1965 1322 1966 1323 1966 1324 1966 
1324 1965 1324 1964 1324 1963 1323 1961 1321 1955 1321 1953 1321 1951 1320 1949 1320 1948 1321 1947 1323 1946 1324 1946 1326 1947 1327 1949 1329 1951 
1328 1952 1328 1951 1326 1949 1325 1948 1324 1948 1324 1949 1324 1949 1324 1949 1324 1951 1325 1952 1327 1960 1328 1963 1328 1965 1327 1968 1325 1969 
1324 1969 1323 1968 1321 1967 1320 1966 1319 1965 1318 1963 1316 1962 1315 1959 1316 1962 1316 1964 1317 1965 1317 1966 1316 1968 1314 1969 1313 1969 
1311 1968 1310 1967 1308 1965 1307 1964 1306 1962 1305 1961 1304 1959 1306 1969 1298 1968 1298 1967 1300 1967 1301 1966 1301 1965 1301 1964 1301 1963 
90 _pl _cp 
0 g _f _s _s 
0 g 1394 1986 _m
_sp 1394 1986 1398 1986 1400 1992 1401 1995 1402 1997 1403 1998 1404 2000 1404 2001 1405 2002 1406 2003 1408 2005 1409 2006 1410 2006 1411 2005 1411 2004 
1411 2004 1411 2003 1411 2001 1408 1992 1408 1990 1407 1988 1408 1986 1410 1985 1412 1985 1413 1987 1415 1988 1417 1991 1416 1992 1414 1989 1412 1988 
1412 1988 1412 1989 1412 1989 1412 1990 1412 1992 1415 2001 1415 2003 1415 2005 1414 2008 1412 2009 1410 2008 1408 2006 1407 2005 1405 2004 1404 2002 
1402 1999 1402 1999 1401 1998 1404 2009 1396 2007 1396 2006 1398 2006 1399 2006 1399 2005 1399 2004 1399 2002 56 _pl _cp 
0 g _f _s _s 
0 g 1439 1986 _m
_sp 1439 1986 1443 1986 1445 1992 1446 1995 1447 1997 1448 1998 1449 2000 1449 2001 1450 2002 1451 2003 1453 2005 1454 2006 1455 2006 1456 2005 1456 2004 
1456 2004 1456 2003 1456 2001 1453 1992 1453 1990 1452 1988 1453 1986 1455 1985 1457 1985 1458 1987 1460 1988 1462 1991 1461 1992 1459 1989 1457 1988 
1457 1988 1457 1989 1457 1989 1457 1990 1457 1992 1460 2001 1460 2003 1460 2005 1459 2008 1457 2009 1455 2008 1453 2006 1452 2005 1450 2004 1449 2002 
1447 1999 1447 1999 1446 1998 1449 2009 1441 2007 1441 2006 1443 2006 1444 2006 1444 2005 1444 2004 1444 2002 56 _pl _cp 
0 g _f _s _s 
0 g 1581 2008 _m
_sp 1581 2008 1580 2005 1579 2003 1578 2000 1577 1999 1576 1997 1575 1995 1573 1992 1572 1990 1570 1989 1569 1988 1569 1989 1568 1989 1568 1990 1568 1991 
1573 2009 1565 2007 1565 2006 1566 2006 1567 2006 1568 2005 1568 2004 1567 2002 1565 1993 1565 1992 1564 1990 1564 1989 1564 1988 1565 1986 1567 1985 
1568 1985 1570 1986 1571 1987 1572 1988 1573 1989 1575 1991 1576 1993 1578 1996 1577 1992 1576 1990 1576 1988 1577 1986 1579 1985 1581 1985 1582 1987 
1584 1988 1586 1991 1585 1992 1584 1991 1583 1989 1582 1988 1581 1988 1580 1988 1580 1989 1580 1990 1580 1991 1581 1992 1581 1993 1582 1995 1582 1997 
1582 1998 1583 2000 1584 2005 1585 2008 64 _pl _cp 
0 g _f _s _s 
0 g 1626 2008 _m
_sp 1626 2008 1625 2005 1624 2003 1623 2000 1622 1999 1621 1997 1620 1995 1618 1992 1617 1990 1615 1989 1614 1988 1614 1989 1613 1989 1613 1990 1613 1991 
1618 2009 1610 2007 1610 2006 1611 2006 1612 2006 1613 2005 1613 2004 1612 2002 1610 1993 1610 1992 1609 1990 1609 1989 1609 1988 1610 1986 1612 1985 
1613 1985 1615 1986 1616 1987 1617 1988 1618 1989 1620 1991 1621 1993 1623 1996 1622 1992 1621 1990 1621 1988 1622 1986 1624 1985 1626 1985 1627 1987 
1629 1988 1631 1991 1630 1992 1629 1991 1628 1989 1627 1988 1626 1988 1625 1988 1625 1989 1625 1990 1625 1991 1626 1992 1626 1993 1627 1995 1627 1997 
1627 1998 1628 2000 1629 2005 1630 2008 64 _pl _cp 
0 g _f _s _s 
0 g 920 2507 _m
_sp 920 2507 901 2507 901 2506 920 2506 4 _pl _cp 920 2500 _m
_sp 920 2500 901 2500 901 2498 920 2498 4 _pl _cp 
0 g _f _s _s 
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_sp 1075 2526 1075 2476 1076 2476 1076 2526 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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_sp 1279 2526 1279 2476 1281 2476 1281 2526 4 _pl _cp 
0 g _f _s _s 
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_sp 1332 2526 1332 2476 1334 2476 1334 2526 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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_sp 916 2345 897 2345 897 2344 916 2344 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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_sp 916 2171 897 2171 897 2170 916 2170 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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_sp 1554 2158 1554 2108 1555 2108 1555 2158 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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_sp 1661 2175 1642 2175 1642 2174 1661 2174 4 _pl _cp 
0 g _f _s _s 
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_sp 1723 2197 1723 2148 1725 2148 1725 2197 4 _pl _cp 
0 g _f _s _s 
0 g 1768 2197 _m
_sp 1768 2197 1768 2148 1770 2148 1770 2197 4 _pl _cp 
0 g _f _s _s 
0 g 916 2005 _m
_sp 916 2005 897 2005 897 2004 916 2004 4 _pl _cp 916 1997 _m
_sp 916 1997 897 1997 897 1996 916 1996 4 _pl _cp 
0 g _f _s _s 
0 g 1429 2023 _m
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0 g _f _s _s 
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_sp 1474 2023 1474 1974 1476 1974 1476 2023 4 _pl _cp 
0 g _f _s _s 
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_sp 1537 2001 1518 2001 1518 2000 1537 2000 4 _pl _cp 
0 g _f _s _s 
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0 g _f _s 
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/Times-BoldR 600 _ff
(\(6.42\))_S /Times-RomanR 600 _ff
2400 7058 _m
(The)_S 67 _t
(propulsion)_S 67 _t
(contribution)_S 67 _t
(\(due)_S 67 _t
(to)_S 67 _t
(propeller)_S 67 _t
(rpm)_S 67 _t
/Times-BoldItalicR 600 _ff
(n)_S /Times-RomanR 600 _ff
(\))_S 67 _t
(and)_S 67 _t
(opposing)_S 67 _t
(drag)_S 1500 6707 _m
(contribution)_S 67 _t
(\(due)_S 67 _t
(to)_S 67 _t
(forward)_S 67 _t
(surge)_S 67 _t
(velocity)_S 67 _t
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
(\))_S 67 _t
(are)_S 67 _t
(now)_S 67 _t
(evident.)_S 134 _t
(When)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
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(two)_S 67 _t
(propellers,)_S 67 _t
(a)_S 67 _t
(pair)_S 67 _t
(of)_S 67 _t
(forward)_S 67 _t
(forces)_S 67 _t
(contribute)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(expected)_S 67 _t
(speed)_S 67 _t
(per)_S 67 _t
(rpm,)_S 67 _t
(and)_S 1500 6007 _m
(the)_S 67 _t
(preceding)_S 67 _t
/Times-BoldItalicR 600 _ff
(X)_S /Times-BoldItalicR 360 _ff
2800 5962 _m
(prop)_S 3027 5962 _m
/Times-RomanR 600 _ff
3027 6007 _m
67 _t
(term)_S 67 _t
(shown)_S 67 _t
(in)_S 67 _t
(Equation)_S 67 _t
(\(6.42\))_S 67 _t
(is)_S 67 _t
(expanded)_S 67 _t
(to)_S 67 _t
(become:)_S gsave 4 4 scale 16 _sr 
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_s 515 1339 _m
_sp 515 1339 515 1337 553 1337 553 1339 4 _pl _cp 
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0 g 825 1339 _m
_sp 825 1339 825 1337 863 1337 863 1339 4 _pl _cp 
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_sp 1011 1354 1010 1354 1010 1415 1019 1415 1019 1413 1011 1413 6 _pl _cp 
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_sp 1011 1335 1010 1335 1010 1357 1011 1357 4 _pl _cp 
0 g _f _s _s 
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_sp 1010 1338 1011 1338 1011 1275 1019 1275 1019 1273 1010 1273 6 _pl _cp 
0 g _f _s _s 
0 g 1995 1354 _m
_sp 1995 1354 1997 1354 1997 1415 1987 1415 1987 1413 1995 1413 6 _pl _cp 
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_sp 948 851 929 851 929 850 948 850 4 _pl _cp 948 843 _m
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877 791 876 789 875 788 873 786 34 _pl _cp 
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0 g 1058 854 _m
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0 g 1215 864 _m
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1227 864 1225 864 47 _pl _cp 
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0 g 1282 893 _m
_sp 1282 893 1271 851 1275 851 1286 893 4 _pl _cp 
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1293 870 1297 868 1300 866 1301 864 1301 863 1300 861 1298 860 1296 860 1294 861 1291 862 1290 864 1289 867 1288 867 58 _pl _cp 
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0 g 1311 873 _m
_sp 1311 873 1326 873 1325 877 1324 880 1321 881 1317 882 1313 881 1310 879 1308 875 1307 870 1308 865 1310 862 1313 860 1317 859 1320 860 
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_sp 1321 875 1321 878 1320 880 1318 881 1316 881 1314 881 1312 880 1311 878 1311 875 9 _pl _cp 
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0 g 1348 867 _m
_sp 1348 867 1346 865 1345 864 1343 863 1341 863 1338 864 1336 866 1334 868 1333 872 1334 876 1335 878 1337 880 1340 881 1342 880 1343 878 
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0 g 1197 817 _m
_sp 1197 817 1198 817 1200 819 1202 820 1205 821 1215 821 1205 792 1208 792 1219 825 1200 825 10 _pl _cp 
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0 g 1222 808 _m
_sp 1222 808 1222 806 1223 804 1223 801 1224 799 1225 798 1226 797 1226 795 1227 794 1229 793 1230 792 1232 792 1233 792 1237 793 1240 795 
1243 798 1244 803 1245 809 1244 815 1243 819 1240 823 1237 825 1234 826 1230 825 1227 823 1224 819 1223 814 27 _pl _cp 1227 809 _m
_sp 1227 809 1227 804 1228 799 1229 796 1231 795 1234 794 1236 794 1237 795 1238 797 1239 800 1240 804 1240 809 1240 814 1239 819 1238 822 
1236 823 1234 824 1231 823 1229 822 1228 819 1227 814 21 _pl _cp 
0 g _f _s _s 
0 g 1247 808 _m
_sp 1247 808 1247 806 1248 804 1248 801 1249 799 1250 798 1251 797 1251 795 1252 794 1254 793 1255 792 1257 792 1258 792 1262 793 1265 795 
1268 798 1269 803 1270 809 1269 815 1268 819 1265 823 1262 825 1259 826 1255 825 1252 823 1249 819 1248 814 27 _pl _cp 1252 809 _m
_sp 1252 809 1252 804 1253 799 1254 796 1256 795 1259 794 1261 794 1262 795 1263 797 1264 800 1265 804 1265 809 1265 814 1264 819 1263 822 
1261 823 1259 824 1256 823 1254 822 1253 819 1252 814 21 _pl _cp 
0 g _f _s _s 
0 g 1390 883 _m
_sp 1390 883 1392 885 1394 887 1396 889 1397 890 1398 892 1399 894 1400 895 1400 897 1399 899 1398 901 1396 902 1394 903 1391 902 1389 901 
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1389 884 1386 881 1386 880 1399 880 1401 885 1401 885 1400 884 1400 884 1399 883 1398 883 1397 883 41 _pl _cp 
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0 g 1440 889 _m
_sp 1440 889 1440 888 1442 888 1443 889 1443 889 1444 888 1445 886 1445 866 1445 864 1444 862 1443 861 1441 861 1440 861 1440 860 1454 860 
1454 861 1453 861 1451 861 1450 862 1449 864 1449 866 1449 893 22 _pl _cp 
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0 g 1440 796 _m
_sp 1440 796 1443 799 1446 802 1447 803 1448 805 1449 806 1450 807 1452 810 1454 812 1455 815 1455 817 1454 821 1452 823 1450 825 1446 826 
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1452 796 1450 796 47 _pl _cp 
0 g _f _s _s 
0 g 977 844 _m
_sp 977 844 977 842 1015 842 1015 844 4 _pl _cp 
0 g _f _s _s 
0 g 1163 859 _m
_sp 1163 859 1162 859 1162 920 1171 920 1171 918 1163 918 6 _pl _cp 
0 g _f _s _s 
0 g 1163 840 _m
_sp 1163 840 1162 840 1162 862 1163 862 4 _pl _cp 
0 g _f _s _s 
0 g 1162 843 _m
_sp 1162 843 1163 843 1163 780 1171 780 1171 778 1162 778 6 _pl _cp 
0 g _f _s _s 
0 g 1906 859 _m
_sp 1906 859 1908 859 1908 920 1899 920 1899 918 1906 918 6 _pl _cp 
0 g _f _s _s 
0 g 1908 840 _m
_sp 1908 840 1906 840 1906 862 1908 862 4 _pl _cp 
0 g _f _s _s 
0 g 1908 846 _m
_sp 1908 846 1906 846 1906 782 1899 782 1899 780 1908 780 6 _pl _cp 
0 g _f _s _s 
0 g 1175 840 _m
_sp 1175 840 1172 840 1172 852 1172 857 1172 861 1173 865 1173 870 1173 874 1174 877 1175 881 1176 884 1178 887 1180 891 1182 894 1186 899 
1187 899 1183 894 1181 889 1179 886 1178 882 1177 879 1176 876 1176 872 1175 868 1175 863 1175 859 1175 855 1175 851 28 _pl _cp 
0 g _f _s _s 
0 g 1175 840 _m
_sp 1175 840 1172 840 1172 826 1172 821 1172 817 1173 812 1173 808 1173 804 1174 800 1175 797 1176 794 1178 791 1180 787 1182 783 1186 779 
1187 779 1183 784 1181 789 1179 792 1178 796 1177 799 1176 802 1176 806 1175 810 1175 815 1175 819 1175 823 1175 827 28 _pl _cp 
0 g _f _s _s 
0 g 1381 840 _m
_sp 1381 840 1384 840 1384 852 1384 857 1384 861 1383 865 1383 870 1382 874 1382 877 1381 881 1380 884 1378 887 1376 891 1374 894 1370 899 
1369 899 1372 894 1375 889 1377 886 1378 882 1379 879 1380 876 1380 872 1381 868 1381 863 1381 859 1381 855 1381 851 28 _pl _cp 
0 g _f _s _s 
0 g 1381 840 _m
_sp 1381 840 1384 840 1384 826 1384 821 1384 817 1383 812 1383 808 1382 804 1382 800 1381 797 1380 794 1378 791 1376 787 1374 783 1370 779 
1369 779 1372 784 1375 789 1377 792 1378 796 1379 799 1380 802 1380 806 1381 810 1381 815 1381 819 1381 823 1381 827 28 _pl _cp 
0 g _f _s _s 
0 g 1191 844 _m
_sp 1191 844 1191 842 1364 842 1364 844 4 _pl _cp 
0 g _f _s _s 
0 g 1429 844 _m
_sp 1429 844 1429 842 1460 842 1460 844 4 _pl _cp 
0 g _f _s _s 
0 g 1497 866 _m
_sp 1497 866 1497 866 1494 861 1492 855 1491 851 1490 846 1490 843 1490 839 1490 837 1490 835 1490 832 1491 828 1491 824 1492 819 1494 813 
1497 808 1496 808 1494 812 1492 816 1490 820 1489 824 1488 828 1487 833 1487 837 1487 841 1488 846 1489 850 1490 855 1492 859 1494 863 
1496 866 31 _pl _cp 
0 g _f _s _s 
0 g 1717 866 _m
_sp 1717 866 1717 866 1719 861 1721 855 1722 851 1722 846 1723 843 1723 839 1723 837 1723 835 1723 832 1722 828 1722 824 1721 819 1719 813 
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1717 866 31 _pl _cp 
0 g _f _s _s 
0 g 989 850 _m
_sp 989 850 993 850 993 862 994 861 996 860 997 859 999 859 1003 860 1006 862 1008 866 1009 870 1008 875 1006 879 1003 881 999 882 
997 882 995 881 993 880 992 879 991 877 989 875 989 873 989 871 989 869 989 867 25 _pl _cp 1004 870 _m
_sp 1004 870 1004 866 1003 864 1001 862 998 861 996 862 994 864 993 867 993 871 993 875 995 877 996 879 999 880 1001 879 1003 877 
1004 874 16 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 3405 _m
/Times-BoldR 600 _ff
(\(6.44\))_S /Times-RomanR 600 _ff
2400 2397 _m
(Examination)_S 67 _t
(of)_S 67 _t
(Equations)_S 67 _t
(\(6.43\))_S 67 _t
(and)_S 67 _t
(\(6.44\))_S 67 _t
(reveals)_S 67 _t
(that,)_S 67 _t
(as)_S 67 _t
(forward)_S 67 _t
(velocity)_S 1500 2047 _m
/Times-BoldItalicR 600 _ff
(u)_S /Times-RomanR 600 _ff
67 _t
(increases,)_S 67 _t
(the)_S 67 _t
(effective)_S 67 _t
(forward)_S 67 _t
(thrust)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(propeller)_S 67 _t
(rpm)_S 67 _t
/Times-BoldItalicR 600 _ff
(n)_S /Times-RomanR 600 _ff
67 _t
(decreases)_S 67 _t
(according)_S 67 _t
(to)_S 4950 1288 _m
(143)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1500 11855 _m
(the)_S 67 _t
(expected)_S 67 _t
(signed)_S 67 _t
(square)_S 67 _t
(law,)_S 67 _t
(similar)_S 67 _t
(to)_S 67 _t
(a)_S 67 _t
(pump)_S 67 _t
(curve)_S 67 _t
(of)_S 67 _t
(shaft)_S 67 _t
(rpm)_S 67 _t
(versus)_S 67 _t
(pressure)_S 1500 11506 _m
(head.)_S 134 _t
(Note)_S 67 _t
(that)_S 67 _t
(these)_S 67 _t
(equations)_S 67 _t
(also)_S 67 _t
(accurately)_S 67 _t
(describe)_S 67 _t
(drag)_S 67 _t
(forces)_S 67 _t
(against)_S 67 _t
(forward)_S 1500 11157 _m
(motion)_S 67 _t
(when)_S 67 _t
(a)_S 67 _t
(moving)_S 67 _t
(vehicle's)_S 67 _t
(propellers)_S 67 _t
(are)_S 67 _t
(turned)_S 67 _t
(off.)_S 134 _t
(Extensive)_S 67 _t
(test)_S 67 _t
(tank)_S 1500 10808 _m
(experimental)_S 67 _t
(data)_S 67 _t
(is)_S 67 _t
(not)_S 67 _t
(needed)_S 67 _t
(for)_S 67 _t
(measuring)_S 67 _t
(this)_S 67 _t
(predominant)_S 67 _t
(relationship)_S 67 _t
(between)_S 1500 10459 _m
(propeller)_S 67 _t
(thrust)_S 67 _t
(and)_S 67 _t
(forward)_S 67 _t
(speed.)_S 134 _t
(A)_S 67 _t
(straightforward)_S 67 _t
(measurement)_S 67 _t
(of)_S 67 _t
(steady-state)_S 1500 10110 _m
(speed)_S 67 _t
(for)_S 67 _t
(maximum)_S 67 _t
(propeller)_S 67 _t
(rpm)_S 67 _t
(precisely)_S 67 _t
(quantifies)_S 67 _t
(this)_S 67 _t
(relationship.)_S 2400 9761 _m
(Cross-body)_S 67 _t
(thruster)_S 67 _t
(propulsion)_S 67 _t
(terms)_S 67 _t
(have)_S 67 _t
(also)_S 67 _t
(been)_S 67 _t
(added)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(dynamics)_S 1500 9412 _m
(equations)_S 67 _t
(of)_S 67 _t
(motion.)_S 134 _t
(Steady-state)_S 67 _t
(thruster)_S 67 _t
(force)_S 67 _t
(is)_S 67 _t
(closely)_S 67 _t
(proportional)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(signed)_S 1500 9063 _m
(square)_S 67 _t
(of)_S 67 _t
(ordered)_S 67 _t
(motor)_S 67 _t
(voltage)_S 67 _t
(for)_S 67 _t
(the)_S 67 _t
(cross-body)_S 67 _t
(thrusters)_S 67 _t
(designed)_S 67 _t
(and)_S 67 _t
(constructed)_S 1500 8714 _m
(for)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV)_S 67 _t
(II)_S 67 _t
(\(Cody)_S 67 _t
(92\))_S 67 _t
(\(Healey)_S 67 _t
(94b\).)_S 134 _t
(This)_S 67 _t
(signed)_S 67 _t
(square)_S 67 _t
(relationship)_S 67 _t
(between)_S 1500 8365 _m
(control)_S 67 _t
(voltage)_S 67 _t
(and)_S 67 _t
(effective)_S 67 _t
(thruster)_S 67 _t
(force)_S 67 _t
(is)_S 67 _t
(shown)_S 67 _t
(in)_S 67 _t
(Equation)_S 67 _t
(\(6.45\).)_S 134 _t
(The)_S 67 _t
(sign)_S 1500 8016 _m
(convention)_S 67 _t
(for)_S 67 _t
(thruster)_S 67 _t
(voltages)_S 67 _t
(is)_S 67 _t
(that)_S 67 _t
(positive)_S 67 _t
(voltage)_S 67 _t
(results)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(force)_S 67 _t
(which)_S 67 _t
(pushes)_S 1500 7667 _m
(the)_S 67 _t
(vehicle)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(positive)_S 67 _t
(direction)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(lateral)_S 67 _t
(or)_S 67 _t
(depth)_S 67 _t
(axes.)_S 134 _t
(More)_S 67 _t
(precise)_S 1500 7318 _m
(modeling)_S 67 _t
(of)_S 67 _t
(thruster)_S 67 _t
(nonlinearities)_S 67 _t
(and)_S 67 _t
(sinusoidal-exponential)_S 67 _t
(time)_S 67 _t
(response)_S 67 _t
(is)_S 67 _t
(possible)_S 1500 6969 _m
(using)_S 67 _t
(generalized)_S 67 _t
(tunnel)_S 67 _t
(thruster)_S 67 _t
(dynamics)_S 67 _t
(models)_S 67 _t
(\(Cody)_S 67 _t
(92\))_S 67 _t
(\(Healey)_S 67 _t
(94b\))_S 1500 6620 _m
(\(Brown)_S 67 _t
(93\))_S 67 _t
(\(Belton)_S 67 _t
(93\))_S 67 _t
(\(Fossen)_S 67 _t
(94\).)_S 134 _t
(Dynamics-based)_S 67 _t
(models)_S 67 _t
(of)_S 67 _t
(thruster)_S 67 _t
(response)_S 1500 6271 _m
(must)_S 67 _t
(be)_S 67 _t
(used)_S 67 _t
(instead)_S 67 _t
(if)_S 67 _t
(thruster)_S 67 _t
(temporal)_S 67 _t
(response)_S 67 _t
(is)_S 67 _t
(significant.)_S 134 _t
(Similar)_S 67 _t
(results)_S 67 _t
(have)_S 1500 5922 _m
(been)_S 67 _t
(found)_S 67 _t
(for)_S 67 _t
(other)_S 67 _t
(thrusters)_S 67 _t
(that)_S 67 _t
(include)_S 67 _t
(thrust)_S 67 _t
(controller)_S 67 _t
(circuitry)_S 67 _t
(\(Sagatun)_S 67 _t
(91\))_S 1500 5573 _m
(\(Marks)_S 67 _t
(92\).)_S 134 _t
(A)_S 67 _t
(nontemporal)_S 67 _t
(signed)_S 67 _t
(square)_S 67 _t
(voltage)_S 67 _t
(model)_S 67 _t
(was)_S 67 _t
(found)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(reasonably)_S 1500 5224 _m
(accurate)_S 67 _t
(for)_S 67 _t
(the)_S 67 _t
(overall)_S 67 _t
(effects)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV)_S 67 _t
(thrusters.)_S 134 _t
(Open)_S 67 _t
(loop)_S 67 _t
(test)_S 67 _t
(tank)_S 1500 4875 _m
(experiments)_S 67 _t
(can)_S 67 _t
(quantify)_S 67 _t
(installed)_S 67 _t
(thruster)_S 67 _t
(performance)_S 67 _t
(versus)_S 67 _t
(time)_S 67 _t
(with)_S 67 _t
(little)_S 1500 4526 _m
(difficulty.)_S 2400 4177 _m
(Since)_S 67 _t
(an)_S 67 _t
(accurate)_S 67 _t
(force)_S 67 _t
(equation)_S 67 _t
(is)_S 67 _t
(available)_S 67 _t
(to)_S 67 _t
(model)_S 67 _t
(the)_S 67 _t
(four)_S 67 _t
(individual)_S 1500 3828 _m
(thrusters,)_S 67 _t
(force)_S 67 _t
(and)_S 67 _t
(moment)_S 67 _t
(terms)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(added)_S 67 _t
(directly)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(sway,)_S 67 _t
(heave,)_S 67 _t
(pitch)_S 67 _t
(and)_S 1500 3479 _m
(yaw)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion.)_S 134 _t
(Physical)_S 67 _t
(offsets)_S 67 _t
(of)_S 67 _t
(thruster)_S 67 _t
(centerline)_S 67 _t
(away)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(vehicle)_S 1500 3130 _m
(centroid)_S 67 _t
(are)_S 67 _t
(multiplied)_S 67 _t
(against)_S 67 _t
(forces)_S 67 _t
(to)_S 67 _t
(obtain)_S 67 _t
(corresponding)_S 67 _t
(moments,)_S 67 _t
(as)_S 67 _t
(shown)_S 67 _t
(in)_S 1500 2781 _m
(Equation)_S 67 _t
(\(6.46\).)_S 134 _t
(Opposing)_S 67 _t
(moments)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(forward)_S 67 _t
(and)_S 67 _t
(aft)_S 67 _t
(thrusters)_S 67 _t
(are)_S 67 _t
(accounted)_S 1500 2432 _m
(for)_S 67 _t
(by)_S 67 _t
(positive)_S 67 _t
(and)_S 67 _t
(negative)_S 67 _t
(thruster)_S 67 _t
(tube)_S 67 _t
(offset)_S 67 _t
(distances,)_S 67 _t
(respectively.)_S 134 _t
(This)_S 1500 2082 _m
(eliminates)_S 67 _t
(the)_S 67 _t
(need)_S 67 _t
(for)_S 67 _t
(the)_S 67 _t
(previous)_S 67 _t
/Times-BoldItalicR 600 _ff
(N)_S /Times-BoldItalicR 360 _ff
4657 2037 _m
(prop)_S 4884 2037 _m
/Times-RomanR 600 _ff
4884 2082 _m
67 _t
(formulation.)_S 4950 1288 _m
(144)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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60 _pl _cp 
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30 _pl _cp 
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(the)_S 67 _t
(surge)_S 67 _t
(equation.)_S 134 _t
(Transformation)_S 1500 5566 _m
(of)_S 67 _t
(the)_S 67 _t
(remaining)_S 67 _t
(five)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(for)_S 67 _t
(sway,)_S 67 _t
(heave,)_S 67 _t
(roll,)_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(yaw)_S 67 _t
(is)_S 1500 5217 _m
(similarly)_S 67 _t
(performed)_S 67 _t
(by)_S 67 _t
(direct)_S 67 _t
(algebraic)_S 67 _t
(manipulation)_S 67 _t
(from)_S 67 _t
(those)_S 67 _t
(versions)_S 67 _t
(presented)_S 67 _t
(in)_S 1500 4868 _m
(\(Healey)_S 67 _t
(93\).)_S 134 _t
(Thruster)_S 67 _t
(forces,)_S 67 _t
(thruster)_S 67 _t
(moments,)_S 67 _t
(propeller)_S 67 _t
(yaw)_S 67 _t
(moments)_S 67 _t
(and)_S 67 _t
(damping)_S 1500 4519 _m
(drag)_S 67 _t
(moments)_S 67 _t
(have)_S 67 _t
(been)_S 67 _t
(added)_S 67 _t
(where)_S 67 _t
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/Times-BoldR 600 _ff
(9.)_S 2400 4097 _m
(Dynamics)_S 67 _t
(Equations)_S 67 _t
(of)_S 67 _t
(Motion)_S /Times-RomanR 600 _ff
2400 3748 _m
(The)_S 67 _t
(critical)_S 67 _t
(contribution)_S 67 _t
(of)_S 67 _t
(this)_S 67 _t
(chapter)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(unambiguous)_S 67 _t
(definition)_S 67 _t
(of)_S 1500 3399 _m
(variables)_S 67 _t
(and)_S 67 _t
(coefficients,)_S 67 _t
(and)_S 67 _t
(a)_S 67 _t
(revised)_S 67 _t
(set)_S 67 _t
(of)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 1500 3050 _m
(of)_S 67 _t
(motion.)_S 134 _t
(These)_S 67 _t
(equations)_S 67 _t
(and)_S 67 _t
(the)_S 67 _t
(accompanying)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
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(implemented)_S 67 _t
(verbatim)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(accompanying)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(source)_S 67 _t
(code)_S 67 _t
(\(Brutzman)_S 67 _t
(94e\).)_S 67 _t
1500 2352 _m
(Final)_S 67 _t
(and)_S 67 _t
(complete)_S 67 _t
(forms)_S 67 _t
(for)_S 67 _t
(all)_S 67 _t
(six)_S 67 _t
(dynamics)_S 67 _t
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(of)_S 67 _t
(motion)_S 67 _t
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0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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/Times-BoldR 600 _ff
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(Equation)_S 67 _t
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(Motion)_S _u /Times-RomanR 600 _ff
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(\(6.48\))_S /Times-RomanR 600 _ff
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1702 2265 31 _pl _cp 
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_sp 1658 2237 1658 2240 1658 2242 1657 2244 1657 2246 1656 2249 1656 2251 1656 2252 1655 2253 1649 2252 1649 2251 1650 2251 1652 2251 1652 2249 1653 2246 
1654 2242 1654 2238 1654 2235 1655 2231 1655 2230 1665 2247 1667 2231 1668 2231 1671 2234 1673 2237 1676 2240 1678 2243 1679 2245 1680 2247 1681 2248 
1681 2250 1680 2252 1678 2253 1677 2252 1676 2251 1676 2250 1677 2249 1678 2248 1678 2247 1678 2246 1678 2245 1677 2244 1676 2243 1675 2241 1674 2239 
1672 2237 1670 2235 1668 2253 1668 2253 49 _pl _cp 
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_sp 1717 2246 1710 2237 1708 2235 1706 2233 1705 2232 1703 2232 1703 2231 1712 2231 1712 2232 1711 2232 1710 2232 1710 2233 1711 2234 1712 2237 1718 2244 
1720 2237 1721 2235 1721 2234 1721 2233 1721 2232 1720 2232 1718 2232 1718 2231 1730 2231 1730 2232 1729 2232 1727 2233 1726 2235 1725 2237 1721 2248 
1722 2250 1723 2251 1724 2253 1725 2254 1726 2256 1728 2257 1729 2259 1730 2260 1732 2261 1734 2262 1734 2264 1725 2264 1725 2262 1725 2262 1727 2262 
1727 2261 1727 2260 1726 2259 1725 2258 1725 2257 1720 2251 1718 2257 1717 2259 1717 2260 1716 2261 1717 2262 1718 2262 1719 2262 1720 2264 1708 2264 
1708 2262 1709 2262 1710 2262 1711 2261 1712 2259 1713 2257 66 _pl _cp 
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_sp 1745 2229 1745 2228 1744 2226 1743 2225 1743 2223 1742 2222 1741 2220 1739 2217 1737 2216 1737 2216 1737 2217 1737 2218 1737 2218 1740 2230 1735 2229 
1735 2228 1735 2228 1736 2228 1737 2227 1737 2227 1736 2226 1734 2219 1734 2219 1734 2218 1734 2217 1734 2216 1735 2215 1736 2214 1738 2215 1739 2216 
1740 2217 1741 2218 1742 2220 1743 2222 1742 2219 1742 2218 1742 2216 1743 2215 1744 2214 1746 2215 1748 2218 1748 2219 1747 2218 1746 2217 1746 2216 
1745 2216 1745 2216 1745 2216 1745 2217 1745 2218 1745 2219 1745 2220 1746 2222 1746 2224 1747 2227 1748 2229 56 _pl _cp 
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_sp 1756 2219 1756 2221 1756 2222 1756 2224 1756 2225 1755 2228 1755 2230 1750 2229 1750 2228 1751 2228 1752 2228 1753 2227 1754 2224 1754 2221 1754 2218 
1754 2215 1755 2214 1761 2225 1763 2215 1763 2215 1765 2217 1767 2219 1768 2221 1770 2223 1771 2225 1772 2227 1771 2229 1770 2230 1769 2229 1769 2228 
1769 2228 1769 2227 1770 2226 1770 2226 1770 2225 1770 2224 1769 2222 1767 2220 1766 2219 1765 2218 1763 2229 1763 2230 42 _pl _cp 
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_sp 1802 2225 1806 2238 1800 2237 1800 2236 1801 2236 1802 2236 1802 2235 1802 2234 1802 2233 1797 2218 1797 2216 1797 2216 1797 2216 1797 2216 1797 2216 
1799 2215 1801 2214 1803 2214 1805 2215 1807 2216 1809 2218 1810 2220 1811 2222 1812 2223 1812 2225 1812 2227 1811 2229 1810 2230 1808 2230 1808 2230 
1807 2229 1806 2229 1805 2228 1803 2227 34 _pl _cp 1800 2216 _m
_sp 1800 2216 1801 2216 1802 2215 1804 2216 1806 2217 1807 2219 1808 2221 1809 2223 1809 2225 1808 2227 1807 2228 1806 2227 1804 2226 1803 2224 1802 2222 
1801 2220 1801 2219 1800 2217 18 _pl _cp 
0 g _f _s _s 
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_sp 1850 2226 1851 2230 1845 2229 1845 2228 1846 2228 1847 2228 1847 2227 1847 2227 1847 2226 1843 2211 1843 2209 1841 2209 1841 2209 1841 2208 1847 2208 
1848 2209 1847 2209 1846 2209 1846 2210 1846 2210 1846 2210 1846 2211 1847 2215 1848 2214 1849 2214 1851 2214 1852 2215 1854 2216 1855 2217 1857 2219 
1858 2221 1859 2223 1859 2225 1859 2227 1858 2229 1857 2230 1855 2230 1854 2230 1853 2229 1851 2228 40 _pl _cp 1848 2217 _m
_sp 1848 2217 1847 2217 1847 2216 1848 2216 1849 2215 1851 2216 1852 2217 1854 2219 1855 2221 1856 2224 1856 2226 1855 2227 1854 2228 1853 2228 1851 2227 
1850 2226 1850 2224 1849 2223 1849 2221 19 _pl _cp 
0 g _f _s _s 
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_sp 1867 2225 1870 2238 1864 2237 1864 2236 1865 2236 1866 2236 1866 2235 1866 2234 1866 2233 1862 2218 1861 2216 1861 2216 1861 2216 1861 2216 1862 2216 
1864 2215 1866 2214 1868 2214 1870 2215 1871 2216 1873 2218 1874 2220 1875 2222 1876 2223 1876 2225 1876 2227 1875 2229 1874 2230 1873 2230 1872 2230 
1871 2229 1869 2228 32 _pl _cp 1864 2216 _m
_sp 1864 2216 1865 2216 1866 2215 1868 2216 1870 2217 1871 2219 1872 2221 1873 2223 1873 2225 1873 2227 1871 2228 1870 2227 1868 2226 1867 2224 1866 2222 
1865 2220 1865 2219 1864 2217 18 _pl _cp 
0 g _f _s _s 
0 g 1965 2246 _m
_sp 1965 2246 1958 2237 1956 2235 1955 2233 1953 2232 1952 2232 1951 2231 1960 2231 1960 2232 1960 2232 1959 2232 1958 2233 1959 2234 1961 2237 1966 2244 
1969 2237 1970 2235 1970 2234 1970 2233 1969 2232 1968 2232 1967 2232 1966 2231 1978 2231 1979 2232 1978 2232 1976 2233 1974 2235 1974 2237 1969 2248 
1970 2250 1972 2251 1973 2253 1974 2254 1975 2256 1976 2257 1977 2259 1978 2260 1980 2261 1982 2262 1983 2264 1974 2264 1973 2262 1974 2262 1975 2262 
1976 2261 1975 2260 1974 2259 1974 2258 1973 2257 1968 2251 1966 2257 1965 2259 1965 2260 1965 2261 1965 2262 1967 2262 1968 2262 1968 2264 1957 2264 
1956 2262 1957 2262 1958 2262 1959 2261 1960 2259 1961 2257 66 _pl _cp 
0 g _f _s _s 
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_sp 1994 2229 1993 2228 1993 2226 1992 2225 1992 2223 1991 2222 1990 2220 1988 2217 1986 2216 1985 2216 1985 2217 1985 2218 1985 2218 1988 2230 1983 2229 
1983 2228 1984 2228 1985 2228 1985 2227 1985 2227 1985 2226 1983 2219 1983 2219 1983 2218 1982 2217 1982 2216 1983 2215 1984 2214 1986 2215 1988 2216 
1989 2217 1989 2218 1990 2220 1992 2222 1991 2219 1991 2218 1990 2216 1991 2215 1992 2214 1993 2214 1995 2215 1996 2216 1997 2218 1996 2219 1996 2218 
1995 2217 1994 2216 1994 2216 1993 2216 1993 2216 1993 2217 1993 2218 1994 2219 1994 2220 1995 2222 1995 2224 1996 2227 1996 2229 58 _pl _cp 
0 g _f _s _s 
0 g 2005 2219 _m
_sp 2005 2219 2005 2221 2005 2222 2005 2224 2004 2225 2004 2228 2003 2230 1999 2229 1999 2228 2000 2228 2001 2228 2001 2227 2002 2224 2002 2221 2003 2218 
2003 2215 2003 2214 2010 2225 2011 2215 2012 2215 2014 2217 2015 2219 2017 2221 2018 2223 2020 2225 2020 2227 2019 2229 2018 2230 2018 2229 2017 2228 
2017 2228 2018 2227 2019 2226 2019 2226 2019 2225 2018 2224 2017 2222 2015 2220 2014 2219 2013 2218 2012 2229 2011 2230 42 _pl _cp 
0 g _f _s _s 
0 g 2045 2220 _m
_sp 2045 2220 2044 2214 2045 2214 2045 2215 2046 2215 2046 2215 2046 2215 2047 2215 2048 2215 2049 2214 2050 2214 2052 2214 2054 2215 2055 2217 2055 2218 
2055 2219 2055 2221 2054 2222 2052 2223 2050 2225 2050 2227 2051 2228 2052 2229 2054 2228 2056 2225 2056 2225 2057 2230 2057 2230 2056 2229 2055 2229 
2055 2229 2054 2229 2053 2230 2052 2230 2050 2230 2048 2229 2047 2227 2047 2226 2047 2225 2048 2224 2049 2223 2050 2221 2052 2219 2052 2217 2051 2216 
2050 2215 2048 2215 2047 2216 2046 2218 2045 2220 50 _pl _cp 
0 g _f _s _s 
0 g 2095 2226 _m
_sp 2095 2226 2096 2230 2090 2229 2090 2228 2091 2228 2092 2228 2092 2227 2092 2227 2092 2226 2088 2211 2087 2209 2086 2209 2086 2209 2086 2208 2092 2208 
2092 2209 2091 2209 2091 2209 2090 2210 2090 2210 2090 2210 2091 2211 2092 2215 2093 2214 2094 2214 2096 2214 2097 2215 2099 2216 2100 2217 2101 2219 
2103 2221 2104 2223 2104 2225 2104 2227 2103 2229 2101 2230 2100 2230 2099 2230 2097 2229 2096 2228 40 _pl _cp 2092 2217 _m
_sp 2092 2217 2092 2217 2092 2216 2093 2216 2094 2215 2096 2216 2097 2217 2098 2219 2100 2221 2101 2224 2101 2226 2100 2227 2099 2228 2098 2228 2096 2227 
2095 2226 2095 2224 2094 2223 2093 2221 19 _pl _cp 
0 g _f _s _s 
0 g 2105 2220 _m
_sp 2105 2220 2105 2214 2105 2214 2106 2215 2106 2215 2106 2215 2106 2215 2107 2215 2108 2215 2109 2214 2110 2214 2112 2214 2114 2215 2115 2217 2116 2218 
2116 2219 2115 2221 2114 2222 2113 2223 2111 2225 2110 2227 2111 2228 2112 2229 2115 2228 2116 2225 2117 2225 2118 2230 2117 2230 2117 2229 2116 2229 
2115 2229 2114 2229 2113 2230 2112 2230 2109 2229 2108 2226 2108 2225 2108 2224 2109 2223 2111 2221 2113 2219 2113 2217 2112 2216 2110 2215 2109 2215 
2107 2216 2106 2218 2106 2220 48 _pl _cp 
0 g _f _s _s 
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_sp 942 2144 941 2142 941 2141 941 2139 940 2138 939 2136 938 2134 937 2132 936 2130 934 2127 932 2126 931 2124 929 2124 929 2124 929 2125 
929 2126 929 2127 934 2144 926 2143 926 2142 927 2142 928 2142 928 2141 928 2140 928 2138 925 2128 925 2127 925 2126 925 2125 925 2124 
926 2122 927 2121 929 2121 930 2122 932 2123 933 2124 934 2125 935 2127 936 2129 938 2132 937 2128 937 2126 937 2124 938 2122 940 2121 
941 2121 942 2122 944 2124 946 2127 945 2128 945 2127 943 2125 942 2124 941 2124 941 2124 941 2124 941 2125 941 2126 941 2128 942 2129 
942 2131 943 2133 943 2134 943 2135 945 2141 946 2144 66 _pl _cp 
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_sp 987 2144 986 2142 986 2141 986 2139 985 2138 984 2136 983 2134 982 2132 981 2130 979 2127 977 2126 976 2124 974 2124 974 2124 974 2125 
974 2126 974 2127 979 2144 971 2143 971 2142 972 2142 973 2142 973 2141 973 2140 973 2138 970 2128 970 2127 970 2126 970 2125 970 2124 
971 2122 972 2121 974 2121 975 2122 977 2123 978 2124 979 2125 980 2127 981 2129 983 2132 982 2128 982 2126 982 2124 983 2122 985 2121 
986 2121 987 2122 989 2124 991 2127 990 2128 990 2127 988 2125 987 2124 986 2124 986 2124 986 2124 986 2125 986 2126 986 2128 987 2129 
987 2131 988 2133 988 2134 988 2135 990 2141 991 2144 66 _pl _cp 
0 g _f _s _s 
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_sp 1049 2137 1042 2128 1040 2126 1039 2124 1037 2123 1036 2123 1035 2122 1044 2122 1044 2123 1044 2123 1043 2123 1042 2124 1043 2125 1045 2128 1050 2135 
1053 2128 1054 2126 1054 2125 1054 2124 1053 2123 1052 2123 1051 2123 1050 2122 1062 2122 1063 2123 1062 2123 1060 2124 1058 2126 1058 2128 1053 2139 
1054 2141 1056 2142 1057 2144 1058 2145 1059 2147 1060 2148 1061 2150 1062 2151 1064 2152 1066 2153 1067 2155 1058 2155 1057 2153 1058 2153 1059 2153 
1060 2152 1059 2151 1058 2150 1058 2149 1057 2148 1052 2142 1050 2148 1049 2150 1049 2151 1049 2152 1049 2153 1051 2153 1052 2153 1052 2155 1041 2155 
1040 2153 1041 2153 1042 2153 1043 2152 1044 2150 1045 2148 66 _pl _cp 
0 g _f _s _s 
0 g 1078 2120 _m
_sp 1078 2120 1077 2119 1077 2117 1076 2116 1076 2114 1075 2113 1074 2111 1072 2108 1070 2107 1069 2107 1069 2108 1069 2109 1069 2109 1072 2121 1067 2120 
1067 2119 1068 2119 1069 2119 1069 2118 1069 2118 1069 2117 1067 2110 1067 2110 1067 2109 1066 2108 1066 2107 1067 2106 1068 2105 1070 2106 1072 2107 
1073 2108 1073 2109 1074 2111 1076 2113 1075 2110 1075 2109 1074 2107 1075 2106 1076 2105 1077 2105 1079 2106 1080 2107 1081 2109 1080 2110 1080 2109 
1079 2108 1078 2107 1078 2107 1077 2107 1077 2107 1077 2108 1077 2109 1078 2110 1078 2111 1079 2113 1079 2115 1080 2118 1080 2120 58 _pl _cp 
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_sp 1108 2120 1107 2119 1107 2117 1106 2116 1106 2114 1105 2113 1104 2111 1102 2108 1100 2107 1099 2107 1099 2108 1099 2109 1099 2109 1102 2121 1097 2120 
1097 2119 1098 2119 1099 2119 1099 2118 1099 2118 1099 2117 1097 2110 1097 2110 1097 2109 1096 2108 1096 2107 1097 2106 1098 2105 1100 2106 1102 2107 
1103 2108 1103 2109 1104 2111 1106 2113 1105 2110 1105 2109 1104 2107 1105 2106 1106 2105 1107 2105 1109 2106 1110 2107 1111 2109 1110 2110 1110 2109 
1109 2108 1108 2107 1108 2107 1107 2107 1107 2107 1107 2108 1107 2109 1108 2110 1108 2111 1109 2113 1109 2115 1110 2118 1110 2120 58 _pl _cp 
0 g _f _s _s 
0 g 1156 2116 _m
_sp 1156 2116 1159 2129 1154 2128 1153 2127 1155 2127 1156 2127 1156 2126 1156 2125 1155 2124 1151 2109 1151 2107 1151 2107 1151 2107 1151 2107 1151 2107 
1153 2106 1155 2105 1157 2105 1159 2106 1160 2107 1162 2109 1163 2111 1165 2113 1166 2114 1166 2116 1166 2118 1165 2120 1163 2121 1162 2121 1161 2121 
1160 2120 1158 2119 32 _pl _cp 1154 2107 _m
_sp 1154 2107 1154 2107 1155 2106 1157 2107 1159 2108 1160 2110 1162 2112 1163 2114 1163 2116 1162 2118 1160 2119 1159 2118 1158 2117 1156 2115 1155 2113 
1154 2111 1154 2110 1154 2108 18 _pl _cp 
0 g _f _s _s 
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_sp 1193 2116 1196 2129 1191 2128 1191 2127 1192 2127 1193 2127 1193 2126 1193 2125 1193 2124 1188 2109 1188 2107 1188 2107 1188 2107 1188 2107 1188 2107 
1190 2106 1192 2105 1194 2105 1196 2106 1197 2107 1199 2109 1201 2111 1202 2113 1203 2114 1203 2116 1203 2118 1202 2120 1200 2121 1199 2121 1198 2121 
1197 2120 1195 2119 32 _pl _cp 1191 2107 _m
_sp 1191 2107 1191 2107 1193 2106 1195 2107 1196 2108 1198 2110 1199 2112 1200 2114 1200 2116 1199 2118 1198 2119 1197 2118 1195 2117 1194 2115 1192 2113 
1191 2111 1191 2110 1191 2108 18 _pl _cp 
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_sp 1246 2120 1247 2124 1242 2123 1241 2122 1243 2122 1244 2122 1244 2122 1244 2121 1243 2120 1240 2106 1239 2104 1238 2103 1237 2103 1237 2102 1244 2102 
1244 2103 1243 2103 1242 2103 1242 2104 1242 2104 1242 2105 1242 2106 1243 2109 1244 2109 1245 2109 1247 2109 1249 2110 1250 2111 1252 2112 1253 2114 
1254 2116 1255 2118 1255 2120 1254 2123 1252 2124 1251 2124 1249 2123 1248 2122 38 _pl _cp 1244 2112 _m
_sp 1244 2112 1244 2111 1244 2111 1244 2110 1245 2109 1247 2110 1249 2111 1250 2113 1251 2115 1252 2118 1252 2120 1252 2121 1250 2122 1249 2122 1248 2121 
1247 2120 1246 2119 1246 2117 1245 2115 19 _pl _cp 
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_sp 1263 2120 1266 2132 1261 2131 1260 2130 1262 2130 1263 2130 1263 2129 1263 2129 1262 2128 1258 2112 1258 2111 1258 2111 1258 2110 1258 2110 1258 2110 
1260 2109 1262 2109 1264 2109 1266 2110 1267 2111 1269 2112 1270 2114 1272 2116 1273 2117 1273 2119 1273 2121 1272 2123 1270 2124 1269 2124 1268 2124 
1267 2124 1265 2122 32 _pl _cp 1261 2111 _m
_sp 1261 2111 1261 2110 1262 2109 1264 2110 1266 2111 1267 2113 1269 2116 1270 2118 1270 2120 1269 2121 1267 2122 1266 2122 1265 2121 1263 2119 1262 2117 
1261 2115 1261 2113 1261 2112 18 _pl _cp 
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_sp 1362 2137 1354 2128 1352 2126 1351 2124 1349 2123 1348 2123 1348 2122 1356 2122 1357 2123 1356 2123 1355 2123 1355 2124 1356 2125 1357 2128 1362 2135 
1365 2128 1366 2126 1366 2125 1366 2124 1366 2123 1364 2123 1363 2123 1363 2122 1374 2122 1375 2123 1374 2123 1372 2124 1370 2126 1370 2128 1366 2139 
1367 2141 1368 2142 1369 2144 1370 2145 1371 2147 1373 2148 1374 2150 1375 2151 1377 2152 1378 2153 1379 2155 1370 2155 1370 2153 1370 2153 1371 2153 
1372 2152 1372 2151 1371 2150 1370 2149 1369 2148 1365 2142 1362 2148 1362 2150 1361 2151 1361 2152 1362 2153 1363 2153 1364 2153 1364 2155 1353 2155 
1353 2153 1353 2153 1354 2153 1356 2152 1357 2150 1358 2148 66 _pl _cp 
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_sp 1390 2120 1390 2119 1389 2117 1388 2116 1388 2114 1387 2113 1386 2111 1384 2108 1382 2107 1382 2107 1381 2108 1381 2109 1382 2109 1385 2121 1380 2120 
1379 2119 1380 2119 1381 2119 1381 2118 1381 2118 1381 2117 1379 2110 1379 2110 1379 2109 1379 2108 1379 2107 1379 2106 1380 2105 1382 2106 1384 2107 
1385 2108 1386 2109 1387 2111 1388 2113 1387 2110 1387 2109 1387 2107 1387 2106 1389 2105 1391 2106 1393 2109 1393 2110 1392 2109 1391 2108 1390 2107 
1390 2107 1390 2107 1389 2107 1389 2108 1390 2109 1390 2110 1390 2111 1391 2113 1391 2115 1392 2118 1393 2120 56 _pl _cp 
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_sp 1420 2120 1420 2119 1419 2117 1418 2116 1418 2114 1417 2113 1416 2111 1414 2108 1412 2107 1412 2107 1411 2108 1411 2109 1412 2109 1415 2121 1410 2120 
1409 2119 1410 2119 1411 2119 1411 2118 1411 2118 1411 2117 1409 2110 1409 2110 1409 2109 1409 2108 1409 2107 1409 2106 1410 2105 1412 2106 1414 2107 
1415 2108 1416 2109 1417 2111 1418 2113 1417 2110 1417 2109 1417 2107 1417 2106 1419 2105 1421 2106 1423 2109 1423 2110 1422 2109 1421 2108 1420 2107 
1420 2107 1420 2107 1419 2107 1419 2108 1420 2109 1420 2110 1420 2111 1421 2113 1421 2115 1422 2118 1423 2120 56 _pl _cp 
0 g _f _s _s 
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_sp 1462 2111 1461 2105 1462 2105 1462 2106 1463 2106 1463 2106 1463 2106 1464 2106 1465 2106 1466 2105 1467 2105 1469 2105 1471 2106 1472 2108 1472 2109 
1472 2110 1472 2112 1471 2113 1469 2114 1468 2116 1467 2118 1468 2119 1469 2120 1471 2119 1473 2116 1474 2116 1474 2121 1474 2121 1473 2120 1473 2120 
1472 2120 1471 2120 1470 2121 1469 2121 1467 2121 1465 2120 1464 2118 1464 2117 1464 2116 1465 2115 1466 2114 1468 2112 1469 2110 1470 2108 1469 2107 
1467 2106 1466 2106 1464 2107 1463 2109 1463 2111 50 _pl _cp 
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_sp 1495 2111 1495 2105 1495 2105 1496 2106 1496 2106 1496 2106 1496 2106 1497 2106 1498 2106 1499 2105 1500 2105 1503 2105 1505 2106 1506 2108 1506 2109 
1506 2110 1505 2112 1504 2113 1503 2114 1501 2116 1500 2118 1501 2119 1502 2120 1505 2119 1506 2116 1507 2116 1508 2121 1507 2121 1507 2120 1506 2120 
1505 2120 1504 2120 1503 2121 1502 2121 1499 2120 1498 2117 1498 2116 1499 2115 1500 2114 1501 2112 1503 2110 1503 2108 1502 2107 1501 2106 1499 2106 
1498 2107 1497 2109 1496 2111 48 _pl _cp 
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1549 2103 1548 2103 1547 2103 1547 2104 1547 2104 1547 2105 1547 2106 1548 2109 1549 2109 1550 2109 1552 2109 1553 2110 1555 2111 1556 2112 1558 2114 
1559 2116 1560 2118 1560 2120 1559 2123 1556 2124 1555 2124 1554 2123 1552 2122 38 _pl _cp 1549 2112 _m
_sp 1549 2112 1548 2111 1548 2111 1549 2110 1550 2109 1552 2110 1553 2111 1555 2113 1556 2115 1557 2118 1557 2120 1556 2121 1555 2122 1554 2122 1552 2121 
1551 2120 1551 2119 1550 2117 1550 2115 19 _pl _cp 
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_sp 1561 2114 1561 2109 1561 2109 1562 2109 1562 2109 1562 2109 1562 2109 1563 2109 1564 2109 1565 2109 1566 2109 1569 2109 1571 2110 1572 2111 1572 2112 
1572 2113 1571 2115 1570 2116 1569 2118 1567 2120 1566 2121 1567 2122 1568 2123 1571 2122 1572 2119 1573 2119 1574 2124 1573 2124 1573 2123 1572 2123 
1571 2123 1570 2124 1569 2124 1568 2124 1565 2123 1564 2121 1564 2120 1565 2118 1566 2117 1567 2115 1569 2113 1569 2112 1568 2110 1567 2109 1565 2109 
1564 2110 1563 2112 1562 2114 48 _pl _cp 
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1666 2128 1667 2126 1667 2125 1667 2124 1667 2123 1665 2123 1664 2123 1664 2122 1675 2122 1676 2123 1675 2123 1673 2124 1671 2126 1671 2128 1667 2139 
1668 2141 1669 2142 1670 2144 1671 2145 1672 2147 1674 2148 1675 2150 1676 2151 1678 2152 1679 2153 1680 2155 1671 2155 1671 2153 1671 2153 1672 2153 
1673 2152 1673 2151 1672 2150 1671 2149 1670 2148 1666 2142 1663 2148 1663 2150 1662 2151 1662 2152 1663 2153 1664 2153 1665 2153 1665 2155 1654 2155 
1654 2153 1654 2153 1655 2153 1657 2152 1658 2150 1659 2148 66 _pl _cp 
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_sp 1691 2120 1691 2119 1690 2117 1689 2116 1689 2114 1688 2113 1687 2111 1685 2108 1683 2107 1683 2107 1682 2108 1682 2109 1683 2109 1686 2121 1681 2120 
1680 2119 1681 2119 1682 2119 1682 2118 1682 2118 1682 2117 1680 2110 1680 2110 1680 2109 1680 2108 1680 2107 1680 2106 1681 2105 1683 2106 1685 2107 
1686 2108 1687 2109 1688 2111 1689 2113 1688 2110 1688 2109 1688 2107 1688 2106 1690 2105 1692 2106 1694 2109 1694 2110 1693 2109 1692 2108 1691 2107 
1691 2107 1691 2107 1690 2107 1690 2108 1691 2109 1691 2110 1691 2111 1692 2113 1692 2115 1693 2118 1694 2120 56 _pl _cp 
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_sp 1721 2120 1721 2119 1720 2117 1719 2116 1719 2114 1718 2113 1717 2111 1715 2108 1713 2107 1713 2107 1712 2108 1712 2109 1713 2109 1716 2121 1711 2120 
1710 2119 1711 2119 1712 2119 1712 2118 1712 2118 1712 2117 1710 2110 1710 2110 1710 2109 1710 2108 1710 2107 1710 2106 1711 2105 1713 2106 1715 2107 
1716 2108 1717 2109 1718 2111 1719 2113 1718 2110 1718 2109 1718 2107 1718 2106 1720 2105 1722 2106 1724 2109 1724 2110 1723 2109 1722 2108 1721 2107 
1721 2107 1721 2107 1720 2107 1720 2108 1721 2109 1721 2110 1721 2111 1722 2113 1722 2115 1723 2118 1724 2120 56 _pl _cp 
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1683 1880 1683 1881 1683 1881 1688 1901 1683 1900 1682 1899 1684 1899 1685 1899 1685 1898 1685 1897 1684 1896 1683 1891 1682 1892 1680 1893 1679 1893 
1677 1892 1676 1891 1674 1889 1673 1887 1671 1885 1670 1883 1670 1881 1671 1878 1674 1877 1677 1878 1679 1879 1680 1880 42 _pl _cp 1673 1881 _m
_sp 1673 1881 1674 1880 1676 1879 1678 1880 1680 1882 1681 1883 1681 1884 1682 1886 1682 1887 1682 1889 1682 1890 1681 1891 1680 1892 1678 1891 1676 1888 
1675 1886 1674 1885 1673 1883 1673 1881 1673 1881 20 _pl _cp 
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1799 1898 1800 1899 1804 1916 1797 1915 1796 1914 1798 1914 1799 1914 1799 1913 1799 1912 1799 1910 1796 1900 1796 1899 1796 1898 1795 1897 1795 1896 
1796 1894 1798 1893 1800 1893 1801 1894 1803 1895 1804 1896 1805 1897 1806 1899 1807 1901 1809 1904 1808 1900 1808 1898 1807 1896 1808 1894 1810 1893 
1812 1893 1813 1894 1815 1896 1817 1899 1816 1900 1815 1899 1814 1897 1813 1896 1812 1896 1812 1896 1811 1896 1811 1897 1812 1898 1812 1900 1812 1901 
1813 1903 1813 1905 1814 1906 1814 1907 1815 1913 1816 1916 66 _pl _cp 
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1844 1898 1845 1899 1849 1916 1842 1915 1841 1914 1843 1914 1844 1914 1844 1913 1844 1912 1844 1910 1841 1900 1841 1899 1841 1898 1840 1897 1840 1896 
1841 1894 1843 1893 1845 1893 1846 1894 1848 1895 1849 1896 1850 1897 1851 1899 1852 1901 1854 1904 1853 1900 1853 1898 1852 1896 1853 1894 1855 1893 
1857 1893 1858 1894 1860 1896 1862 1899 1861 1900 1860 1899 1859 1897 1858 1896 1857 1896 1857 1896 1856 1896 1856 1897 1857 1898 1857 1900 1857 1901 
1858 1903 1858 1905 1859 1906 1859 1907 1860 1913 1861 1916 66 _pl _cp 
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_sp 1479 2694 1460 2694 1460 2692 1479 2692 4 _pl _cp 
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0 g _f _s _s 
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0 g _f _s _s 
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0 g _f _s _s 
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0 g _f _s _s 
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0 g _f _s _s 
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0 g _f _s _s 
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_sp 1004 2159 1004 2109 1006 2109 1006 2159 4 _pl _cp 
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_sp 1090 2130 1090 2097 1091 2097 1091 2130 4 _pl _cp 
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_sp 1120 2130 1120 2097 1121 2097 1121 2130 4 _pl _cp 
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_sp 1311 2145 1311 2137 1303 2137 1303 2135 1311 2135 1311 2127 1313 2127 1313 2135 1322 2135 1322 2137 1313 2137 1313 2145 12 _pl _cp 
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_sp 1402 2130 1402 2097 1403 2097 1403 2130 4 _pl _cp 
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_sp 1432 2130 1432 2097 1433 2097 1433 2130 4 _pl _cp 
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_sp 1612 2145 1612 2137 1604 2137 1604 2135 1612 2135 1612 2127 1614 2127 1614 2135 1623 2135 1623 2137 1614 2137 1614 2145 12 _pl _cp 
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_sp 1733 2130 1733 2097 1734 2097 1734 2130 4 _pl _cp 
0 g _f _s _s 
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445 2858 443 2857 442 2857 440 2856 439 2854 438 2851 438 2849 437 2847 437 2846 437 2844 25 _pl _cp 453 2847 _m
_sp 453 2847 453 2843 452 2840 450 2839 447 2838 445 2839 443 2840 442 2843 441 2847 442 2851 443 2854 445 2855 447 2856 450 2855 452 2854 
453 2851 16 _pl _cp 
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770 2607 768 2606 767 2605 765 2604 764 2602 763 2600 762 2598 762 2596 762 2594 762 2592 25 _pl _cp 778 2595 _m
_sp 778 2595 777 2591 776 2589 774 2587 772 2586 769 2587 768 2589 766 2592 766 2596 766 2600 768 2602 769 2604 772 2605 775 2604 777 2602 
778 2599 16 _pl _cp 
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_sp 762 2394 766 2394 766 2406 768 2405 769 2404 771 2403 772 2403 776 2404 779 2406 781 2410 782 2414 781 2419 779 2423 776 2425 772 2426 
770 2426 768 2425 767 2424 765 2423 764 2421 763 2419 762 2417 762 2415 762 2413 762 2411 25 _pl _cp 778 2414 _m
_sp 778 2414 777 2410 776 2408 774 2406 772 2405 769 2406 768 2408 766 2411 766 2415 766 2419 768 2421 769 2423 772 2424 775 2423 777 2421 
778 2418 16 _pl _cp 
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1599 2415 1601 2414 1603 2413 1606 2414 1608 2415 1609 2417 1610 2420 1610 2422 1610 2423 1609 2424 1608 2426 1607 2427 1606 2428 1603 2430 1602 2431 
1601 2432 1601 2433 1601 2434 1602 2434 1603 2433 1605 2432 1607 2430 37 _pl _cp 1607 2420 _m
_sp 1607 2420 1607 2418 1606 2416 1605 2415 1604 2414 1602 2415 1601 2416 1600 2418 1600 2420 1600 2423 1601 2425 1602 2426 1604 2426 1605 2426 1606 2425 
1607 2423 16 _pl _cp 
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1639 2448 1637 2444 1636 2439 1637 2435 1639 2432 1642 2430 1646 2429 1650 2430 1653 2432 1655 2436 1656 2440 1656 2443 1655 2445 1654 2447 1653 2448 
1651 2450 1649 2452 1647 2453 1645 2454 1644 2455 1643 2456 1642 2458 1642 2459 1643 2460 1643 2460 1644 2460 1645 2459 1647 2458 1648 2457 1650 2455 
45 _pl _cp 1652 2440 _m
_sp 1652 2440 1651 2436 1650 2433 1648 2432 1646 2431 1643 2432 1642 2433 1640 2436 1640 2440 1640 2444 1642 2446 1643 2448 1646 2449 1649 2448 1651 2447 
1652 2444 16 _pl _cp 
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1842 2415 1844 2414 1846 2413 1849 2414 1851 2415 1852 2417 1853 2420 1853 2422 1853 2423 1852 2424 1851 2426 1850 2427 1849 2428 1846 2430 1845 2431 
1844 2432 1844 2433 1844 2434 1845 2434 1846 2433 1848 2432 1850 2430 37 _pl _cp 1850 2420 _m
_sp 1850 2420 1850 2418 1849 2416 1848 2415 1847 2414 1845 2415 1844 2416 1843 2418 1843 2420 1843 2423 1844 2425 1845 2426 1847 2426 1848 2426 1849 2425 
1850 2423 16 _pl _cp 
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1875 2439 1876 2435 1878 2432 1881 2430 1885 2429 1889 2430 1892 2432 1894 2436 1895 2440 1895 2443 1894 2445 1893 2447 1892 2448 1890 2450 1888 2452 
1886 2453 1885 2454 1883 2455 1882 2456 1882 2458 1881 2459 1882 2460 1883 2460 1884 2460 1885 2459 1886 2458 1888 2457 1890 2455 43 _pl _cp 1891 2440 _m
_sp 1891 2440 1890 2436 1889 2433 1887 2432 1885 2431 1882 2432 1881 2433 1879 2436 1879 2440 1879 2444 1881 2446 1882 2448 1885 2449 1888 2448 1890 2447 
1891 2444 16 _pl _cp 
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1594 2321 1596 2320 1598 2319 1601 2320 1603 2321 1604 2323 1605 2326 1605 2328 1605 2329 1604 2330 1603 2332 1602 2333 1601 2334 1598 2336 1597 2337 
1596 2338 1596 2339 1596 2340 1597 2340 1598 2339 1600 2338 1602 2336 37 _pl _cp 1602 2326 _m
_sp 1602 2326 1602 2324 1601 2322 1600 2321 1599 2320 1597 2321 1596 2322 1595 2324 1595 2326 1595 2329 1596 2331 1597 2332 1599 2332 1600 2332 1601 2331 
1602 2329 16 _pl _cp 
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1637 2354 1635 2350 1634 2345 1635 2341 1637 2338 1640 2336 1644 2335 1648 2336 1651 2338 1653 2342 1654 2346 1654 2349 1654 2351 1653 2353 1652 2354 
1650 2356 1647 2358 1645 2359 1644 2360 1643 2361 1642 2362 1641 2364 1640 2365 1641 2366 1642 2366 1643 2366 1644 2365 1645 2364 1647 2363 1649 2361 
45 _pl _cp 1650 2346 _m
_sp 1650 2346 1650 2342 1649 2339 1647 2338 1644 2337 1642 2338 1640 2339 1639 2342 1639 2346 1639 2350 1640 2352 1642 2354 1644 2355 1647 2354 1649 2353 
1650 2350 16 _pl _cp 
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1833 2321 1835 2320 1837 2319 1840 2320 1842 2321 1843 2323 1844 2326 1844 2328 1844 2329 1843 2330 1842 2332 1841 2333 1840 2334 1837 2336 1836 2337 
1835 2338 1835 2339 1835 2340 1836 2340 1837 2339 1839 2338 1841 2336 37 _pl _cp 1841 2326 _m
_sp 1841 2326 1841 2324 1840 2322 1839 2321 1838 2320 1836 2321 1835 2322 1834 2324 1834 2326 1834 2329 1835 2331 1836 2332 1838 2332 1839 2332 1840 2331 
1841 2329 16 _pl _cp 
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1876 2354 1874 2350 1873 2345 1874 2341 1876 2338 1879 2336 1883 2335 1887 2336 1890 2338 1892 2342 1893 2346 1893 2349 1893 2351 1892 2353 1891 2354 
1889 2356 1886 2358 1884 2359 1883 2360 1882 2361 1881 2362 1880 2364 1879 2365 1880 2366 1881 2366 1882 2366 1883 2365 1884 2364 1886 2363 1888 2361 
45 _pl _cp 1889 2346 _m
_sp 1889 2346 1889 2342 1888 2339 1886 2338 1883 2337 1881 2338 1879 2339 1878 2342 1878 2346 1878 2350 1879 2352 1881 2354 1883 2355 1886 2354 1888 2353 
1889 2350 16 _pl _cp 
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770 2224 768 2223 767 2222 765 2221 764 2219 763 2217 762 2215 762 2213 762 2211 762 2209 25 _pl _cp 778 2212 _m
_sp 778 2212 777 2208 776 2206 774 2204 772 2203 769 2204 768 2206 766 2209 766 2213 766 2217 768 2219 769 2221 772 2222 775 2221 777 2219 
778 2216 16 _pl _cp 
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1463 2217 1465 2215 1468 2215 1471 2216 1473 2217 1474 2219 1475 2222 1475 2224 1474 2225 1474 2226 1473 2228 1472 2229 1470 2230 1468 2232 1466 2233 
1466 2234 1466 2234 1466 2235 1466 2235 1468 2235 1470 2233 1471 2232 37 _pl _cp 1472 2222 _m
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1472 2225 16 _pl _cp 
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1499 2249 1497 2246 1496 2241 1497 2237 1499 2233 1502 2231 1506 2230 1509 2230 1512 2232 1515 2235 1516 2238 1517 2242 1517 2244 1516 2246 1515 2248 
1514 2250 1512 2251 1510 2253 1508 2255 1506 2256 1505 2257 1504 2258 1503 2259 1503 2260 1503 2261 1504 2262 1505 2262 1506 2261 1507 2260 1509 2258 
1511 2257 46 _pl _cp 1512 2241 _m
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1512 2245 16 _pl _cp 
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1780 2217 1782 2215 1785 2215 1788 2216 1790 2217 1791 2219 1792 2222 1792 2224 1791 2225 1791 2226 1790 2228 1789 2229 1787 2230 1785 2232 1783 2233 
1783 2234 1783 2234 1783 2235 1783 2235 1785 2235 1787 2233 1788 2232 37 _pl _cp 1789 2222 _m
_sp 1789 2222 1789 2219 1788 2218 1786 2216 1785 2216 1784 2216 1782 2218 1781 2219 1781 2222 1781 2224 1782 2226 1784 2227 1785 2228 1787 2228 1788 2227 
1789 2225 16 _pl _cp 
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1820 2249 1818 2246 1817 2241 1818 2237 1820 2233 1823 2231 1827 2230 1831 2231 1834 2233 1836 2237 1837 2242 1837 2244 1837 2246 1836 2248 1835 2250 
1833 2251 1830 2253 1828 2255 1827 2256 1826 2257 1825 2258 1824 2259 1823 2260 1824 2261 1825 2262 1826 2262 1827 2261 1828 2260 1830 2258 1832 2257 
45 _pl _cp 1833 2241 _m
_sp 1833 2241 1833 2237 1832 2235 1830 2233 1827 2232 1825 2233 1823 2235 1822 2237 1822 2241 1822 2245 1823 2248 1825 2249 1827 2250 1830 2249 1832 2248 
1833 2245 16 _pl _cp 
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2029 2217 2031 2215 2033 2215 2036 2216 2038 2217 2039 2219 2040 2222 2040 2224 2040 2225 2039 2226 2038 2228 2037 2229 2036 2230 2033 2232 2032 2233 
2031 2234 2031 2234 2031 2235 2032 2235 2033 2235 2035 2233 2037 2232 37 _pl _cp 2037 2222 _m
_sp 2037 2222 2037 2219 2036 2218 2035 2216 2034 2216 2032 2216 2031 2218 2030 2219 2030 2222 2030 2224 2031 2226 2032 2227 2034 2228 2035 2228 2036 2227 
2037 2225 16 _pl _cp 
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2065 2249 2063 2246 2062 2241 2063 2237 2065 2233 2068 2231 2072 2230 2076 2231 2079 2233 2081 2237 2082 2242 2082 2244 2081 2246 2080 2248 2079 2250 
2077 2251 2075 2253 2073 2255 2072 2256 2070 2257 2069 2258 2069 2259 2068 2260 2069 2261 2070 2262 2071 2262 2072 2261 2073 2260 2075 2258 2077 2257 
45 _pl _cp 2078 2241 _m
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2078 2245 16 _pl _cp 
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1134 2108 1136 2106 1138 2106 1141 2107 1143 2108 1144 2110 1145 2113 1145 2115 1145 2116 1144 2117 1143 2119 1142 2120 1141 2121 1138 2123 1137 2124 
1136 2125 1136 2125 1136 2126 1137 2126 1138 2126 1140 2124 1142 2123 37 _pl _cp 1142 2113 _m
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1142 2116 16 _pl _cp 
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1171 2108 1173 2106 1176 2106 1179 2107 1181 2108 1182 2110 1183 2113 1183 2115 1182 2116 1181 2117 1180 2119 1179 2120 1178 2121 1176 2123 1174 2124 
1174 2125 1173 2125 1174 2126 1174 2126 1176 2126 1177 2124 1179 2123 37 _pl _cp 1180 2113 _m
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1180 2116 16 _pl _cp 
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1216 2140 1214 2137 1213 2132 1214 2128 1216 2124 1219 2122 1223 2121 1226 2121 1229 2123 1232 2126 1233 2129 1234 2133 1234 2135 1233 2137 1232 2139 
1231 2141 1229 2142 1227 2144 1225 2146 1223 2147 1222 2148 1221 2149 1220 2150 1220 2151 1220 2152 1221 2153 1222 2153 1223 2152 1224 2151 1226 2149 
1228 2148 46 _pl _cp 1229 2132 _m
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1229 2136 16 _pl _cp 
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1446 2108 1448 2106 1451 2106 1454 2107 1456 2108 1457 2110 1458 2113 1458 2115 1457 2116 1456 2117 1455 2119 1454 2120 1453 2121 1451 2123 1449 2124 
1449 2125 1448 2125 1449 2126 1449 2126 1451 2126 1452 2124 1454 2123 37 _pl _cp 1455 2113 _m
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1455 2116 16 _pl _cp 
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1480 2108 1482 2106 1484 2106 1487 2107 1489 2108 1490 2110 1491 2113 1491 2115 1491 2116 1490 2117 1489 2119 1488 2120 1486 2121 1484 2123 1483 2124 
1482 2125 1482 2125 1482 2126 1483 2126 1484 2126 1486 2124 1487 2123 37 _pl _cp 1488 2113 _m
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1488 2116 16 _pl _cp 
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45 _pl _cp 1534 2132 _m
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1534 2136 16 _pl _cp 
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1747 2108 1749 2106 1752 2106 1755 2107 1757 2108 1758 2110 1759 2113 1759 2115 1758 2116 1757 2117 1756 2119 1755 2120 1754 2121 1752 2123 1750 2124 
1750 2125 1749 2125 1750 2126 1750 2126 1752 2126 1753 2124 1755 2123 37 _pl _cp 1756 2113 _m
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1756 2116 16 _pl _cp 
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1781 2108 1783 2106 1785 2106 1788 2107 1790 2108 1791 2110 1792 2113 1792 2115 1792 2116 1791 2117 1790 2119 1789 2120 1787 2121 1785 2123 1784 2124 
1783 2125 1783 2125 1783 2126 1784 2126 1785 2126 1787 2124 1788 2123 37 _pl _cp 1789 2113 _m
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1789 2116 16 _pl _cp 
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1822 2140 1820 2137 1819 2132 1820 2128 1822 2124 1825 2122 1829 2121 1833 2122 1836 2124 1838 2128 1839 2133 1839 2135 1839 2137 1838 2139 1837 2141 
1835 2142 1832 2144 1830 2146 1829 2147 1828 2148 1827 2149 1826 2150 1825 2151 1826 2152 1827 2153 1828 2153 1829 2152 1830 2151 1832 2149 1834 2148 
45 _pl _cp 1835 2132 _m
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1835 2136 16 _pl _cp 
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2048 2108 2050 2106 2053 2106 2056 2107 2058 2108 2059 2110 2060 2113 2060 2115 2059 2116 2058 2117 2057 2119 2056 2120 2055 2121 2053 2123 2051 2124 
2051 2125 2050 2125 2051 2126 2051 2126 2053 2126 2054 2124 2056 2123 37 _pl _cp 2057 2113 _m
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2057 2116 16 _pl _cp 
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2082 2108 2084 2106 2086 2106 2089 2107 2091 2108 2092 2110 2093 2113 2093 2115 2093 2116 2092 2117 2091 2119 2090 2120 2088 2121 2086 2123 2085 2124 
2084 2125 2084 2125 2084 2126 2085 2126 2086 2126 2088 2124 2089 2123 37 _pl _cp 2090 2113 _m
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2090 2116 16 _pl _cp 
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2123 2140 2121 2137 2120 2132 2121 2128 2123 2124 2126 2122 2130 2121 2134 2122 2137 2124 2139 2128 2140 2133 2140 2135 2140 2137 2139 2139 2138 2141 
2136 2142 2133 2144 2131 2146 2130 2147 2129 2148 2128 2149 2127 2150 2126 2151 2127 2152 2128 2153 2129 2153 2130 2152 2131 2151 2133 2149 2135 2148 
45 _pl _cp 2136 2132 _m
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2136 2136 16 _pl _cp 
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973 2033 975 2030 978 2028 981 2027 984 2027 986 2028 988 2030 990 2032 991 2034 992 2037 992 2041 992 2045 992 2046 28 _pl _cp 976 2048 _m
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_sp 988 2046 988 2044 988 2042 988 2040 988 2039 987 2035 986 2032 984 2030 982 2029 980 2030 978 2031 977 2034 976 2039 976 2044 976 2045 
976 2046 16 _pl _cp 
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770 1944 768 1943 767 1942 765 1941 764 1939 763 1937 762 1935 762 1932 762 1931 762 1929 25 _pl _cp 778 1932 _m
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778 1936 16 _pl _cp 
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444 2802 442 2801 441 2801 439 2800 438 2798 437 2797 436 2795 435 2792 436 2792 438 2794 439 2796 441 2797 444 2798 447 2797 449 2796 
450 2794 451 2791 450 2788 449 2785 447 2782 444 2778 440 2774 435 2769 435 2769 455 2769 458 2775 457 2776 456 2775 455 2774 454 2773 
453 2773 451 2773 47 _pl _cp 
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513 2836 514 2833 513 2830 510 2829 509 2829 507 2830 506 2831 505 2831 504 2830 504 2829 505 2828 508 2828 512 2829 514 2830 516 2832 
517 2835 517 2837 516 2839 515 2840 513 2841 514 2842 515 2844 516 2845 516 2846 516 2847 515 2849 513 2850 511 2850 509 2850 507 2849 
505 2847 46 _pl _cp 
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1143 2718 1142 2717 1142 2715 1141 2714 1142 2714 1143 2715 1144 2716 1145 2717 1147 2718 1148 2718 1150 2717 1151 2715 1151 2713 1151 2711 1150 2709 
1149 2707 1147 2704 1144 2702 1141 2699 1141 2698 1154 2698 1156 2703 1156 2703 1155 2702 1154 2702 1154 2701 1153 2701 1151 2701 43 _pl _cp 
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1226 2717 1225 2714 1226 2714 1227 2715 1227 2716 1229 2717 1231 2718 1232 2718 1234 2717 1235 2715 1235 2713 1235 2711 1234 2709 1232 2707 1230 2704 
1228 2702 1225 2699 1225 2698 1238 2698 1240 2703 1239 2703 1239 2702 1238 2702 1238 2701 1237 2701 1235 2701 41 _pl _cp 
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769 2551 767 2550 765 2549 763 2548 762 2547 761 2545 761 2544 760 2541 761 2540 762 2543 763 2545 766 2546 768 2547 771 2546 773 2545 
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777 2521 775 2521 47 _pl _cp 
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_sp 829 2584 836 2584 836 2594 3 _pl _cp 
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969 2596 968 2595 968 2594 967 2592 968 2592 969 2594 970 2595 971 2596 973 2596 974 2596 976 2595 977 2593 977 2591 977 2589 976 2587 
975 2585 973 2583 970 2580 967 2577 967 2576 980 2576 982 2581 982 2581 981 2581 980 2580 980 2579 979 2579 977 2579 43 _pl _cp 
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1167 2595 1166 2592 1166 2592 1167 2594 1168 2595 1170 2596 1171 2596 1173 2596 1175 2595 1176 2593 1176 2591 1176 2589 1175 2587 1173 2585 1171 2583 
1168 2580 1165 2577 1165 2576 1178 2576 1180 2581 1180 2581 1179 2581 1179 2580 1178 2579 1177 2579 1176 2579 41 _pl _cp 
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1352 2595 1351 2592 1351 2592 1352 2594 1353 2595 1355 2596 1356 2596 1358 2596 1360 2595 1361 2593 1361 2591 1361 2589 1360 2587 1358 2585 1356 2583 
1354 2580 1351 2577 1351 2576 1364 2576 1366 2581 1365 2581 1365 2581 1364 2580 1363 2579 1362 2579 1361 2579 41 _pl _cp 
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769 2370 767 2369 765 2368 763 2367 762 2366 761 2364 761 2363 760 2360 761 2359 762 2362 763 2364 766 2365 768 2366 771 2365 773 2364 
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777 2340 775 2340 47 _pl _cp 
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832 2406 833 2406 835 2406 837 2405 838 2403 839 2401 839 2399 838 2397 836 2396 835 2396 834 2396 832 2397 831 2398 830 2398 829 2398 
828 2397 829 2396 832 2395 836 2396 839 2397 840 2400 841 2403 841 2405 840 2407 839 2408 837 2409 839 2411 840 2413 840 2415 839 2417 
837 2418 835 2418 833 2418 831 2417 830 2416 830 2415 829 2413 52 _pl _cp 
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769 2168 767 2167 765 2166 763 2165 762 2164 761 2162 761 2161 760 2158 761 2157 762 2160 763 2162 766 2163 768 2164 771 2163 773 2162 
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777 2138 775 2138 47 _pl _cp 
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829 2212 828 2209 828 2209 829 2211 830 2212 832 2213 833 2213 835 2213 837 2212 838 2210 838 2208 838 2206 837 2204 835 2202 833 2200 
830 2197 827 2194 827 2193 840 2193 842 2198 842 2198 841 2198 841 2197 840 2196 839 2196 838 2196 41 _pl _cp 
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1028 2269 1027 2266 1028 2266 1029 2267 1029 2268 1031 2269 1033 2270 1034 2270 1036 2269 1037 2267 1037 2265 1037 2263 1036 2261 1034 2259 1032 2256 
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1242 2168 1241 2167 1241 2165 1240 2164 1241 2164 1242 2165 1243 2166 1244 2167 1246 2168 1247 2168 1249 2167 1250 2165 1250 2163 1250 2161 1249 2159 
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1546 2167 1545 2164 1546 2164 1547 2165 1547 2166 1549 2167 1551 2168 1552 2168 1554 2167 1555 2165 1555 2163 1555 2161 1554 2159 1552 2157 1550 2154 
1548 2152 1545 2149 1545 2148 1558 2148 1560 2153 1559 2153 1559 2152 1558 2152 1558 2151 1557 2151 1555 2151 41 _pl _cp 
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1847 2167 1846 2164 1847 2164 1848 2165 1848 2166 1850 2167 1852 2168 1853 2168 1855 2167 1856 2165 1856 2163 1856 2161 1855 2159 1853 2157 1851 2154 
1849 2152 1846 2149 1846 2148 1859 2148 1861 2153 1860 2153 1860 2152 1859 2152 1859 2151 1858 2151 1856 2151 41 _pl _cp 
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2148 2167 2147 2164 2148 2164 2149 2165 2149 2166 2151 2167 2153 2168 2154 2168 2156 2167 2157 2165 2157 2163 2157 2161 2156 2159 2154 2157 2152 2154 
2150 2152 2147 2149 2147 2148 2160 2148 2162 2153 2161 2153 2161 2152 2160 2152 2160 2151 2159 2151 2157 2151 41 _pl _cp 
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758 2021 761 2019 762 2020 760 2022 758 2024 757 2025 756 2027 755 2028 755 2029 754 2031 754 2034 754 2037 754 2040 754 2043 754 2046 
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870 2060 867 2062 866 2060 867 2059 869 2058 870 2057 871 2056 872 2054 873 2051 874 2049 874 2046 875 2043 875 2040 875 2037 874 2034 
874 2031 873 2029 872 2027 871 2024 870 2023 869 2022 867 2021 866 2020 38 _pl _cp 
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907 2039 905 2040 903 2041 901 2042 899 2044 898 2045 898 2046 899 2048 902 2049 905 2049 907 2048 908 2046 909 2043 910 2043 910 2050 
909 2050 908 2050 908 2050 908 2050 907 2050 905 2050 904 2051 902 2051 899 2050 897 2049 895 2047 894 2044 894 2043 896 2041 897 2040 
900 2038 904 2036 907 2034 908 2032 908 2031 907 2030 905 2029 903 2029 901 2029 898 2030 897 2031 897 2032 896 2034 895 2035 894 2035 
60 _pl _cp 
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937 1157 939 1156 941 1154 941 1151 940 1148 937 1147 936 1147 934 1148 934 1149 933 1149 932 1148 931 1147 932 1146 935 1146 939 1147 
941 1148 943 1150 944 1153 944 1155 943 1157 942 1158 940 1159 941 1160 942 1162 943 1163 943 1164 943 1165 942 1167 940 1168 938 1168 
936 1168 934 1167 933 1165 48 _pl _cp 
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871 971 869 970 868 969 866 968 865 967 864 965 863 964 863 961 864 960 865 963 866 965 868 966 871 967 874 966 876 965 
877 963 878 960 878 957 876 954 874 951 871 947 867 943 862 938 862 937 882 937 885 944 884 944 883 943 882 942 882 942 
880 941 878 941 47 _pl _cp 
0 g _f _s _s 
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932 1016 931 1015 931 1014 930 1012 931 1012 932 1014 933 1015 934 1016 936 1016 937 1016 939 1015 940 1013 940 1011 940 1009 939 1007 
938 1005 936 1003 933 1000 930 997 930 996 943 996 945 1001 945 1001 944 1001 943 1000 943 999 942 999 940 999 43 _pl _cp 
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871 821 869 820 868 820 866 819 865 817 864 816 863 814 863 811 864 811 865 813 866 815 868 816 871 817 874 816 876 815 
877 813 878 810 878 807 876 804 874 801 871 797 867 793 862 788 862 788 882 788 885 794 884 795 883 794 882 793 882 792 
880 792 878 792 47 _pl _cp 
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1158 820 1161 818 1162 819 1161 820 1160 822 1159 823 1158 824 1157 825 1156 826 1155 828 1155 829 1154 831 1154 834 1154 837 1154 840 
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1190 859 1187 861 1186 860 1187 859 1189 858 1190 857 1191 856 1192 855 1192 853 1193 852 1193 850 1194 848 1194 846 1195 843 1195 840 
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1609 859 1606 861 1605 860 1607 858 1609 856 1610 855 1611 853 1611 852 1612 850 1613 848 1613 846 1613 843 1613 840 1613 837 1613 834 
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861 687 864 685 865 686 864 687 863 688 861 689 860 690 859 693 858 695 857 697 857 700 856 703 856 706 856 709 857 712 
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1024 710 1024 707 1024 706 18 _pl _cp 
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60 _pl _cp 
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60 _pl _cp 
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1163 695 1163 698 17 _pl _cp 1157 725 _m
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45 _pl _cp 
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930 619 931 616 931 613 929 610 927 607 924 603 920 599 916 594 916 594 935 594 938 600 937 601 937 600 936 599 935 598 
933 598 931 598 47 _pl _cp 
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_s grestore 4950 1288 _m
(147)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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3944 11855 _m
/Times-BoldR 600 _ff
_U (Heave)_S 67 _t
(Equation)_S 67 _t
(of)_S 67 _t
(Motion)_S _u /Times-RomanR 600 _ff
8217 11855 _m
/Times-BoldR 600 _ff
(\(6.50\))_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr 
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1281 2417 1282 2420 1282 2424 1282 2427 1281 2429 1279 2430 1277 2430 1274 2430 1272 2429 1270 2427 40 _pl _cp 1265 2412 _m
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1273 2427 1270 2426 1269 2424 1268 2422 1267 2420 1266 2417 21 _pl _cp 
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1362 2432 1363 2432 1364 2434 1365 2436 1367 2437 1368 2437 1371 2438 1374 2438 1380 2438 24 _pl _cp 
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1394 2393 1395 2394 1396 2396 1397 2397 1399 2399 1400 2401 1401 2403 1401 2404 1400 2405 1399 2406 1398 2406 1398 2405 1398 2405 1398 2404 1399 2403 
1399 2403 1399 2402 1398 2400 1398 2399 1397 2398 1395 2396 1394 2394 1394 2396 1393 2398 1393 2400 1393 2401 1393 2403 1392 2405 1392 2406 44 _pl _cp 
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1413 2406 1412 2406 1411 2406 1410 2405 1409 2404 1408 2402 1407 2401 1407 2401 1408 2406 1403 2406 1403 2405 1404 2405 1405 2405 1405 2404 1405 2403 
1405 2402 31 _pl _cp 
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1436 2420 1435 2422 1435 2424 1434 2426 1434 2428 1433 2429 1433 2430 52 _pl _cp 
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1466 2425 1467 2427 1466 2429 1465 2430 1463 2429 1461 2428 1460 2427 1459 2426 1458 2425 1457 2423 1457 2422 1456 2421 1459 2430 1451 2429 1450 2428 
1452 2428 1453 2427 1454 2426 1454 2425 1453 2424 35 _pl _cp 
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926 2258 929 2266 928 2267 927 2265 925 2263 924 2262 922 2261 921 2261 919 2261 918 2260 916 2260 916 2260 916 2260 914 2260 913 2261 
912 2262 912 2263 912 2265 918 2284 919 2286 919 2288 920 2289 922 2289 922 2289 922 2291 910 2291 41 _pl _cp 
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998 2291 975 2291 973 2283 974 2283 975 2285 976 2286 978 2287 979 2288 981 2288 984 2288 991 2288 26 _pl _cp 
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1010 2244 1010 2243 1009 2243 1009 2243 1009 2244 1009 2244 1009 2245 1009 2246 1009 2247 1010 2249 1010 2251 1011 2254 1012 2256 58 _pl _cp 
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1018 2242 1019 2242 1025 2253 1027 2242 1027 2242 1029 2244 1031 2246 1032 2248 1034 2250 1035 2253 1036 2255 1035 2256 1034 2257 1033 2257 1033 2256 
1033 2255 1033 2254 1034 2254 1034 2253 1034 2252 1034 2252 1033 2250 1031 2248 1030 2246 1029 2245 1027 2256 1027 2257 42 _pl _cp 
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1058 2281 1050 2279 1050 2278 1051 2278 1052 2278 1052 2277 1052 2276 1052 2274 1049 2265 1049 2264 1049 2262 1049 2261 1049 2260 1050 2258 1051 2257 
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1068 2260 1070 2263 1069 2264 1069 2263 1067 2261 1066 2260 1065 2260 1065 2260 1065 2261 1065 2262 1065 2263 1065 2264 1066 2265 1066 2267 1067 2269 
1067 2270 1067 2272 1069 2277 1070 2280 64 _pl _cp 
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1078 2269 1079 2265 1079 2262 1079 2258 1080 2257 1090 2274 1092 2258 1092 2258 1095 2261 1098 2264 1100 2267 1102 2270 1103 2272 1104 2274 1105 2275 
1105 2277 1104 2279 1103 2280 1101 2280 1100 2279 1101 2278 1101 2277 1103 2276 1103 2275 1103 2274 1102 2272 1101 2271 1100 2270 1099 2268 1098 2266 
1096 2264 1095 2262 1093 2280 1092 2281 49 _pl _cp 
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1209 2291 1186 2291 1184 2283 1185 2283 1186 2285 1187 2286 1189 2287 1190 2288 1192 2288 1195 2288 1202 2288 26 _pl _cp 
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1214 2243 1215 2245 1216 2246 1217 2247 1219 2250 1221 2251 1222 2253 1222 2255 1221 2256 1220 2257 1219 2257 1218 2256 1219 2255 1219 2254 1220 2254 
1220 2253 1220 2252 1219 2251 1218 2250 1217 2248 1216 2247 1214 2245 1214 2246 1214 2248 1214 2250 1214 2251 1213 2253 1213 2255 1212 2257 44 _pl _cp 
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1233 2243 1234 2245 1235 2246 1236 2247 1238 2250 1239 2251 1240 2253 1240 2255 1239 2256 1238 2257 1237 2257 1237 2256 1237 2255 1237 2254 1238 2254 
1238 2253 1238 2252 1237 2251 1237 2250 1236 2248 1234 2247 1233 2245 1233 2246 1232 2248 1232 2250 1232 2251 1232 2253 1231 2255 1231 2257 44 _pl _cp 
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1262 2270 1261 2273 1261 2275 1260 2277 1260 2278 1259 2280 1259 2281 52 _pl _cp 
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1392 2260 1394 2263 1393 2264 1392 2263 1391 2261 1390 2260 1389 2260 1388 2260 1388 2261 1388 2262 1388 2263 1389 2264 1389 2265 1390 2267 1390 2269 
1390 2270 1391 2272 1392 2277 1393 2280 64 _pl _cp 
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1426 2281 1418 2279 1418 2278 1419 2278 1420 2278 1421 2277 1421 2276 1420 2274 1418 2265 1418 2264 1417 2262 1417 2261 1417 2260 1418 2258 1420 2257 
1421 2257 1423 2258 1424 2259 1425 2260 1426 2261 1428 2263 1429 2265 1431 2268 1430 2264 1429 2262 1429 2260 1430 2258 1432 2257 1434 2257 1435 2259 
1437 2260 1439 2263 1438 2264 1437 2263 1436 2261 1435 2260 1434 2260 1433 2260 1433 2261 1433 2262 1433 2263 1434 2264 1434 2265 1435 2267 1435 2269 
1435 2270 1436 2272 1437 2277 1438 2280 64 _pl _cp 
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1512 2291 1489 2291 1486 2283 1488 2283 1489 2285 1490 2286 1491 2287 1493 2288 1495 2288 1498 2288 1504 2288 26 _pl _cp 
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1517 2257 1512 2256 1511 2255 1512 2255 1513 2255 1513 2255 1513 2254 1513 2253 1511 2246 1511 2246 1511 2245 1511 2244 1511 2243 1511 2242 1512 2242 
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1523 2244 1522 2243 1522 2243 1522 2243 1521 2244 1521 2244 1522 2245 1522 2246 1522 2247 1523 2249 1523 2251 1524 2254 1525 2256 58 _pl _cp 
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1547 2257 1542 2256 1541 2255 1542 2255 1543 2255 1543 2255 1543 2254 1543 2253 1541 2246 1541 2246 1541 2245 1541 2244 1541 2243 1541 2242 1542 2242 
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1553 2244 1552 2243 1552 2243 1552 2243 1551 2244 1551 2244 1552 2245 1552 2246 1552 2247 1553 2249 1553 2251 1554 2254 1555 2256 58 _pl _cp 
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1597 2242 1599 2242 1601 2242 1603 2243 1604 2244 1606 2245 1608 2247 1609 2249 1610 2250 1610 2252 1610 2254 1609 2256 1607 2257 1606 2257 1605 2257 
1604 2257 1602 2255 32 _pl _cp 1598 2244 _m
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1598 2248 1598 2246 1598 2245 18 _pl _cp 
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1648 2253 1648 2252 1647 2250 1646 2248 19 _pl _cp 
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1669 2257 1668 2256 1667 2255 1665 2254 34 _pl _cp 1662 2244 _m
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1663 2248 1663 2246 1662 2245 18 _pl _cp 
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60 _pl _cp 
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1813 2257 1808 2256 1808 2255 1809 2255 1810 2255 1810 2255 1810 2254 1810 2253 1808 2246 1808 2246 1808 2245 1807 2244 1807 2243 1808 2242 1809 2242 
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1821 2246 1821 2245 1820 2244 1819 2243 1819 2243 1818 2243 1818 2244 1818 2244 1818 2245 1819 2246 1819 2247 1820 2249 1820 2251 1821 2254 1821 2256 
60 _pl _cp 
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1871 2246 1871 2248 1870 2249 1868 2251 1866 2253 1866 2254 1867 2255 1868 2256 1870 2255 1872 2252 1872 2252 1873 2257 1873 2257 1872 2256 1871 2256 
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1866 2242 1864 2242 1863 2243 1862 2245 1861 2247 50 _pl _cp 
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1919 2249 1920 2251 1920 2253 1919 2256 1916 2257 1915 2257 1913 2256 1912 2255 38 _pl _cp 1908 2245 _m
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1911 2253 1911 2252 1910 2250 1909 2248 19 _pl _cp 
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1932 2246 1931 2248 1930 2249 1929 2251 1927 2253 1926 2254 1927 2255 1928 2256 1931 2255 1932 2252 1933 2252 1934 2257 1933 2257 1933 2256 1932 2256 
1931 2256 1930 2257 1929 2257 1928 2257 1925 2256 1924 2254 1924 2253 1924 2251 1925 2250 1927 2248 1929 2246 1929 2245 1928 2243 1926 2242 1925 2242 
1923 2243 1922 2245 1922 2247 48 _pl _cp 
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943 2142 943 2142 945 2144 946 2146 946 2147 946 2146 947 2144 948 2141 949 2141 951 2141 953 2144 953 2144 952 2145 951 2143 950 2143 
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951 2155 949 2154 948 2152 948 2151 948 2153 947 2155 946 2156 945 2156 943 2155 941 2155 942 2154 943 2154 943 2154 943 2154 944 2153 
945 2150 61 _pl _cp 
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979 2144 978 2142 979 2141 980 2141 981 2141 982 2141 984 2142 985 2144 984 2145 982 2143 981 2142 981 2143 981 2143 981 2143 981 2143 
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972 2154 973 2154 973 2154 973 2153 972 2152 50 _pl _cp 
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989 2146 989 2145 989 2145 18 _pl _cp 
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1013 2145 1012 2147 1011 2148 1010 2150 1008 2152 1007 2153 1008 2154 1009 2155 1012 2154 1013 2151 1014 2151 1015 2156 1014 2156 1014 2155 1013 2155 
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1005 2142 1004 2144 1003 2146 48 _pl _cp 
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1017 2149 1016 2147 1016 2145 1016 2143 1017 2142 1019 2141 1021 2141 1023 2141 1025 2142 1026 2143 1027 2144 1027 2145 1025 2144 1024 2143 1023 2142 
1022 2142 1020 2143 1019 2145 1019 2146 34 _pl _cp 1020 2148 _m
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930 2077 930 2078 932 2080 933 2082 933 2082 933 2082 934 2080 935 2077 936 2076 938 2077 940 2079 940 2080 939 2080 938 2078 937 2078 
937 2079 936 2082 935 2085 935 2085 937 2089 938 2089 939 2089 939 2089 940 2089 940 2089 941 2089 941 2090 941 2091 940 2091 939 2091 
938 2091 936 2089 935 2087 935 2087 935 2088 934 2091 933 2091 932 2091 930 2091 928 2090 929 2090 930 2090 930 2090 930 2090 931 2089 
932 2085 61 _pl _cp 
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959 2079 960 2079 960 2081 962 2090 965 2090 966 2091 963 2091 964 2095 963 2095 962 2093 960 2092 959 2091 957 2091 957 2090 29 _pl _cp 
0 g _f _s _s 
0 g 975 2081 _m
_sp 975 2081 975 2079 975 2077 975 2076 976 2076 977 2076 978 2077 980 2078 981 2080 980 2080 979 2079 978 2078 977 2078 977 2079 977 2080 
978 2082 979 2087 980 2090 980 2091 978 2091 978 2090 977 2091 975 2091 973 2091 970 2089 968 2087 966 2085 965 2082 965 2080 966 2077 
969 2076 971 2076 972 2077 974 2079 34 _pl _cp 968 2081 _m
_sp 968 2081 969 2079 970 2078 971 2078 973 2079 974 2080 975 2081 976 2083 976 2085 977 2087 977 2088 976 2089 975 2090 974 2090 973 2089 
971 2088 970 2087 969 2085 969 2083 968 2082 20 _pl _cp 
0 g _f _s _s 
0 g 989 2080 _m
_sp 989 2080 987 2078 986 2078 986 2078 986 2078 986 2079 986 2080 989 2091 984 2091 984 2090 985 2090 986 2090 986 2089 986 2088 985 2087 
984 2081 983 2080 983 2078 984 2077 985 2076 987 2077 989 2080 22 _pl _cp 987 2097 _m
_sp 987 2097 988 2096 988 2095 989 2096 990 2097 989 2098 988 2098 988 2098 8 _pl _cp 
0 g _f _s _s 
0 g 1001 2099 _m
_sp 1001 2099 995 2098 995 2098 996 2098 997 2098 997 2097 997 2096 997 2095 993 2081 992 2079 992 2078 993 2077 994 2076 996 2076 997 2078 
998 2079 999 2080 999 2080 998 2080 997 2078 995 2077 995 2078 995 2078 995 2079 995 2080 25 _pl _cp 
0 g _f _s _s 
0 g 1079 2116 _m
_sp 1079 2116 1076 2113 1074 2112 1071 2110 1068 2110 1066 2110 1065 2111 1063 2112 1062 2113 1061 2115 1060 2116 1059 2118 1059 2120 1060 2125 1061 2130 
1063 2134 1066 2137 1070 2139 1073 2140 1075 2140 1077 2139 1078 2139 1080 2138 1081 2137 1081 2135 1081 2134 1081 2132 1083 2132 1084 2142 1083 2142 
1083 2141 1082 2141 1081 2141 1080 2141 1078 2142 1076 2142 1075 2142 1074 2142 1069 2141 1065 2140 1061 2137 1058 2134 1056 2130 1054 2125 1054 2121 
1054 2118 1055 2116 1056 2114 1057 2112 1059 2110 1062 2109 1065 2108 1067 2108 1069 2108 1070 2108 1072 2108 1073 2109 1075 2110 1077 2111 1078 2113 
1080 2115 61 _pl _cp 
0 g _f _s _s 
0 g 1095 2096 _m
_sp 1095 2096 1095 2095 1095 2095 1095 2094 1095 2093 1096 2092 1097 2092 1099 2093 1100 2094 1101 2096 1101 2096 1100 2096 1099 2094 1098 2094 1098 2094 
1098 2095 1098 2095 1098 2096 1103 2115 1098 2114 1097 2114 1099 2114 1100 2114 1100 2113 1100 2112 1099 2111 1098 2106 1097 2107 1095 2107 1094 2107 
1092 2106 1091 2105 1089 2104 1088 2102 1086 2100 1085 2098 1085 2096 1086 2093 1089 2092 1092 2093 1094 2094 1095 2095 42 _pl _cp 1088 2096 _m
_sp 1088 2096 1089 2095 1091 2094 1093 2095 1095 2097 1096 2098 1096 2099 1097 2102 1097 2104 1096 2106 1095 2106 1093 2105 1091 2103 1090 2101 1089 2100 
1088 2098 1088 2096 1088 2096 18 _pl _cp 
0 g _f _s _s 
0 g 1102 2106 _m
_sp 1102 2106 1102 2106 1103 2106 1104 2106 1105 2105 1106 2104 1107 2102 1107 2101 1107 2099 1108 2097 1108 2095 1109 2092 1108 2091 1107 2090 1106 2088 
1104 2088 1104 2088 1104 2088 1104 2088 1103 2088 1103 2089 1102 2089 1102 2088 1101 2087 1102 2086 1103 2086 1104 2086 1105 2086 1106 2087 1107 2088 
1108 2089 1109 2091 1110 2093 1112 2095 1113 2096 1114 2099 1115 2101 1115 2103 1116 2104 1116 2105 1115 2106 1114 2107 1113 2107 1113 2106 1113 2105 
1114 2105 1115 2104 1115 2103 1115 2103 1115 2103 1114 2102 1114 2101 1113 2099 1112 2098 1112 2097 1111 2096 1111 2096 1111 2095 1111 2096 1111 2096 
1110 2099 1110 2101 1109 2102 1109 2104 1108 2107 1107 2107 66 _pl _cp 
0 g _f _s _s 
0 g 1129 2108 _m
_sp 1129 2108 1133 2108 1134 2114 1135 2117 1136 2118 1137 2120 1138 2121 1138 2122 1139 2124 1141 2125 1142 2126 1144 2128 1145 2128 1146 2128 1146 2127 
1146 2126 1146 2125 1143 2114 1142 2112 1142 2110 1143 2109 1144 2108 1146 2108 1148 2109 1149 2111 1151 2113 1151 2114 1149 2111 1147 2110 1146 2111 
1146 2111 1146 2112 1147 2113 1149 2123 1150 2125 1150 2127 1150 2128 1149 2130 1147 2131 1145 2131 1143 2130 1143 2129 1142 2128 1141 2127 1140 2126 
1138 2124 1137 2122 1142 2143 1134 2142 1134 2141 1135 2141 1136 2140 1137 2139 1137 2138 1136 2137 55 _pl _cp 
0 g _f _s _s 
0 g 1179 2119 _m
_sp 1179 2119 1178 2118 1175 2114 1174 2112 1173 2111 1172 2111 1171 2111 1171 2112 1170 2112 1169 2111 1168 2110 1169 2109 1170 2108 1172 2108 1173 2109 
1174 2110 1175 2111 1176 2112 1177 2113 1178 2115 1179 2117 1179 2117 1180 2116 1180 2113 1181 2111 1182 2109 1183 2108 1184 2108 1185 2108 1187 2109 
1188 2111 1190 2113 1190 2114 1189 2114 1187 2112 1186 2111 1185 2111 1185 2112 1184 2114 1183 2118 1182 2122 1183 2122 1185 2125 1186 2127 1186 2128 
1187 2128 1188 2128 1189 2127 1190 2127 1190 2127 1191 2128 1192 2129 1191 2130 1189 2131 1188 2131 1186 2130 1185 2128 1183 2125 1182 2124 1182 2126 
1181 2128 1181 2130 1180 2131 1179 2131 1177 2131 1175 2130 1172 2129 1173 2128 1174 2129 1175 2129 1175 2129 1176 2129 1177 2127 1178 2125 1179 2122 
75 _pl _cp 
0 g _f _s _s 
0 g 1231 2130 _m
_sp 1231 2130 1230 2129 1231 2129 1231 2129 1233 2128 1235 2127 1235 2125 1236 2124 1236 2122 1236 2121 1237 2118 1237 2115 1237 2112 1237 2108 1238 2108 
1239 2109 1240 2109 1242 2111 1243 2113 1245 2114 1246 2116 1247 2118 1249 2120 1250 2121 1251 2123 1252 2126 1253 2128 1252 2130 1250 2131 1248 2130 
1247 2129 1248 2128 1249 2127 1250 2126 1250 2125 1249 2124 1248 2122 1247 2120 1246 2118 1245 2117 1244 2116 1242 2114 1241 2113 1241 2115 1241 2118 
1241 2121 1240 2123 1240 2125 1239 2127 1239 2129 1238 2130 1238 2131 52 _pl _cp 
0 g _f _s _s 
0 g 1336 2119 _m
_sp 1336 2119 1335 2118 1332 2114 1331 2112 1329 2111 1329 2111 1328 2111 1327 2112 1326 2112 1326 2111 1325 2110 1326 2109 1327 2108 1329 2108 1330 2109 
1331 2110 1332 2111 1333 2112 1334 2113 1335 2115 1336 2117 1336 2117 1336 2116 1337 2113 1338 2111 1339 2109 1340 2108 1341 2108 1342 2108 1343 2109 
1345 2111 1346 2113 1347 2114 1346 2114 1344 2112 1343 2111 1342 2111 1342 2112 1341 2114 1340 2118 1339 2122 1339 2122 1341 2125 1342 2127 1343 2128 
1344 2128 1344 2128 1345 2127 1346 2127 1347 2127 1348 2128 1348 2129 1347 2130 1346 2131 1345 2131 1343 2130 1342 2128 1339 2125 1339 2124 1338 2126 
1337 2130 1336 2131 1334 2131 1332 2130 1329 2129 1329 2128 1331 2129 1332 2129 1332 2129 1333 2129 1334 2127 1335 2125 1335 2122 73 _pl _cp 
0 g _f _s _s 
0 g 1350 2108 _m
_sp 1350 2108 1354 2108 1355 2113 1356 2116 1357 2118 1358 2120 1359 2121 1359 2123 1360 2124 1362 2126 1363 2127 1364 2127 1364 2126 1365 2126 1366 2125 
1367 2126 1368 2128 1367 2130 1366 2131 1364 2130 1362 2129 1361 2128 1360 2127 1359 2126 1358 2124 1358 2123 1357 2122 1360 2131 1352 2130 1352 2129 
1353 2129 1354 2128 1355 2127 1355 2126 1354 2125 35 _pl _cp 
0 g _f _s _s 
0 g 1500 2116 _m
_sp 1500 2116 1497 2113 1495 2112 1492 2110 1489 2110 1487 2110 1485 2111 1484 2112 1483 2113 1482 2115 1481 2116 1480 2118 1480 2120 1480 2125 1482 2130 
1484 2134 1487 2137 1490 2139 1494 2140 1496 2140 1497 2139 1499 2139 1500 2138 1501 2137 1501 2135 1502 2134 1502 2132 1503 2132 1505 2142 1504 2142 
1503 2141 1502 2141 1502 2141 1501 2141 1499 2142 1497 2142 1496 2142 1494 2142 1489 2141 1485 2140 1481 2137 1478 2134 1476 2130 1474 2125 1474 2121 
1474 2118 1475 2116 1476 2114 1478 2112 1480 2110 1482 2109 1485 2108 1488 2108 1491 2108 1493 2109 1495 2110 1497 2111 1499 2113 1501 2115 59 _pl _cp 
0 g _f _s _s 
0 g 1516 2096 _m
_sp 1516 2096 1515 2095 1515 2095 1515 2094 1516 2093 1517 2092 1518 2092 1519 2093 1520 2094 1522 2096 1521 2096 1521 2096 1519 2094 1519 2094 1518 2094 
1518 2095 1518 2095 1518 2096 1524 2115 1518 2114 1518 2114 1519 2114 1520 2114 1520 2113 1520 2112 1520 2111 1518 2106 1517 2107 1516 2107 1515 2107 
1513 2106 1512 2105 1510 2104 1508 2102 1507 2100 1506 2098 1506 2096 1507 2093 1510 2092 1512 2093 1514 2094 1515 2095 42 _pl _cp 1509 2096 _m
_sp 1509 2096 1510 2095 1511 2094 1513 2095 1515 2097 1516 2098 1516 2099 1517 2102 1518 2104 1517 2106 1516 2106 1515 2106 1514 2105 1512 2104 1511 2103 
1510 2101 1510 2100 1509 2098 1509 2096 1509 2096 20 _pl _cp 
0 g _f _s _s 
0 g 1522 2093 _m
_sp 1522 2093 1522 2092 1523 2093 1524 2093 1526 2093 1527 2092 1529 2091 1530 2090 1531 2090 1534 2091 1535 2092 1534 2093 1533 2094 1533 2094 1532 2093 
1532 2092 1532 2092 1533 2092 1533 2092 1533 2091 1532 2091 1531 2092 1529 2093 1527 2095 1525 2095 1535 2106 1534 2107 1525 2107 1524 2103 1525 2103 
1526 2105 1529 2105 1532 2105 1524 2095 1523 2094 35 _pl _cp 
0 g _f _s _s 
0 g 1556 2125 _m
_sp 1556 2125 1561 2143 1553 2142 1552 2141 1554 2141 1555 2140 1556 2139 1556 2138 1555 2137 1549 2113 1548 2111 1548 2111 1548 2111 1548 2110 1549 2110 
1550 2109 1552 2108 1553 2108 1555 2108 1558 2108 1561 2109 1563 2111 1566 2113 1568 2116 1570 2119 1571 2122 1571 2124 1571 2127 1570 2129 1568 2130 
1565 2131 1564 2131 1563 2131 1561 2130 1560 2128 1558 2127 36 _pl _cp 1553 2111 _m
_sp 1553 2111 1554 2110 1555 2109 1557 2109 1558 2110 1560 2111 1561 2112 1563 2115 1565 2119 1566 2122 1567 2125 1566 2127 1563 2128 1561 2127 1559 2126 
1557 2123 1555 2120 1554 2117 1554 2115 1553 2113 20 _pl _cp 
0 g _f _s _s 
0 g 1598 2119 _m
_sp 1598 2119 1597 2118 1594 2114 1593 2112 1591 2111 1591 2111 1590 2111 1589 2112 1588 2112 1588 2111 1587 2110 1588 2109 1589 2108 1591 2108 1592 2109 
1593 2110 1594 2111 1595 2112 1596 2113 1597 2115 1598 2117 1598 2117 1598 2116 1599 2113 1600 2111 1601 2109 1602 2108 1603 2108 1604 2108 1605 2109 
1607 2111 1608 2113 1609 2114 1608 2114 1606 2112 1605 2111 1604 2111 1604 2112 1603 2114 1602 2118 1601 2122 1601 2122 1603 2125 1604 2127 1605 2128 
1606 2128 1606 2128 1607 2127 1608 2127 1609 2127 1610 2128 1610 2129 1609 2130 1608 2131 1607 2131 1605 2130 1604 2128 1601 2125 1601 2124 1600 2126 
1599 2130 1598 2131 1596 2131 1594 2130 1591 2129 1591 2128 1593 2129 1594 2129 1594 2129 1595 2129 1596 2127 1597 2125 1597 2122 73 _pl _cp 
0 g _f _s _s 
0 g 1659 2115 _m
_sp 1659 2115 1659 2118 1659 2120 1658 2122 1658 2124 1657 2127 1657 2129 1657 2130 1656 2131 1650 2129 1650 2129 1651 2129 1653 2128 1653 2127 1654 2123 
1655 2120 1655 2116 1655 2112 1656 2108 1656 2108 1666 2125 1668 2108 1669 2108 1672 2111 1674 2114 1677 2117 1679 2120 1680 2123 1681 2125 1682 2126 
1682 2128 1681 2130 1679 2131 1678 2130 1677 2129 1677 2128 1678 2127 1679 2126 1679 2125 1679 2124 1679 2123 1678 2122 1677 2120 1676 2119 1675 2117 
1673 2114 1671 2113 1669 2130 1669 2131 49 _pl _cp 
0 g _f _s _s 
0 g 1766 2119 _m
_sp 1766 2119 1764 2118 1762 2114 1761 2112 1759 2111 1759 2111 1758 2111 1757 2112 1756 2112 1756 2111 1755 2110 1756 2109 1757 2108 1759 2108 1760 2109 
1761 2110 1761 2111 1762 2112 1764 2113 1765 2115 1766 2117 1766 2117 1766 2116 1767 2113 1768 2111 1769 2109 1769 2108 1770 2108 1772 2108 1773 2109 
1775 2111 1776 2113 1777 2114 1776 2114 1774 2112 1772 2111 1771 2111 1771 2112 1771 2114 1770 2118 1769 2122 1769 2122 1771 2125 1772 2127 1773 2128 
1774 2128 1774 2128 1775 2127 1776 2127 1776 2127 1777 2128 1778 2129 1777 2130 1776 2131 1774 2131 1773 2130 1771 2128 1769 2125 1769 2124 1768 2126 
1767 2128 1767 2130 1766 2131 1765 2131 1764 2131 1762 2130 1759 2129 1759 2128 1761 2129 1762 2129 1762 2129 1763 2129 1764 2127 1764 2125 1765 2122 
75 _pl _cp 
0 g _f _s _s 
0 g 1797 2128 _m
_sp 1797 2128 1796 2130 1794 2131 1792 2131 1789 2130 1786 2128 1784 2126 1782 2123 1780 2120 1779 2117 1779 2114 1779 2111 1781 2110 1782 2108 1785 2108 
1787 2108 1788 2108 1789 2109 1790 2110 1792 2112 1794 2114 1791 2103 1790 2100 1788 2100 1786 2100 1786 2099 1797 2099 1798 2100 1796 2100 1795 2100 
1794 2101 1794 2102 1795 2103 1802 2130 1798 2130 35 _pl _cp 1784 2114 _m
_sp 1784 2114 1785 2112 1786 2111 1788 2111 1790 2112 1791 2114 1793 2117 1794 2119 1795 2122 1796 2124 1796 2126 1795 2128 1794 2129 1792 2129 1789 2127 
1787 2124 1785 2121 1784 2118 1784 2115 1784 2115 20 _pl _cp 
0 g _f _s _s 
0 g 1892 2143 _m
_sp 1892 2143 1892 2146 1892 2148 1891 2150 1891 2152 1890 2155 1890 2156 1890 2158 1889 2159 1883 2157 1883 2156 1884 2156 1886 2156 1886 2154 1887 2151 
1888 2147 1888 2144 1888 2140 1889 2136 1889 2136 1899 2152 1901 2136 1902 2136 1905 2139 1907 2142 1910 2145 1912 2148 1913 2151 1914 2153 1915 2154 
1915 2156 1914 2158 1912 2159 1911 2158 1910 2157 1910 2156 1911 2155 1912 2154 1912 2153 1912 2152 1912 2151 1911 2150 1910 2148 1909 2147 1908 2145 
1906 2142 1904 2141 1902 2158 1902 2159 49 _pl _cp 
0 g _f _s _s 
0 g 1999 2147 _m
_sp 1999 2147 1997 2145 1995 2141 1994 2140 1992 2139 1992 2139 1991 2139 1990 2140 1989 2140 1989 2139 1988 2138 1989 2136 1990 2136 1992 2136 1993 2137 
1994 2138 1994 2138 1995 2140 1997 2141 1998 2143 1999 2144 1999 2145 1999 2144 2000 2141 2001 2139 2002 2137 2002 2136 2003 2136 2005 2136 2006 2137 
2008 2139 2009 2141 2010 2141 2009 2142 2007 2139 2005 2139 2004 2139 2004 2140 2004 2142 2003 2145 2002 2149 2002 2150 2004 2153 2005 2155 2006 2156 
2007 2156 2007 2156 2008 2155 2009 2155 2009 2155 2010 2156 2011 2157 2010 2158 2009 2159 2007 2159 2006 2158 2004 2156 2002 2153 2002 2152 2001 2154 
2000 2156 2000 2158 1999 2159 1998 2159 1997 2159 1995 2158 1992 2157 1992 2156 1994 2156 1995 2157 1995 2157 1996 2157 1997 2155 1997 2153 1998 2149 
75 _pl _cp 
0 g _f _s _s 
0 g 2030 2156 _m
_sp 2030 2156 2029 2158 2027 2159 2025 2159 2022 2158 2019 2156 2017 2154 2015 2151 2013 2148 2012 2145 2012 2142 2012 2139 2014 2138 2015 2136 2018 2136 
2020 2136 2021 2136 2022 2137 2023 2138 2025 2140 2027 2142 2024 2131 2023 2128 2021 2127 2019 2127 2019 2126 2030 2126 2031 2127 2029 2127 2028 2128 
2027 2129 2027 2130 2028 2131 2035 2158 2031 2158 35 _pl _cp 2017 2142 _m
_sp 2017 2142 2018 2139 2019 2138 2021 2138 2023 2140 2024 2141 2026 2144 2027 2147 2028 2150 2029 2152 2029 2154 2028 2156 2027 2157 2025 2156 2022 2155 
2020 2152 2018 2149 2017 2146 2017 2143 2017 2143 20 _pl _cp 
0 g _f _s _s 
0 g 1903 2102 _m
_sp 1903 2102 1902 2100 1904 2100 1905 2100 1906 2098 1906 2098 1906 2097 1905 2095 1902 2085 1901 2082 1901 2080 1901 2078 1901 2077 1902 2073 1904 2071 
1907 2069 1912 2068 1914 2068 1917 2069 1919 2070 1921 2071 1922 2073 1924 2075 1925 2078 1926 2083 1929 2095 1930 2097 1931 2099 1932 2100 1933 2100 
1933 2100 1934 2102 1924 2102 1924 2100 1925 2100 1926 2100 1927 2098 1927 2098 1927 2097 1926 2095 1924 2086 1922 2080 1921 2077 1920 2074 1919 2073 
1918 2072 1916 2071 1915 2070 1913 2070 1910 2071 1908 2072 1907 2074 1906 2076 1906 2077 1906 2079 1906 2081 1907 2084 1910 2095 1911 2097 1912 2099 
1913 2100 1914 2100 1915 2100 1915 2102 64 _pl _cp 
0 g _f _s _s 
0 g 1943 2056 _m
_sp 1943 2056 1941 2054 1939 2053 1937 2054 1936 2057 1937 2061 1938 2064 1940 2066 1942 2067 1943 2067 1943 2066 1943 2066 1943 2066 1943 2065 1943 2065 
1943 2065 1943 2064 1944 2063 1945 2064 1946 2065 1945 2067 1942 2068 1941 2068 1939 2067 1938 2066 1936 2065 1935 2063 1934 2062 1933 2060 1933 2058 
1933 2055 1934 2054 1936 2052 1938 2052 1940 2052 1941 2053 1943 2054 1944 2056 38 _pl _cp 
0 g _f _s _s 
0 g 1951 2066 _m
_sp 1951 2066 1951 2064 1949 2059 1948 2053 1947 2051 1947 2049 1947 2048 1946 2047 1945 2047 1944 2047 1944 2047 1944 2047 1944 2047 1944 2047 1944 2047 
1944 2048 1944 2048 1944 2048 1944 2049 1943 2049 1942 2049 1942 2048 1943 2047 1944 2046 1946 2046 1948 2048 1949 2050 1950 2051 1951 2054 1952 2057 
1954 2066 1957 2066 1958 2067 1954 2067 1954 2068 1955 2070 1956 2072 1957 2074 1958 2074 1959 2074 1959 2074 1959 2074 1959 2074 1959 2073 1959 2073 
1958 2073 1959 2072 1960 2072 1961 2072 1961 2073 1960 2075 1958 2075 1956 2075 1954 2073 1953 2072 1953 2071 1952 2069 1951 2067 1948 2067 1948 2066 
60 _pl _cp 
0 g _f _s _s 
0 g 1993 2079 _m
_sp 1993 2079 1992 2078 1990 2074 1988 2072 1987 2071 1986 2071 1986 2072 1985 2072 1984 2072 1983 2071 1983 2070 1984 2069 1985 2068 1987 2069 1988 2069 
1989 2070 1989 2071 1990 2072 1991 2074 1992 2075 1993 2077 1994 2077 1994 2077 1995 2074 1996 2071 1996 2069 1997 2068 1998 2068 2000 2068 2001 2069 
2003 2071 2004 2073 2004 2074 2003 2074 2002 2072 2000 2071 1999 2071 1999 2072 1999 2074 1998 2078 1997 2082 1997 2082 1999 2085 2000 2087 2001 2088 
2002 2088 2002 2088 2003 2088 2004 2087 2004 2087 2005 2088 2006 2089 2005 2090 2004 2091 2002 2091 2001 2090 1999 2088 1997 2085 1996 2084 1996 2086 
1995 2088 1995 2090 1994 2091 1993 2091 1991 2091 1989 2090 1987 2089 1987 2089 1989 2089 1989 2089 1990 2089 1991 2089 1992 2087 1992 2085 1993 2082 
75 _pl _cp 
0 g _f _s _s 
0 g 2084 2114 _m
_sp 2084 2114 2084 2113 2084 2112 2084 2110 2085 2109 2086 2108 2087 2108 2089 2109 2091 2111 2093 2113 2093 2114 2092 2113 2090 2111 2089 2111 2088 2111 
2088 2112 2088 2113 2088 2114 2096 2143 2088 2142 2088 2141 2089 2141 2090 2140 2091 2139 2091 2138 2090 2137 2088 2129 2087 2130 2085 2131 2083 2131 
2080 2130 2077 2128 2075 2126 2073 2123 2071 2120 2070 2117 2070 2114 2070 2111 2071 2110 2073 2108 2075 2108 2077 2108 2079 2109 2080 2110 2082 2111 
2083 2113 46 _pl _cp 2074 2114 _m
_sp 2074 2114 2075 2111 2077 2110 2079 2110 2081 2112 2082 2113 2084 2116 2085 2118 2085 2119 2086 2121 2086 2123 2087 2125 2087 2126 2086 2129 2084 2130 
2083 2130 2081 2129 2080 2127 2078 2124 2077 2122 2075 2119 2074 2116 2074 2114 2074 2114 24 _pl _cp 
0 g _f _s _s 
0 g 2104 2119 _m
_sp 2104 2119 2103 2118 2100 2114 2099 2112 2097 2111 2097 2111 2096 2111 2095 2112 2094 2112 2094 2111 2093 2110 2094 2109 2095 2108 2097 2108 2098 2109 
2099 2110 2100 2111 2101 2112 2102 2113 2103 2115 2104 2117 2104 2117 2104 2116 2105 2113 2106 2111 2107 2109 2108 2108 2109 2108 2110 2108 2111 2109 
2113 2111 2114 2113 2115 2114 2114 2114 2112 2112 2111 2111 2110 2111 2110 2112 2109 2114 2108 2118 2107 2122 2107 2122 2109 2125 2110 2127 2111 2128 
2112 2128 2112 2128 2113 2127 2114 2127 2115 2127 2116 2128 2116 2129 2115 2130 2114 2131 2113 2131 2111 2130 2110 2128 2107 2125 2107 2124 2106 2126 
2105 2130 2104 2131 2102 2131 2100 2130 2097 2129 2097 2128 2099 2129 2100 2129 2100 2129 2101 2129 2102 2127 2103 2125 2103 2122 73 _pl _cp 
0 g _f _s _s 
0 g 886 1984 _m
_sp 886 1984 886 2001 886 2001 886 2001 886 2003 886 2005 887 2006 889 2006 889 2006 890 2008 878 2008 878 2006 878 2006 879 2006 880 2005 
881 2003 881 2001 881 1974 882 1974 896 1996 896 1974 897 1974 914 2001 915 2003 917 2005 918 2006 919 2006 920 2008 910 2008 910 2006 
911 2006 912 2006 913 2005 912 2004 911 2001 901 1984 901 2001 901 2002 901 2002 901 2005 903 2006 904 2006 904 2008 893 2008 892 2006 
893 2006 895 2005 896 2002 896 2001 896 2001 896 2000 51 _pl _cp 
0 g _f _s _s 
0 g 966 1992 _m
_sp 966 1992 968 1993 970 1993 971 1994 972 1995 973 1997 974 2000 973 2003 972 2005 970 2006 969 2007 966 2008 962 2008 952 2008 952 2006 
953 2006 954 2006 955 2004 955 2003 955 2001 949 1981 948 1979 947 1977 946 1976 945 1976 945 1976 944 1975 954 1975 959 1975 962 1975 
964 1975 966 1976 969 1977 971 1979 972 1982 972 1984 972 1986 971 1988 971 1989 970 1990 968 1991 41 _pl _cp 957 1991 _m
_sp 957 1991 954 1981 954 1980 954 1979 955 1977 957 1977 961 1978 964 1979 965 1982 966 1985 966 1988 964 1990 962 1991 959 1991 958 1991 
15 _pl _cp 958 1993 _m
_sp 958 1993 959 1993 960 1993 963 1993 965 1994 966 1995 968 1996 969 1998 969 2000 969 2002 968 2004 966 2005 964 2005 963 2005 962 2005 
961 2005 960 2002 17 _pl _cp 
0 g _f _s _s 
0 g 972 1909 _m
_sp 972 1909 963 1908 963 1907 965 1907 966 1907 967 1906 967 1905 966 1903 960 1882 959 1878 959 1877 960 1875 962 1874 965 1875 967 1876 
968 1878 970 1880 969 1881 968 1880 966 1877 964 1876 964 1877 963 1877 963 1879 964 1880 25 _pl _cp 
0 g _f _s _s 
0 g 981 1891 _m
_sp 981 1891 986 1909 977 1908 977 1907 979 1907 980 1907 981 1906 981 1905 980 1903 974 1879 973 1877 973 1877 973 1877 973 1877 974 1876 
975 1875 976 1875 978 1874 980 1874 982 1874 985 1875 988 1877 990 1879 993 1882 995 1885 996 1888 996 1891 995 1894 994 1896 992 1897 
990 1897 989 1897 987 1897 986 1896 984 1895 983 1893 36 _pl _cp 978 1877 _m
_sp 978 1877 978 1876 980 1875 982 1875 983 1876 985 1878 986 1879 988 1882 990 1885 991 1888 991 1891 990 1894 988 1895 986 1894 984 1892 
982 1890 980 1886 979 1883 978 1881 978 1879 20 _pl _cp 
0 g _f _s _s 
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1856 1833 1857 1835 1857 1835 1856 1835 1855 1833 1853 1832 1853 1832 1853 1833 1853 1833 1853 1834 25 _pl _cp 
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30 _pl _cp 
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1919 1835 1919 1837 1918 1838 1916 1840 1915 1842 1914 1843 1915 1844 1916 1845 1918 1844 1920 1841 1921 1841 1921 1846 1921 1846 1920 1845 1920 1845 
1919 1845 1918 1846 1917 1846 1916 1846 1914 1846 1912 1845 1911 1844 1911 1843 1911 1842 1912 1840 1913 1839 1915 1837 1916 1835 1917 1834 1916 1832 
1914 1831 1913 1831 1911 1832 1910 1834 1910 1836 50 _pl _cp 
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1925 1833 1926 1834 1926 1835 1928 1844 1931 1844 1932 1845 1929 1845 1930 1849 1929 1849 1928 1848 1926 1846 1925 1846 1923 1845 1923 1844 29 _pl _cp 
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1933 1839 1932 1837 1932 1835 1932 1833 1933 1832 1935 1831 1937 1831 1939 1831 1941 1832 1942 1833 1943 1834 1943 1835 1941 1834 1940 1833 1939 1832 
1938 1832 1936 1833 1935 1835 1935 1836 34 _pl _cp 1936 1838 _m
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1958 1845 1957 1846 1956 1845 1954 1844 1954 1843 1952 1841 1952 1841 1952 1840 1953 1846 1948 1845 1948 1844 1949 1844 1950 1844 1950 1844 1950 1843 
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1969 1834 1968 1832 1969 1831 1970 1831 1971 1831 1972 1831 1974 1832 1975 1834 1974 1835 1972 1833 1971 1832 1971 1833 1971 1833 1971 1833 1971 1833 
1971 1835 1973 1841 1974 1843 1974 1844 1973 1845 1972 1846 1970 1845 1968 1844 1967 1842 1965 1840 1965 1840 1964 1839 1966 1846 1961 1845 1961 1844 
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2003 1832 2004 1834 2005 1835 2006 1836 2008 1839 2009 1840 2010 1842 2010 1844 2010 1845 2008 1846 2007 1846 2007 1845 2007 1844 2008 1843 2008 1843 
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2037 1845 2036 1846 2035 1845 2034 1844 2033 1843 2032 1841 2031 1841 2031 1840 2032 1846 2027 1845 2027 1844 2028 1844 2029 1844 2029 1844 2029 1843 
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1080 2319 1080 2320 1085 2340 1088 2313 1089 2313 1107 2340 1101 2320 1100 2318 1099 2316 1098 2315 1097 2315 1097 2315 1097 2313 1109 2313 1109 2315 
1108 2315 1107 2315 1106 2317 1106 2317 1106 2318 1107 2320 1112 2340 1113 2342 1113 2344 1114 2345 1115 2345 1116 2345 1116 2346 1108 2346 1092 2322 
1089 2346 1080 2346 1080 2345 1080 2345 1082 2345 50 _pl _cp 
0 g _f _s _s 
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1123 2299 1124 2300 1125 2302 1126 2303 1128 2305 1129 2307 1130 2309 1130 2310 1129 2311 1128 2312 1127 2312 1127 2311 1127 2311 1127 2310 1128 2309 
1128 2309 1128 2308 1127 2306 1127 2305 1126 2304 1124 2302 1123 2300 1123 2302 1122 2304 1122 2306 1122 2307 1122 2309 1121 2311 1121 2312 44 _pl _cp 
0 g _f _s _s 
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_sp 1136 2309 1137 2312 1132 2312 1132 2311 1133 2311 1134 2311 1134 2310 1134 2309 1134 2308 1130 2294 1129 2292 1128 2292 1127 2292 1127 2291 1134 2291 
1134 2292 1133 2292 1132 2292 1132 2293 1132 2293 1132 2293 1132 2294 1133 2297 1135 2297 1136 2297 1138 2297 1139 2298 1141 2299 1142 2300 1143 2302 
1145 2304 1146 2306 1146 2308 1145 2311 1142 2312 1141 2312 1139 2311 1138 2310 38 _pl _cp 1134 2300 _m
_sp 1134 2300 1134 2300 1134 2299 1134 2298 1135 2298 1137 2299 1139 2300 1140 2302 1142 2304 1143 2306 1143 2308 1142 2310 1141 2311 1140 2310 1138 2309 
1137 2308 1137 2307 1136 2306 1135 2304 19 _pl _cp 
0 g _f _s _s 
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1167 2314 1168 2314 1169 2316 1171 2318 1172 2319 1174 2321 1175 2323 1176 2325 1178 2326 1178 2328 1180 2331 1180 2333 1179 2335 1177 2336 1176 2335 
1175 2334 1175 2333 1176 2332 1177 2331 1177 2330 1177 2329 1176 2327 1175 2325 1173 2323 1172 2322 1171 2321 1170 2319 1169 2318 1169 2320 1168 2323 
1168 2326 1168 2328 1167 2330 1167 2332 1167 2334 1166 2335 1166 2336 52 _pl _cp 
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1186 2305 1185 2305 1184 2305 1183 2306 1183 2307 1183 2307 1184 2308 1185 2313 1187 2313 1189 2313 1191 2313 1194 2314 1196 2315 1198 2317 1201 2320 
1203 2323 1204 2326 1204 2330 1203 2333 1202 2335 1200 2336 1198 2336 1196 2336 1194 2335 1192 2333 40 _pl _cp 1186 2318 _m
_sp 1186 2318 1186 2317 1186 2316 1187 2315 1188 2314 1190 2314 1191 2315 1193 2316 1194 2317 1196 2320 1198 2323 1199 2327 1199 2330 1198 2333 1196 2334 
1194 2333 1192 2332 1191 2330 1190 2328 1189 2326 1188 2323 21 _pl _cp 
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1286 2319 1286 2320 1291 2340 1295 2313 1296 2313 1313 2340 1308 2320 1307 2318 1306 2316 1305 2315 1304 2315 1304 2315 1303 2313 1315 2313 1316 2315 
1315 2315 1313 2315 1312 2317 1312 2317 1313 2318 1313 2320 1318 2340 1319 2342 1320 2344 1321 2345 1322 2345 1322 2345 1323 2346 1314 2346 1298 2322 
1295 2346 1287 2346 1286 2345 1287 2345 1289 2345 50 _pl _cp 
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1329 2299 1330 2300 1331 2302 1332 2303 1334 2305 1335 2307 1336 2309 1337 2310 1336 2311 1335 2312 1334 2312 1333 2311 1333 2311 1334 2310 1335 2309 
1335 2309 1335 2308 1334 2306 1333 2305 1332 2304 1331 2302 1329 2300 1329 2302 1329 2304 1329 2306 1328 2307 1328 2309 1328 2311 1327 2312 44 _pl _cp 
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1349 2312 1348 2312 1347 2312 1345 2311 1344 2310 1343 2308 1343 2307 1342 2307 1344 2312 1339 2312 1338 2311 1340 2311 1341 2311 1341 2310 1341 2309 
1340 2308 31 _pl _cp 
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1370 2314 1370 2314 1372 2316 1373 2318 1375 2319 1376 2321 1377 2323 1379 2325 1380 2326 1381 2328 1382 2331 1383 2333 1382 2335 1380 2336 1379 2335 
1378 2334 1378 2333 1379 2332 1380 2331 1380 2330 1380 2329 1379 2327 1378 2325 1376 2323 1375 2322 1374 2321 1373 2319 1372 2318 1372 2320 1371 2323 
1371 2326 1371 2328 1370 2330 1369 2332 1369 2334 1369 2335 1369 2336 52 _pl _cp 
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1402 2331 1403 2333 1402 2335 1400 2336 1398 2335 1396 2334 1395 2333 1395 2332 1394 2331 1393 2329 1393 2328 1392 2327 1394 2336 1386 2335 1386 2334 
1388 2334 1389 2333 1389 2332 1389 2331 1389 2330 35 _pl _cp 
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820 2164 823 2172 822 2173 820 2171 819 2169 817 2168 816 2167 815 2167 813 2167 812 2166 810 2166 810 2166 809 2166 808 2166 806 2167 
805 2168 805 2169 806 2171 811 2190 812 2192 813 2194 814 2195 815 2195 815 2195 816 2197 803 2197 41 _pl _cp 
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869 2169 869 2170 874 2190 877 2164 878 2164 896 2191 891 2170 890 2168 889 2166 888 2165 887 2165 886 2165 886 2164 898 2164 899 2165 
897 2165 896 2166 895 2167 895 2168 895 2168 896 2170 901 2190 902 2192 903 2194 904 2195 905 2195 905 2195 905 2197 897 2197 881 2172 
878 2197 869 2197 869 2195 869 2195 872 2195 50 _pl _cp 
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_sp 917 2162 916 2161 916 2159 915 2158 915 2157 914 2155 913 2154 912 2152 911 2150 910 2149 909 2149 908 2150 908 2150 908 2151 908 2151 
911 2163 906 2162 906 2161 907 2161 908 2161 908 2161 908 2160 908 2159 906 2152 906 2152 906 2151 905 2150 905 2149 906 2148 907 2148 
909 2148 911 2149 912 2150 912 2151 913 2153 915 2155 914 2152 914 2151 913 2149 914 2148 915 2148 916 2148 918 2148 919 2149 920 2151 
919 2152 919 2151 918 2150 917 2149 917 2149 916 2149 916 2150 916 2150 916 2151 917 2152 917 2153 918 2155 918 2157 919 2160 919 2162 
60 _pl _cp 
0 g _f _s _s 
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_sp 928 2152 928 2154 928 2155 928 2157 927 2158 927 2161 926 2163 922 2162 922 2161 923 2161 924 2161 924 2160 925 2157 925 2154 926 2151 
926 2148 926 2148 933 2159 934 2148 935 2148 937 2150 938 2152 940 2154 941 2156 943 2159 943 2161 942 2162 941 2163 941 2163 940 2162 
940 2161 941 2160 942 2160 942 2159 942 2158 941 2158 940 2156 938 2154 937 2152 936 2151 935 2162 934 2163 42 _pl _cp 
0 g _f _s _s 
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_sp 973 2186 972 2183 971 2181 970 2178 969 2177 968 2175 967 2173 965 2170 964 2168 962 2167 961 2166 961 2167 960 2167 960 2168 960 2169 
965 2187 957 2185 957 2184 958 2184 959 2184 960 2183 960 2182 959 2180 957 2171 957 2170 956 2168 956 2167 956 2166 957 2164 959 2163 
960 2163 962 2164 963 2165 964 2166 965 2167 967 2169 968 2171 970 2174 969 2170 968 2168 968 2166 969 2164 971 2163 973 2163 974 2165 
976 2166 978 2169 977 2170 976 2169 975 2167 974 2166 973 2166 972 2166 972 2167 972 2168 972 2169 973 2170 973 2171 974 2173 974 2175 
974 2176 975 2178 976 2183 977 2186 64 _pl _cp 
0 g _f _s _s 
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985 2175 986 2171 986 2168 986 2164 987 2163 997 2180 999 2164 1000 2164 1003 2167 1005 2170 1008 2173 1010 2176 1011 2178 1012 2180 1013 2181 
1013 2183 1012 2185 1010 2186 1009 2186 1008 2185 1008 2184 1009 2183 1010 2182 1010 2181 1010 2180 1009 2178 1009 2177 1008 2176 1007 2174 1005 2172 
1004 2170 1002 2168 1000 2186 999 2187 49 _pl _cp 
0 g _f _s _s 
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_sp 1098 2193 1091 2170 1090 2168 1089 2166 1088 2165 1087 2165 1087 2165 1087 2164 1097 2164 1097 2165 1096 2165 1094 2166 1094 2167 1094 2168 1094 2168 
1094 2169 1094 2170 1099 2190 1102 2164 1103 2164 1121 2191 1116 2170 1115 2168 1114 2166 1113 2165 1112 2165 1111 2165 1111 2164 1123 2164 1124 2165 
1122 2165 1121 2166 1120 2167 1120 2168 1120 2168 1121 2170 1126 2190 1127 2192 1128 2194 1129 2195 1130 2195 1130 2195 1130 2197 1122 2197 1106 2172 
1103 2197 1094 2197 1094 2195 1094 2195 1097 2195 50 _pl _cp 
0 g _f _s _s 
0 g 1129 2162 _m
_sp 1129 2162 1129 2161 1129 2161 1129 2161 1131 2161 1132 2160 1132 2158 1133 2156 1133 2155 1133 2153 1133 2150 1133 2148 1134 2148 1135 2148 1135 2148 
1136 2149 1137 2151 1138 2152 1139 2153 1141 2156 1142 2157 1143 2159 1143 2161 1143 2162 1141 2163 1140 2163 1140 2162 1140 2161 1141 2160 1141 2160 
1141 2159 1141 2158 1140 2157 1140 2156 1139 2154 1138 2153 1136 2151 1136 2152 1135 2154 1135 2156 1135 2157 1135 2159 1134 2161 1134 2163 44 _pl _cp 
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_sp 1147 2162 1147 2161 1147 2161 1147 2161 1149 2161 1150 2160 1151 2158 1151 2156 1151 2155 1151 2153 1151 2150 1152 2148 1152 2148 1153 2148 1153 2148 
1154 2149 1155 2151 1156 2152 1157 2153 1159 2156 1160 2157 1161 2159 1162 2161 1161 2162 1160 2163 1159 2163 1158 2162 1158 2161 1159 2160 1160 2160 
1160 2159 1160 2158 1159 2157 1158 2156 1157 2154 1156 2153 1154 2151 1154 2152 1154 2154 1154 2156 1153 2157 1153 2159 1153 2161 1152 2163 44 _pl _cp 
0 g _f _s _s 
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_sp 1173 2185 1173 2184 1173 2184 1174 2184 1176 2184 1177 2182 1178 2181 1178 2179 1178 2178 1179 2176 1179 2174 1180 2171 1180 2167 1180 2164 1181 2163 
1182 2164 1182 2165 1184 2167 1185 2168 1187 2170 1188 2172 1189 2174 1191 2175 1192 2177 1193 2178 1194 2181 1195 2183 1194 2186 1192 2187 1191 2186 
1190 2185 1190 2184 1191 2182 1192 2182 1192 2181 1192 2179 1191 2177 1190 2176 1188 2174 1187 2172 1186 2171 1185 2170 1184 2169 1184 2170 1183 2173 
1183 2176 1183 2179 1182 2181 1181 2183 1181 2184 1181 2186 1181 2187 52 _pl _cp 
0 g _f _s _s 
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_sp 1311 2186 1310 2183 1309 2181 1308 2178 1307 2177 1306 2175 1305 2173 1303 2170 1301 2168 1300 2167 1298 2166 1298 2167 1298 2167 1298 2168 1298 2169 
1303 2187 1295 2185 1295 2184 1296 2184 1297 2184 1297 2183 1297 2182 1297 2180 1294 2171 1294 2170 1294 2168 1294 2167 1294 2166 1295 2164 1296 2163 
1298 2163 1299 2164 1301 2165 1302 2166 1303 2167 1304 2169 1305 2171 1307 2174 1306 2170 1306 2168 1306 2166 1307 2164 1309 2163 1310 2163 1311 2165 
1313 2166 1315 2169 1314 2170 1314 2169 1312 2167 1311 2166 1310 2166 1310 2166 1310 2167 1310 2168 1310 2169 1310 2170 1311 2171 1311 2173 1312 2175 
1312 2176 1312 2178 1314 2183 1315 2186 64 _pl _cp 
0 g _f _s _s 
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1348 2187 1340 2185 1340 2184 1341 2184 1342 2184 1342 2183 1342 2182 1342 2180 1339 2171 1339 2170 1339 2168 1339 2167 1339 2166 1340 2164 1341 2163 
1343 2163 1344 2164 1346 2165 1347 2166 1348 2167 1349 2169 1350 2171 1352 2174 1351 2170 1351 2168 1351 2166 1352 2164 1354 2163 1355 2163 1356 2165 
1358 2166 1360 2169 1359 2170 1359 2169 1357 2167 1356 2166 1355 2166 1355 2166 1355 2167 1355 2168 1355 2169 1355 2170 1356 2171 1356 2173 1357 2175 
1357 2176 1357 2178 1359 2183 1360 2186 64 _pl _cp 
0 g _f _s _s 
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_sp 1403 2193 1397 2170 1396 2168 1395 2166 1394 2165 1393 2165 1393 2165 1392 2164 1402 2164 1403 2165 1401 2165 1400 2166 1399 2167 1399 2168 1399 2168 
1400 2169 1400 2170 1405 2190 1408 2164 1409 2164 1427 2191 1421 2170 1420 2168 1419 2166 1418 2165 1417 2165 1417 2165 1417 2164 1429 2164 1429 2165 
1428 2165 1427 2166 1426 2167 1426 2168 1426 2168 1427 2170 1432 2190 1433 2192 1433 2194 1434 2195 1435 2195 1436 2195 1436 2197 1428 2197 1412 2172 
1409 2197 1400 2197 1400 2195 1400 2195 1402 2195 50 _pl _cp 
0 g _f _s _s 
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1436 2161 1437 2161 1438 2161 1438 2161 1438 2160 1437 2159 1436 2152 1436 2152 1435 2151 1435 2150 1435 2149 1436 2148 1437 2148 1439 2148 1441 2149 
1442 2150 1442 2151 1443 2153 1444 2155 1444 2152 1443 2151 1443 2149 1444 2148 1445 2148 1446 2148 1447 2148 1449 2149 1450 2151 1449 2152 1449 2151 
1448 2150 1447 2149 1446 2149 1446 2149 1446 2150 1446 2150 1446 2151 1446 2152 1447 2153 1447 2155 1448 2157 1449 2160 1449 2162 58 _pl _cp 
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1466 2161 1467 2161 1468 2161 1468 2161 1468 2160 1467 2159 1466 2152 1466 2152 1465 2151 1465 2150 1465 2149 1466 2148 1467 2148 1469 2148 1471 2149 
1472 2150 1472 2151 1473 2153 1474 2155 1474 2152 1473 2151 1473 2149 1474 2148 1475 2148 1476 2148 1477 2148 1479 2149 1480 2151 1479 2152 1479 2151 
1478 2150 1477 2149 1476 2149 1476 2149 1476 2150 1476 2150 1476 2151 1476 2152 1477 2153 1477 2155 1478 2157 1479 2160 1479 2162 58 _pl _cp 
0 g _f _s _s 
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1522 2148 1524 2148 1526 2148 1528 2149 1529 2150 1531 2151 1532 2153 1533 2155 1534 2156 1534 2158 1534 2160 1533 2162 1532 2163 1531 2163 1530 2163 
1529 2163 1527 2161 32 _pl _cp 1522 2150 _m
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1523 2154 1523 2152 1522 2151 18 _pl _cp 
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1570 2142 1569 2142 1568 2142 1568 2143 1568 2143 1568 2144 1568 2145 1569 2148 1570 2148 1571 2148 1573 2148 1575 2149 1576 2150 1578 2151 1579 2153 
1580 2155 1581 2157 1581 2159 1580 2162 1578 2163 1577 2163 1575 2162 1574 2161 38 _pl _cp 1570 2151 _m
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1573 2159 1572 2158 1572 2156 1571 2154 19 _pl _cp 
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1586 2148 1588 2148 1590 2148 1592 2149 1593 2150 1595 2151 1596 2153 1598 2155 1599 2156 1599 2158 1599 2160 1598 2162 1596 2163 1595 2163 1594 2163 
1593 2163 1591 2161 32 _pl _cp 1587 2150 _m
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1587 2154 1587 2152 1587 2151 18 _pl _cp 
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1680 2169 1681 2170 1686 2190 1689 2164 1690 2164 1708 2191 1702 2170 1701 2168 1700 2166 1699 2165 1698 2165 1698 2165 1697 2164 1710 2164 1710 2165 
1709 2165 1707 2166 1707 2167 1707 2168 1707 2168 1707 2170 1712 2190 1713 2192 1714 2194 1715 2195 1716 2195 1717 2195 1717 2197 1708 2197 1693 2172 
1689 2197 1681 2197 1681 2195 1681 2195 1683 2195 50 _pl _cp 
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1722 2163 1717 2162 1717 2161 1717 2161 1718 2161 1719 2161 1719 2160 1718 2159 1716 2152 1716 2152 1716 2151 1716 2150 1716 2149 1717 2148 1718 2148 
1720 2148 1721 2149 1722 2150 1723 2151 1724 2153 1725 2155 1724 2152 1724 2151 1724 2149 1725 2148 1726 2148 1728 2148 1730 2151 1730 2152 1729 2151 
1728 2150 1728 2149 1727 2149 1727 2149 1727 2150 1727 2150 1727 2151 1727 2152 1727 2153 1728 2155 1728 2157 1729 2160 1730 2162 58 _pl _cp 
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1752 2163 1747 2162 1747 2161 1747 2161 1748 2161 1749 2161 1749 2160 1748 2159 1746 2152 1746 2152 1746 2151 1746 2150 1746 2149 1747 2148 1748 2148 
1750 2148 1751 2149 1752 2150 1753 2151 1754 2153 1755 2155 1754 2152 1754 2151 1754 2149 1755 2148 1756 2148 1758 2148 1760 2151 1760 2152 1759 2151 
1758 2150 1758 2149 1757 2149 1757 2149 1757 2150 1757 2150 1757 2151 1757 2152 1757 2153 1758 2155 1758 2157 1759 2160 1760 2162 58 _pl _cp 
0 g _f _s _s 
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_sp 1799 2153 1799 2148 1799 2148 1800 2148 1800 2148 1800 2148 1800 2148 1801 2148 1802 2148 1803 2148 1804 2148 1806 2148 1808 2149 1809 2150 1810 2151 
1810 2152 1809 2154 1808 2155 1807 2157 1805 2159 1804 2160 1805 2161 1806 2162 1809 2161 1810 2158 1811 2158 1812 2163 1811 2163 1811 2162 1810 2162 
1809 2162 1808 2163 1807 2163 1806 2163 1803 2162 1802 2160 1802 2159 1802 2157 1803 2156 1805 2154 1807 2152 1807 2151 1806 2149 1804 2148 1803 2148 
1801 2149 1800 2151 1800 2153 48 _pl _cp 
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1847 2142 1846 2142 1845 2142 1845 2143 1845 2143 1845 2144 1845 2145 1846 2148 1847 2148 1848 2148 1850 2148 1852 2149 1853 2150 1855 2151 1856 2153 
1857 2155 1858 2157 1858 2159 1857 2162 1855 2163 1854 2163 1852 2162 1851 2161 38 _pl _cp 1847 2151 _m
_sp 1847 2151 1847 2150 1847 2150 1847 2149 1848 2148 1850 2149 1852 2150 1853 2152 1854 2154 1855 2157 1855 2159 1855 2160 1853 2161 1852 2161 1851 2160 
1850 2159 1849 2158 1849 2156 1848 2154 19 _pl _cp 
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1870 2152 1870 2154 1869 2155 1867 2157 1865 2159 1865 2160 1866 2161 1867 2162 1869 2161 1871 2158 1871 2158 1872 2163 1872 2163 1871 2162 1870 2162 
1870 2162 1869 2163 1868 2163 1867 2163 1865 2163 1863 2162 1862 2161 1862 2160 1862 2159 1863 2157 1864 2156 1865 2154 1867 2152 1867 2151 1866 2149 
1865 2148 1863 2148 1862 2149 1861 2151 1860 2153 50 _pl _cp 
0 g _f _s _s 
0 g 839 2054 _m
_sp 839 2054 838 2053 837 2050 836 2049 835 2049 835 2049 834 2049 834 2049 833 2049 833 2049 832 2048 833 2047 833 2047 834 2047 835 2047 
836 2048 836 2048 838 2050 839 2052 840 2053 840 2052 840 2050 841 2047 842 2047 844 2047 846 2050 847 2050 846 2051 845 2049 844 2049 
843 2050 842 2053 841 2056 842 2056 844 2059 845 2060 845 2060 846 2059 846 2059 846 2059 847 2060 848 2061 847 2062 846 2062 844 2061 
842 2058 841 2057 841 2059 840 2061 839 2062 838 2062 837 2061 835 2061 835 2060 836 2060 837 2060 837 2060 838 2059 839 2056 59 _pl _cp 
0 g _f _s _s 
0 g 863 2047 _m
_sp 863 2047 866 2047 867 2051 868 2053 868 2054 869 2056 870 2058 872 2059 874 2060 874 2060 874 2059 874 2059 874 2058 874 2057 872 2051 
872 2050 872 2048 872 2047 873 2047 874 2047 876 2047 877 2048 878 2050 877 2051 876 2049 875 2048 875 2049 875 2049 875 2049 875 2049 
875 2051 877 2057 877 2059 877 2060 876 2061 875 2062 874 2061 872 2060 870 2058 868 2056 868 2056 868 2055 870 2062 864 2061 864 2060 
865 2060 866 2060 866 2060 866 2059 866 2058 50 _pl _cp 
0 g _f _s _s 
0 g 880 2051 _m
_sp 880 2051 880 2049 881 2048 883 2047 885 2047 887 2047 888 2047 890 2048 891 2050 892 2052 893 2053 894 2055 894 2057 894 2059 893 2061 
891 2062 889 2062 888 2062 886 2061 885 2060 883 2059 882 2057 881 2056 880 2054 880 2052 880 2052 26 _pl _cp 883 2050 _m
_sp 883 2050 884 2048 886 2047 888 2048 889 2051 890 2053 891 2054 891 2056 891 2057 890 2060 889 2061 888 2061 887 2060 885 2059 884 2057 
884 2055 884 2054 883 2052 883 2051 883 2051 20 _pl _cp 
0 g _f _s _s 
0 g 896 2052 _m
_sp 896 2052 895 2047 896 2047 896 2047 897 2047 897 2047 897 2047 898 2047 899 2047 900 2047 901 2047 903 2047 905 2048 906 2049 906 2050 
906 2051 906 2053 905 2054 903 2056 902 2058 901 2059 902 2060 903 2061 905 2060 907 2057 908 2057 908 2062 908 2062 907 2061 907 2061 
906 2061 905 2062 904 2062 903 2062 901 2062 899 2061 898 2060 898 2059 898 2058 899 2056 900 2055 902 2053 903 2051 904 2050 903 2048 
901 2047 900 2047 898 2048 897 2050 897 2052 50 _pl _cp 
0 g _f _s _s 
0 g 913 2053 _m
_sp 913 2053 913 2053 916 2054 918 2054 920 2055 921 2057 922 2058 922 2059 921 2061 919 2062 918 2062 916 2061 915 2060 913 2059 912 2057 
911 2055 910 2053 910 2051 911 2048 914 2047 917 2047 919 2048 920 2049 921 2050 920 2051 918 2049 916 2048 914 2049 913 2051 913 2052 
30 _pl _cp 913 2054 _m
_sp 913 2054 915 2055 916 2055 917 2056 919 2057 920 2059 920 2060 920 2061 919 2061 918 2061 916 2060 915 2059 915 2057 914 2056 14 _pl _cp 
0 g _f _s _s 
0 g 826 1989 _m
_sp 826 1989 825 1988 824 1986 823 1985 822 1984 822 1984 821 1984 821 1985 820 1985 820 1984 819 1983 820 1982 820 1982 821 1982 822 1983 
823 1983 823 1984 825 1986 826 1988 827 1988 827 1988 827 1986 828 1983 829 1982 831 1983 833 1985 834 1986 833 1986 832 1984 831 1984 
830 1985 829 1988 828 1991 829 1991 831 1995 832 1995 832 1995 833 1995 833 1995 833 1995 834 1995 835 1996 834 1997 833 1997 831 1997 
829 1993 828 1993 828 1994 827 1997 826 1997 825 1997 824 1997 822 1996 822 1996 823 1996 824 1996 824 1996 825 1995 826 1991 59 _pl _cp 
0 g _f _s _s 
0 g 853 1996 _m
_sp 853 1996 851 1986 850 1985 850 1984 851 1983 852 1982 854 1982 855 1983 856 1984 857 1986 856 1986 855 1984 854 1984 853 1984 853 1984 
853 1985 853 1985 853 1987 856 1996 859 1996 859 1997 856 1997 857 2001 857 2001 855 1999 854 1998 853 1997 851 1997 851 1996 29 _pl _cp 
0 g _f _s _s 
0 g 869 1987 _m
_sp 869 1987 868 1985 868 1983 869 1982 869 1982 870 1982 872 1983 873 1984 874 1986 874 1986 872 1985 871 1984 871 1984 871 1985 871 1986 
871 1988 873 1993 874 1996 874 1997 871 1997 871 1996 870 1997 868 1997 866 1997 864 1995 862 1993 860 1991 859 1988 859 1986 860 1983 
862 1982 864 1982 866 1983 867 1985 34 _pl _cp 862 1987 _m
_sp 862 1987 862 1985 864 1984 866 1985 868 1987 869 1989 869 1991 870 1993 870 1994 870 1995 868 1996 866 1995 864 1993 863 1991 862 1989 
862 1988 16 _pl _cp 
0 g _f _s _s 
0 g 882 1986 _m
_sp 882 1986 881 1984 880 1984 879 1984 879 1984 879 1985 880 1986 883 1997 877 1997 877 1996 878 1996 879 1996 879 1995 879 1994 879 1993 
877 1987 877 1986 877 1984 877 1983 878 1982 879 1982 881 1983 882 1984 883 1986 24 _pl _cp 880 2003 _m
_sp 880 2003 881 2002 882 2001 883 2002 884 2003 883 2004 882 2004 881 2004 8 _pl _cp 
0 g _f _s _s 
0 g 894 2005 _m
_sp 894 2005 889 2004 888 2004 890 2004 891 2004 891 2003 891 2002 890 2001 886 1987 886 1985 886 1984 887 1983 888 1982 890 1982 891 1984 
892 1985 893 1986 892 1986 892 1986 890 1984 889 1983 889 1984 888 1984 889 1985 889 1986 25 _pl _cp 
0 g _f _s _s 
0 g 973 2022 _m
_sp 973 2022 970 2019 968 2018 965 2016 962 2016 960 2016 958 2017 957 2018 956 2019 955 2021 954 2022 953 2024 953 2026 953 2031 955 2036 
957 2040 960 2043 963 2045 967 2046 969 2046 970 2045 972 2045 973 2044 974 2043 974 2041 975 2040 975 2038 976 2038 978 2048 977 2048 
976 2047 975 2047 975 2047 974 2047 972 2048 970 2048 969 2048 967 2048 962 2047 958 2046 954 2043 951 2040 949 2036 947 2032 947 2027 
947 2024 948 2022 949 2020 951 2018 953 2016 955 2015 958 2014 961 2014 964 2014 966 2015 968 2016 970 2017 972 2019 974 2021 59 _pl _cp 
0 g _f _s _s 
0 g 989 2002 _m
_sp 989 2002 988 2001 988 2001 988 2000 989 1999 990 1998 991 1998 992 1999 993 2000 995 2002 994 2002 994 2002 992 2000 992 2000 991 2000 
991 2001 991 2001 991 2002 997 2021 991 2020 991 2020 992 2020 993 2020 993 2019 993 2018 993 2017 991 2012 990 2013 989 2013 988 2013 
986 2012 985 2011 983 2010 981 2008 980 2006 979 2004 979 2002 980 1999 983 1998 985 1999 987 2000 988 2001 42 _pl _cp 982 2002 _m
_sp 982 2002 983 2001 984 2000 986 2001 988 2003 989 2004 989 2005 990 2008 991 2010 990 2012 989 2012 988 2012 987 2011 985 2010 984 2009 
983 2007 983 2006 982 2004 982 2002 982 2002 20 _pl _cp 
0 g _f _s _s 
0 g 996 2012 _m
_sp 996 2012 996 2012 997 2012 997 2012 998 2011 999 2010 1000 2008 1000 2007 1001 2005 1001 2003 1002 2001 1002 1998 1001 1997 1000 1996 999 1994 
998 1994 998 1994 998 1994 997 1994 997 1994 997 1995 996 1995 995 1994 995 1993 995 1992 996 1992 998 1992 999 1992 1000 1993 1001 1994 
1001 1995 1002 1997 1004 1999 1005 2001 1006 2002 1007 2005 1008 2007 1009 2009 1010 2010 1010 2011 1009 2012 1008 2013 1007 2013 1006 2012 1007 2011 
1007 2011 1008 2010 1008 2009 1008 2009 1008 2009 1008 2008 1007 2007 1007 2005 1006 2004 1006 2003 1005 2002 1005 2002 1004 2001 1004 2002 1004 2002 
1003 2005 1003 2007 1003 2008 1002 2010 1001 2013 1001 2013 66 _pl _cp 
0 g _f _s _s 
0 g 1022 2014 _m
_sp 1022 2014 1026 2014 1028 2020 1029 2023 1030 2024 1030 2026 1031 2027 1032 2028 1033 2030 1034 2031 1035 2032 1037 2034 1039 2034 1040 2034 1040 2033 
1040 2032 1039 2031 1036 2020 1036 2018 1035 2016 1036 2015 1038 2014 1040 2014 1041 2015 1043 2017 1045 2019 1044 2020 1042 2017 1040 2016 1040 2017 
1040 2017 1040 2018 1040 2019 1043 2029 1043 2031 1044 2033 1044 2034 1043 2036 1041 2037 1039 2037 1037 2036 1036 2035 1035 2034 1034 2033 1033 2032 
1032 2030 1030 2028 1036 2049 1027 2048 1027 2047 1029 2047 1030 2046 1030 2045 1030 2044 1030 2043 55 _pl _cp 
0 g _f _s _s 
0 g 1073 2025 _m
_sp 1073 2025 1071 2024 1069 2020 1068 2018 1066 2017 1066 2017 1065 2017 1064 2018 1063 2018 1063 2017 1062 2016 1063 2015 1064 2014 1066 2014 1067 2015 
1068 2016 1068 2017 1069 2018 1071 2019 1072 2021 1073 2023 1073 2023 1073 2022 1074 2019 1075 2017 1076 2015 1076 2014 1077 2014 1079 2014 1080 2015 
1082 2017 1083 2019 1084 2020 1083 2020 1081 2018 1079 2017 1078 2017 1078 2018 1078 2020 1077 2024 1076 2028 1076 2028 1078 2031 1079 2033 1080 2034 
1081 2034 1081 2034 1082 2033 1083 2033 1083 2033 1084 2034 1085 2035 1084 2036 1083 2037 1081 2037 1080 2036 1078 2034 1076 2031 1076 2030 1075 2032 
1074 2034 1074 2036 1073 2037 1072 2037 1071 2037 1069 2036 1066 2035 1066 2034 1068 2035 1069 2035 1069 2035 1070 2035 1071 2033 1071 2031 1072 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1124 2036 _m
_sp 1124 2036 1124 2035 1124 2035 1125 2035 1127 2034 1128 2033 1129 2031 1129 2030 1129 2028 1130 2027 1130 2024 1131 2021 1131 2018 1131 2014 1132 2014 
1133 2015 1133 2015 1135 2017 1136 2019 1138 2020 1139 2022 1140 2024 1142 2026 1143 2027 1144 2029 1145 2032 1146 2034 1145 2036 1143 2037 1142 2036 
1141 2035 1141 2034 1142 2033 1143 2032 1143 2031 1143 2030 1142 2028 1141 2026 1139 2024 1138 2023 1137 2022 1136 2020 1135 2019 1135 2021 1134 2024 
1134 2027 1134 2029 1133 2031 1132 2033 1132 2035 1132 2036 1132 2037 52 _pl _cp 
0 g _f _s _s 
0 g 1229 2025 _m
_sp 1229 2025 1228 2024 1226 2020 1224 2018 1223 2017 1222 2017 1222 2017 1221 2018 1220 2018 1219 2017 1219 2016 1220 2015 1221 2014 1223 2014 1224 2015 
1225 2016 1225 2017 1226 2018 1227 2019 1228 2021 1229 2023 1230 2023 1230 2022 1231 2019 1232 2017 1232 2015 1233 2014 1234 2014 1236 2014 1237 2015 
1239 2017 1240 2019 1240 2020 1239 2020 1238 2018 1236 2017 1235 2017 1235 2018 1235 2020 1234 2024 1233 2028 1233 2028 1235 2031 1236 2033 1237 2034 
1238 2034 1238 2034 1239 2033 1240 2033 1240 2033 1241 2034 1242 2035 1241 2036 1240 2037 1238 2037 1237 2036 1235 2034 1233 2031 1232 2030 1232 2032 
1231 2034 1231 2036 1230 2037 1229 2037 1227 2037 1225 2036 1223 2035 1223 2034 1225 2035 1225 2035 1226 2035 1227 2035 1228 2033 1228 2031 1229 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1243 2014 _m
_sp 1243 2014 1248 2014 1249 2019 1250 2022 1250 2024 1251 2026 1252 2027 1253 2029 1254 2030 1256 2032 1257 2033 1257 2033 1258 2032 1259 2032 1260 2031 
1261 2032 1262 2034 1261 2036 1259 2037 1257 2036 1255 2035 1254 2034 1254 2033 1253 2032 1252 2030 1252 2029 1251 2028 1253 2037 1245 2036 1245 2035 
1247 2035 1248 2034 1248 2033 1248 2032 1248 2031 35 _pl _cp 
0 g _f _s _s 
0 g 1393 2022 _m
_sp 1393 2022 1390 2019 1388 2018 1385 2016 1382 2016 1380 2016 1379 2017 1377 2018 1376 2019 1375 2021 1374 2022 1373 2024 1373 2026 1373 2031 1375 2036 
1377 2040 1380 2043 1383 2045 1387 2046 1389 2046 1391 2045 1392 2045 1394 2044 1395 2043 1395 2041 1395 2040 1395 2038 1397 2038 1398 2048 1397 2048 
1397 2047 1396 2047 1395 2047 1394 2047 1392 2048 1390 2048 1389 2048 1388 2048 1383 2047 1379 2046 1375 2043 1372 2040 1370 2036 1368 2032 1368 2027 
1368 2024 1369 2022 1370 2020 1371 2018 1373 2016 1376 2015 1379 2014 1381 2014 1383 2014 1384 2014 1386 2014 1387 2015 1389 2016 1391 2017 1392 2019 
1394 2021 61 _pl _cp 
0 g _f _s _s 
0 g 1409 2002 _m
_sp 1409 2002 1409 2001 1409 2001 1409 2000 1409 1999 1410 1998 1411 1998 1413 1999 1414 2000 1415 2002 1415 2002 1414 2002 1413 2000 1412 2000 1412 2000 
1412 2001 1412 2001 1412 2002 1417 2021 1412 2020 1411 2020 1413 2020 1414 2020 1414 2019 1414 2018 1413 2017 1412 2012 1411 2013 1409 2013 1408 2013 
1406 2012 1405 2011 1403 2010 1402 2008 1400 2006 1399 2004 1399 2002 1400 1999 1403 1998 1406 1999 1408 2000 1409 2001 42 _pl _cp 1402 2002 _m
_sp 1402 2002 1403 2001 1405 2000 1407 2001 1409 2003 1410 2004 1410 2005 1411 2008 1411 2010 1410 2012 1409 2012 1407 2011 1405 2009 1404 2007 1403 2006 
1402 2004 1402 2002 1402 2002 18 _pl _cp 
0 g _f _s _s 
0 g 1416 1999 _m
_sp 1416 1999 1416 1998 1417 1999 1418 1999 1419 1999 1420 1998 1423 1997 1424 1996 1425 1996 1427 1997 1428 1998 1428 1999 1427 2000 1426 2000 1426 1999 
1426 1998 1426 1998 1426 1998 1426 1998 1426 1997 1425 1997 1424 1998 1423 1999 1421 2001 1419 2001 1428 2012 1428 2013 1419 2013 1418 2009 1418 2009 
1419 2011 1422 2011 1426 2011 1418 2001 1417 2000 35 _pl _cp 
0 g _f _s _s 
0 g 1450 2031 _m
_sp 1450 2031 1454 2049 1446 2048 1446 2047 1448 2047 1449 2046 1449 2045 1449 2044 1449 2043 1442 2019 1442 2017 1442 2017 1442 2017 1442 2016 1442 2016 
1444 2015 1445 2014 1447 2014 1448 2014 1451 2014 1454 2015 1457 2017 1459 2019 1462 2022 1464 2025 1465 2028 1465 2030 1464 2033 1463 2035 1461 2036 
1459 2037 1458 2037 1456 2037 1455 2036 1453 2034 1452 2033 36 _pl _cp 1446 2017 _m
_sp 1446 2017 1447 2016 1449 2015 1451 2015 1452 2016 1454 2017 1455 2018 1457 2021 1459 2025 1460 2028 1460 2031 1459 2033 1457 2034 1455 2033 1452 2032 
1450 2029 1449 2026 1448 2023 1447 2021 1446 2019 20 _pl _cp 
0 g _f _s _s 
0 g 1491 2025 _m
_sp 1491 2025 1490 2024 1488 2020 1486 2018 1485 2017 1484 2017 1484 2017 1483 2018 1482 2018 1481 2017 1481 2016 1482 2015 1483 2014 1485 2014 1486 2015 
1487 2016 1487 2017 1488 2018 1489 2019 1490 2021 1491 2023 1492 2023 1492 2022 1493 2019 1494 2017 1494 2015 1495 2014 1496 2014 1498 2014 1499 2015 
1501 2017 1502 2019 1502 2020 1501 2020 1500 2018 1498 2017 1497 2017 1497 2018 1497 2020 1496 2024 1495 2028 1495 2028 1497 2031 1498 2033 1499 2034 
1500 2034 1500 2034 1501 2033 1502 2033 1502 2033 1503 2034 1504 2035 1503 2036 1502 2037 1500 2037 1499 2036 1497 2034 1495 2031 1494 2030 1494 2032 
1493 2034 1493 2036 1492 2037 1491 2037 1489 2037 1487 2036 1485 2035 1485 2034 1487 2035 1487 2035 1488 2035 1489 2035 1490 2033 1490 2031 1491 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1552 2021 _m
_sp 1552 2021 1552 2024 1552 2026 1552 2028 1551 2030 1551 2033 1551 2035 1550 2036 1550 2037 1543 2035 1543 2035 1545 2035 1546 2034 1547 2033 1548 2029 
1548 2026 1548 2022 1549 2018 1549 2014 1550 2014 1560 2031 1562 2014 1563 2014 1565 2017 1568 2020 1570 2023 1572 2026 1574 2029 1575 2031 1575 2032 
1575 2034 1574 2036 1573 2037 1571 2036 1571 2035 1571 2034 1572 2033 1573 2032 1573 2031 1573 2030 1572 2029 1571 2028 1571 2026 1570 2025 1568 2023 
1566 2020 1565 2019 1563 2036 1562 2037 49 _pl _cp 
0 g _f _s _s 
0 g 1659 2025 _m
_sp 1659 2025 1658 2024 1655 2020 1654 2018 1653 2017 1652 2017 1651 2017 1651 2018 1650 2018 1649 2017 1648 2016 1649 2015 1650 2014 1652 2014 1653 2015 
1654 2016 1655 2017 1656 2018 1657 2019 1658 2021 1659 2023 1659 2023 1660 2022 1660 2019 1661 2017 1662 2015 1663 2014 1664 2014 1665 2014 1667 2015 
1668 2017 1670 2019 1670 2020 1669 2020 1667 2018 1666 2017 1665 2017 1665 2018 1664 2020 1663 2024 1662 2028 1663 2028 1665 2031 1666 2033 1666 2034 
1667 2034 1668 2034 1669 2033 1670 2033 1670 2033 1671 2034 1672 2035 1671 2036 1669 2037 1668 2037 1666 2036 1665 2034 1663 2031 1662 2030 1662 2032 
1661 2034 1661 2036 1660 2037 1659 2037 1657 2037 1655 2036 1652 2035 1653 2034 1654 2035 1655 2035 1655 2035 1656 2035 1657 2033 1658 2031 1659 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1691 2034 _m
_sp 1691 2034 1689 2036 1687 2037 1685 2037 1683 2036 1680 2034 1678 2032 1676 2029 1674 2026 1673 2023 1673 2020 1673 2017 1674 2016 1676 2014 1678 2014 
1680 2014 1681 2014 1682 2015 1684 2016 1685 2018 1687 2020 1684 2009 1683 2006 1681 2006 1679 2006 1679 2005 1691 2005 1691 2006 1689 2006 1688 2006 
1688 2007 1688 2008 1688 2009 1695 2036 1691 2036 35 _pl _cp 1677 2020 _m
_sp 1677 2020 1678 2018 1680 2017 1682 2017 1683 2018 1685 2020 1687 2023 1688 2025 1689 2028 1690 2030 1690 2032 1689 2034 1687 2035 1685 2035 1683 2033 
1680 2030 1679 2027 1677 2024 1677 2021 1677 2021 20 _pl _cp 
0 g _f _s _s 
0 g 1785 2049 _m
_sp 1785 2049 1785 2052 1785 2054 1785 2056 1784 2058 1784 2061 1784 2062 1783 2064 1783 2065 1776 2063 1776 2062 1778 2062 1779 2062 1780 2060 1781 2057 
1781 2053 1781 2050 1782 2046 1782 2042 1783 2042 1793 2058 1795 2042 1796 2042 1798 2045 1801 2048 1803 2051 1805 2054 1807 2057 1808 2059 1808 2060 
1808 2062 1807 2064 1806 2065 1804 2064 1804 2063 1804 2062 1805 2061 1806 2060 1806 2059 1806 2058 1805 2057 1804 2056 1804 2054 1803 2053 1801 2051 
1799 2048 1798 2047 1796 2064 1795 2065 49 _pl _cp 
0 g _f _s _s 
0 g 1892 2053 _m
_sp 1892 2053 1891 2051 1888 2047 1887 2046 1886 2045 1885 2045 1884 2045 1884 2046 1883 2046 1882 2045 1881 2044 1882 2042 1883 2042 1885 2042 1886 2043 
1887 2044 1888 2044 1889 2046 1890 2047 1891 2049 1892 2050 1892 2051 1893 2050 1893 2047 1894 2045 1895 2043 1896 2042 1897 2042 1898 2042 1900 2043 
1901 2045 1903 2047 1903 2047 1902 2048 1900 2045 1899 2045 1898 2045 1898 2046 1897 2048 1896 2051 1895 2055 1896 2056 1898 2059 1899 2061 1899 2062 
1900 2062 1901 2062 1902 2061 1903 2061 1903 2061 1904 2062 1905 2063 1904 2064 1902 2065 1901 2065 1899 2064 1898 2062 1896 2059 1895 2058 1895 2060 
1894 2062 1894 2064 1893 2065 1892 2065 1890 2065 1888 2064 1885 2063 1886 2062 1887 2062 1888 2063 1888 2063 1889 2063 1890 2061 1891 2059 1892 2055 
75 _pl _cp 
0 g _f _s _s 
0 g 1924 2062 _m
_sp 1924 2062 1922 2064 1920 2065 1918 2065 1916 2064 1913 2062 1911 2060 1909 2057 1907 2054 1906 2051 1906 2048 1906 2045 1907 2044 1909 2042 1911 2042 
1913 2042 1914 2042 1915 2043 1917 2044 1918 2046 1920 2048 1917 2037 1916 2034 1914 2033 1912 2033 1912 2032 1924 2032 1924 2033 1922 2033 1921 2034 
1921 2035 1921 2036 1921 2037 1928 2064 1924 2064 35 _pl _cp 1910 2048 _m
_sp 1910 2048 1911 2045 1913 2044 1915 2044 1916 2046 1918 2047 1920 2050 1921 2053 1922 2056 1923 2058 1923 2060 1922 2062 1920 2063 1918 2062 1916 2061 
1913 2058 1912 2055 1910 2052 1910 2049 1910 2049 20 _pl _cp 
0 g _f _s _s 
0 g 1796 2008 _m
_sp 1796 2008 1796 2006 1797 2006 1799 2006 1799 2004 1799 2004 1799 2003 1799 2001 1796 1991 1795 1988 1795 1986 1794 1984 1794 1983 1795 1979 1797 1977 
1801 1975 1805 1974 1808 1974 1810 1975 1812 1976 1814 1977 1815 1979 1817 1981 1818 1984 1819 1989 1822 2001 1823 2003 1824 2005 1825 2006 1826 2006 
1827 2006 1827 2008 1817 2008 1817 2006 1818 2006 1820 2006 1821 2004 1821 2004 1820 2003 1820 2001 1817 1992 1816 1986 1815 1983 1813 1980 1812 1979 
1811 1978 1809 1977 1808 1976 1806 1976 1803 1977 1801 1978 1800 1980 1799 1982 1799 1983 1800 1985 1800 1987 1801 1990 1804 2001 1805 2003 1806 2005 
1807 2006 1808 2006 1808 2006 1808 2008 64 _pl _cp 
0 g _f _s _s 
0 g 1837 1962 _m
_sp 1837 1962 1836 1961 1835 1960 1833 1959 1832 1959 1830 1960 1829 1963 1830 1967 1831 1970 1833 1972 1835 1973 1836 1973 1837 1972 1837 1972 1837 1972 
1836 1971 1836 1971 1836 1971 1837 1970 1838 1969 1839 1970 1839 1971 1838 1973 1836 1974 1834 1974 1832 1973 1831 1972 1829 1971 1828 1969 1827 1968 
1826 1966 1826 1964 1826 1961 1828 1960 1829 1958 1832 1958 1833 1958 1835 1959 1836 1960 1837 1962 40 _pl _cp 
0 g _f _s _s 
0 g 1845 1972 _m
_sp 1845 1972 1844 1970 1843 1965 1841 1959 1841 1957 1840 1955 1840 1954 1839 1953 1839 1953 1838 1953 1838 1953 1837 1953 1837 1953 1838 1953 1838 1953 
1838 1954 1838 1954 1838 1954 1837 1955 1836 1955 1836 1955 1835 1954 1836 1953 1838 1952 1840 1952 1841 1954 1842 1956 1843 1957 1844 1960 1845 1963 
1847 1972 1851 1972 1851 1973 1848 1973 1848 1974 1849 1976 1849 1978 1851 1980 1852 1980 1852 1980 1852 1980 1852 1980 1852 1980 1852 1979 1852 1979 
1852 1979 1853 1978 1853 1978 1854 1978 1855 1979 1854 1981 1852 1981 1850 1981 1848 1979 1847 1978 1847 1977 1846 1975 1845 1973 1842 1973 1842 1972 
60 _pl _cp 
0 g _f _s _s 
0 g 1887 1985 _m
_sp 1887 1985 1886 1984 1883 1980 1882 1978 1880 1977 1880 1977 1879 1978 1878 1978 1877 1978 1877 1977 1876 1976 1877 1975 1878 1974 1880 1975 1881 1975 
1882 1976 1883 1977 1884 1978 1885 1980 1886 1981 1887 1983 1887 1983 1887 1983 1888 1980 1889 1977 1890 1975 1891 1974 1892 1974 1893 1974 1894 1975 
1896 1977 1897 1979 1898 1980 1897 1980 1895 1978 1894 1977 1893 1977 1893 1978 1892 1980 1891 1984 1890 1988 1890 1988 1892 1991 1893 1993 1894 1994 
1895 1994 1895 1994 1896 1994 1897 1993 1898 1993 1899 1994 1899 1995 1898 1996 1897 1997 1896 1997 1894 1996 1893 1994 1890 1991 1890 1990 1889 1992 
1888 1996 1887 1997 1885 1997 1883 1996 1880 1995 1880 1995 1882 1995 1883 1995 1883 1995 1884 1995 1885 1993 1886 1991 1886 1988 73 _pl _cp 
0 g _f _s _s 
0 g 1972 2025 _m
_sp 1972 2025 1971 2024 1969 2020 1967 2018 1966 2017 1965 2017 1965 2017 1964 2018 1963 2018 1962 2017 1962 2016 1963 2015 1964 2014 1966 2014 1967 2015 
1968 2016 1968 2017 1969 2018 1970 2019 1971 2021 1972 2023 1973 2023 1973 2022 1974 2019 1975 2017 1975 2015 1976 2014 1977 2014 1979 2014 1980 2015 
1982 2017 1983 2019 1983 2020 1982 2020 1981 2018 1979 2017 1978 2017 1978 2018 1978 2020 1977 2024 1976 2028 1976 2028 1978 2031 1979 2033 1980 2034 
1981 2034 1981 2034 1982 2033 1983 2033 1983 2033 1984 2034 1985 2035 1984 2036 1983 2037 1981 2037 1980 2036 1978 2034 1976 2031 1975 2030 1975 2032 
1974 2034 1974 2036 1973 2037 1972 2037 1970 2037 1968 2036 1966 2035 1966 2034 1968 2035 1968 2035 1969 2035 1970 2035 1971 2033 1971 2031 1972 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 2011 2020 _m
_sp 2011 2020 2011 2019 2010 2018 2010 2016 2011 2015 2013 2014 2014 2014 2016 2015 2018 2017 2020 2019 2019 2020 2018 2019 2016 2017 2015 2017 2015 2017 
2015 2018 2015 2019 2015 2020 2023 2049 2015 2048 2014 2047 2016 2047 2017 2046 2018 2045 2018 2044 2017 2043 2015 2035 2013 2036 2011 2037 2009 2037 
2007 2036 2004 2034 2002 2032 2000 2029 1998 2026 1997 2023 1996 2020 1997 2017 1998 2016 2000 2014 2002 2014 2004 2014 2005 2015 2007 2016 2009 2017 
2010 2019 46 _pl _cp 2001 2020 _m
_sp 2001 2020 2002 2017 2004 2016 2006 2016 2008 2018 2009 2019 2011 2022 2012 2024 2012 2025 2013 2027 2013 2029 2014 2031 2014 2032 2013 2035 2011 2036 
2010 2036 2008 2035 2007 2033 2005 2030 2003 2028 2002 2025 2001 2022 2001 2020 2001 2020 24 _pl _cp 
0 g _f _s _s 
0 g 2031 2025 _m
_sp 2031 2025 2029 2024 2027 2020 2026 2018 2024 2017 2024 2017 2023 2017 2022 2018 2021 2018 2021 2017 2020 2016 2021 2015 2022 2014 2024 2014 2025 2015 
2026 2016 2026 2017 2027 2018 2029 2019 2030 2021 2031 2023 2031 2023 2031 2022 2032 2019 2033 2017 2034 2015 2034 2014 2035 2014 2037 2014 2038 2015 
2040 2017 2041 2019 2042 2020 2041 2020 2039 2018 2037 2017 2036 2017 2036 2018 2036 2020 2035 2024 2034 2028 2034 2028 2036 2031 2037 2033 2038 2034 
2039 2034 2039 2034 2040 2033 2041 2033 2041 2033 2042 2034 2043 2035 2042 2036 2041 2037 2039 2037 2038 2036 2036 2034 2034 2031 2034 2030 2033 2032 
2032 2034 2032 2036 2031 2037 2030 2037 2029 2037 2027 2036 2024 2035 2024 2034 2026 2035 2027 2035 2027 2035 2028 2035 2029 2033 2029 2031 2030 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 775 1891 _m
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30 _pl _cp 908 2054 _m
_sp 908 2054 910 2055 911 2055 912 2056 914 2057 915 2059 915 2060 915 2061 914 2061 913 2061 911 2060 910 2059 910 2057 909 2056 14 _pl _cp 
0 g _f _s _s 
0 g 821 1989 _m
_sp 821 1989 820 1988 819 1986 818 1985 817 1984 817 1984 816 1984 816 1985 815 1985 815 1984 814 1983 815 1982 815 1982 816 1982 817 1983 
818 1983 818 1984 820 1986 821 1988 822 1988 822 1988 822 1986 823 1983 824 1982 826 1983 828 1985 829 1986 828 1986 827 1984 826 1984 
825 1985 824 1988 823 1991 824 1991 826 1995 827 1995 827 1995 828 1995 828 1995 828 1995 829 1995 830 1996 829 1997 828 1997 826 1997 
824 1993 823 1993 823 1994 822 1997 821 1997 820 1997 819 1997 817 1996 817 1996 818 1996 819 1996 819 1996 820 1995 821 1991 59 _pl _cp 
0 g _f _s _s 
0 g 848 1996 _m
_sp 848 1996 846 1986 845 1985 845 1984 846 1983 847 1982 849 1982 850 1983 851 1984 852 1986 851 1986 850 1984 849 1984 848 1984 848 1984 
848 1985 848 1985 848 1987 851 1996 854 1996 854 1997 851 1997 852 2001 852 2001 850 1999 849 1998 848 1997 846 1997 846 1996 29 _pl _cp 
0 g _f _s _s 
0 g 864 1987 _m
_sp 864 1987 863 1985 863 1983 864 1982 864 1982 865 1982 867 1983 868 1984 869 1986 869 1986 867 1985 866 1984 866 1984 866 1985 866 1986 
866 1988 868 1993 869 1996 869 1997 866 1997 866 1996 865 1997 863 1997 861 1997 859 1995 857 1993 855 1991 854 1988 854 1986 855 1983 
857 1982 859 1982 861 1983 862 1985 34 _pl _cp 857 1987 _m
_sp 857 1987 857 1985 859 1984 861 1985 863 1987 864 1989 864 1991 865 1993 865 1994 865 1995 863 1996 861 1995 859 1993 858 1991 857 1989 
857 1988 16 _pl _cp 
0 g _f _s _s 
0 g 877 1986 _m
_sp 877 1986 876 1984 875 1984 874 1984 874 1984 874 1985 875 1986 878 1997 872 1997 872 1996 873 1996 874 1996 874 1995 874 1994 874 1993 
872 1987 872 1986 872 1984 872 1983 873 1982 874 1982 876 1983 877 1984 878 1986 24 _pl _cp 875 2003 _m
_sp 875 2003 876 2002 877 2001 878 2002 879 2003 878 2004 877 2004 876 2004 8 _pl _cp 
0 g _f _s _s 
0 g 889 2005 _m
_sp 889 2005 884 2004 883 2004 885 2004 886 2004 886 2003 886 2002 885 2001 881 1987 881 1985 881 1984 882 1983 883 1982 885 1982 886 1984 
887 1985 888 1986 887 1986 887 1986 885 1984 884 1983 884 1984 883 1984 884 1985 884 1986 25 _pl _cp 
0 g _f _s _s 
0 g 968 2022 _m
_sp 968 2022 965 2019 963 2018 960 2016 957 2016 955 2016 953 2017 952 2018 951 2019 950 2021 949 2022 948 2024 948 2026 948 2031 950 2036 
952 2040 955 2043 958 2045 962 2046 964 2046 965 2045 967 2045 968 2044 969 2043 969 2041 970 2040 970 2038 971 2038 973 2048 972 2048 
971 2047 970 2047 970 2047 969 2047 967 2048 965 2048 964 2048 962 2048 957 2047 953 2046 949 2043 946 2040 944 2036 942 2032 942 2027 
942 2024 943 2022 944 2020 946 2018 948 2016 950 2015 953 2014 956 2014 959 2014 961 2015 963 2016 965 2017 967 2019 969 2021 59 _pl _cp 
0 g _f _s _s 
0 g 984 2002 _m
_sp 984 2002 983 2001 983 2001 983 2000 984 1999 985 1998 986 1998 987 1999 988 2000 990 2002 989 2002 989 2002 987 2000 987 2000 986 2000 
986 2001 986 2001 986 2002 992 2021 986 2020 986 2020 987 2020 988 2020 988 2019 988 2018 988 2017 986 2012 985 2013 984 2013 983 2013 
981 2012 980 2011 978 2010 976 2008 975 2006 974 2004 974 2002 975 1999 978 1998 980 1999 982 2000 983 2001 42 _pl _cp 977 2002 _m
_sp 977 2002 978 2001 979 2000 981 2001 983 2003 984 2004 984 2005 985 2008 986 2010 985 2012 984 2012 983 2012 982 2011 980 2010 979 2009 
978 2007 978 2006 977 2004 977 2002 977 2002 20 _pl _cp 
0 g _f _s _s 
0 g 991 2012 _m
_sp 991 2012 991 2012 992 2012 992 2012 993 2011 994 2010 995 2008 995 2007 996 2005 996 2003 997 2001 997 1998 996 1997 995 1996 994 1994 
993 1994 993 1994 993 1994 992 1994 992 1994 992 1995 991 1995 990 1994 990 1993 990 1992 991 1992 993 1992 994 1992 995 1993 996 1994 
996 1995 997 1997 999 1999 1000 2001 1001 2002 1002 2005 1003 2007 1004 2009 1005 2010 1005 2011 1004 2012 1003 2013 1002 2013 1001 2012 1002 2011 
1002 2011 1003 2010 1003 2009 1003 2009 1003 2009 1003 2008 1002 2007 1002 2005 1001 2004 1001 2003 1000 2002 1000 2002 999 2001 999 2002 999 2002 
998 2005 998 2007 998 2008 997 2010 996 2013 996 2013 66 _pl _cp 
0 g _f _s _s 
0 g 1017 2014 _m
_sp 1017 2014 1021 2014 1023 2020 1024 2023 1025 2024 1025 2026 1026 2027 1027 2028 1028 2030 1029 2031 1030 2032 1032 2034 1034 2034 1035 2034 1035 2033 
1035 2032 1034 2031 1031 2020 1031 2018 1030 2016 1031 2015 1033 2014 1035 2014 1036 2015 1038 2017 1040 2019 1039 2020 1037 2017 1035 2016 1035 2017 
1035 2017 1035 2018 1035 2019 1038 2029 1038 2031 1039 2033 1039 2034 1038 2036 1036 2037 1034 2037 1032 2036 1031 2035 1030 2034 1029 2033 1028 2032 
1027 2030 1025 2028 1031 2049 1022 2048 1022 2047 1024 2047 1025 2046 1025 2045 1025 2044 1025 2043 55 _pl _cp 
0 g _f _s _s 
0 g 1068 2025 _m
_sp 1068 2025 1066 2024 1064 2020 1063 2018 1061 2017 1061 2017 1060 2017 1059 2018 1058 2018 1058 2017 1057 2016 1058 2015 1059 2014 1061 2014 1062 2015 
1063 2016 1063 2017 1064 2018 1066 2019 1067 2021 1068 2023 1068 2023 1068 2022 1069 2019 1070 2017 1071 2015 1071 2014 1072 2014 1074 2014 1075 2015 
1077 2017 1078 2019 1079 2020 1078 2020 1076 2018 1074 2017 1073 2017 1073 2018 1073 2020 1072 2024 1071 2028 1071 2028 1073 2031 1074 2033 1075 2034 
1076 2034 1076 2034 1077 2033 1078 2033 1078 2033 1079 2034 1080 2035 1079 2036 1078 2037 1076 2037 1075 2036 1073 2034 1071 2031 1071 2030 1070 2032 
1069 2034 1069 2036 1068 2037 1067 2037 1066 2037 1064 2036 1061 2035 1061 2034 1063 2035 1064 2035 1064 2035 1065 2035 1066 2033 1066 2031 1067 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1119 2036 _m
_sp 1119 2036 1119 2035 1119 2035 1120 2035 1122 2034 1123 2033 1124 2031 1124 2030 1124 2028 1125 2027 1125 2024 1126 2021 1126 2018 1126 2014 1127 2014 
1128 2015 1128 2015 1130 2017 1131 2019 1133 2020 1134 2022 1135 2024 1137 2026 1138 2027 1139 2029 1140 2032 1141 2034 1140 2036 1138 2037 1137 2036 
1136 2035 1136 2034 1137 2033 1138 2032 1138 2031 1138 2030 1137 2028 1136 2026 1134 2024 1133 2023 1132 2022 1131 2020 1130 2019 1130 2021 1129 2024 
1129 2027 1129 2029 1128 2031 1127 2033 1127 2035 1127 2036 1127 2037 52 _pl _cp 
0 g _f _s _s 
0 g 1224 2025 _m
_sp 1224 2025 1223 2024 1221 2020 1219 2018 1218 2017 1217 2017 1217 2017 1216 2018 1215 2018 1214 2017 1214 2016 1215 2015 1216 2014 1218 2014 1219 2015 
1220 2016 1220 2017 1221 2018 1222 2019 1223 2021 1224 2023 1225 2023 1225 2022 1226 2019 1227 2017 1227 2015 1228 2014 1229 2014 1231 2014 1232 2015 
1234 2017 1235 2019 1235 2020 1234 2020 1233 2018 1231 2017 1230 2017 1230 2018 1230 2020 1229 2024 1228 2028 1228 2028 1230 2031 1231 2033 1232 2034 
1233 2034 1233 2034 1234 2033 1235 2033 1235 2033 1236 2034 1237 2035 1236 2036 1235 2037 1233 2037 1232 2036 1230 2034 1228 2031 1227 2030 1227 2032 
1226 2034 1226 2036 1225 2037 1224 2037 1222 2037 1220 2036 1218 2035 1218 2034 1220 2035 1220 2035 1221 2035 1222 2035 1223 2033 1223 2031 1224 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1238 2014 _m
_sp 1238 2014 1243 2014 1244 2019 1245 2022 1245 2024 1246 2026 1247 2027 1248 2029 1249 2030 1251 2032 1252 2033 1252 2033 1253 2032 1254 2032 1255 2031 
1256 2032 1257 2034 1256 2036 1254 2037 1252 2036 1250 2035 1249 2034 1249 2033 1248 2032 1247 2030 1247 2029 1246 2028 1248 2037 1240 2036 1240 2035 
1242 2035 1243 2034 1243 2033 1243 2032 1243 2031 35 _pl _cp 
0 g _f _s _s 
0 g 1388 2022 _m
_sp 1388 2022 1385 2019 1383 2018 1380 2016 1377 2016 1375 2016 1374 2017 1372 2018 1371 2019 1370 2021 1369 2022 1368 2024 1368 2026 1368 2031 1370 2036 
1372 2040 1375 2043 1378 2045 1382 2046 1384 2046 1386 2045 1387 2045 1389 2044 1390 2043 1390 2041 1390 2040 1390 2038 1392 2038 1393 2048 1392 2048 
1392 2047 1391 2047 1390 2047 1389 2047 1387 2048 1385 2048 1384 2048 1383 2048 1378 2047 1374 2046 1370 2043 1367 2040 1365 2036 1363 2032 1363 2027 
1363 2024 1364 2022 1365 2020 1366 2018 1368 2016 1371 2015 1374 2014 1376 2014 1378 2014 1379 2014 1381 2014 1382 2015 1384 2016 1386 2017 1387 2019 
1389 2021 61 _pl _cp 
0 g _f _s _s 
0 g 1404 2002 _m
_sp 1404 2002 1404 2001 1404 2001 1404 2000 1404 1999 1405 1998 1406 1998 1408 1999 1409 2000 1410 2002 1410 2002 1409 2002 1408 2000 1407 2000 1407 2000 
1407 2001 1407 2001 1407 2002 1412 2021 1407 2020 1406 2020 1408 2020 1409 2020 1409 2019 1409 2018 1408 2017 1407 2012 1406 2013 1404 2013 1403 2013 
1401 2012 1400 2011 1398 2010 1397 2008 1395 2006 1394 2004 1394 2002 1395 1999 1398 1998 1401 1999 1403 2000 1404 2001 42 _pl _cp 1397 2002 _m
_sp 1397 2002 1398 2001 1400 2000 1402 2001 1404 2003 1405 2004 1405 2005 1406 2008 1406 2010 1405 2012 1404 2012 1402 2011 1400 2009 1399 2007 1398 2006 
1397 2004 1397 2002 1397 2002 18 _pl _cp 
0 g _f _s _s 
0 g 1411 1999 _m
_sp 1411 1999 1411 1998 1412 1999 1413 1999 1414 1999 1415 1998 1418 1997 1419 1996 1420 1996 1422 1997 1423 1998 1423 1999 1422 2000 1421 2000 1421 1999 
1421 1998 1421 1998 1421 1998 1421 1998 1421 1997 1420 1997 1419 1998 1418 1999 1416 2001 1414 2001 1423 2012 1423 2013 1414 2013 1413 2009 1413 2009 
1414 2011 1417 2011 1421 2011 1413 2001 1412 2000 35 _pl _cp 
0 g _f _s _s 
0 g 1445 2031 _m
_sp 1445 2031 1449 2049 1441 2048 1441 2047 1443 2047 1444 2046 1444 2045 1444 2044 1444 2043 1437 2019 1437 2017 1437 2017 1437 2017 1437 2016 1437 2016 
1439 2015 1440 2014 1442 2014 1443 2014 1446 2014 1449 2015 1452 2017 1454 2019 1457 2022 1459 2025 1460 2028 1460 2030 1459 2033 1458 2035 1456 2036 
1454 2037 1453 2037 1451 2037 1450 2036 1448 2034 1447 2033 36 _pl _cp 1441 2017 _m
_sp 1441 2017 1442 2016 1444 2015 1446 2015 1447 2016 1449 2017 1450 2018 1452 2021 1454 2025 1455 2028 1455 2031 1454 2033 1452 2034 1450 2033 1447 2032 
1445 2029 1444 2026 1443 2023 1442 2021 1441 2019 20 _pl _cp 
0 g _f _s _s 
0 g 1486 2025 _m
_sp 1486 2025 1485 2024 1483 2020 1481 2018 1480 2017 1479 2017 1479 2017 1478 2018 1477 2018 1476 2017 1476 2016 1477 2015 1478 2014 1480 2014 1481 2015 
1482 2016 1482 2017 1483 2018 1484 2019 1485 2021 1486 2023 1487 2023 1487 2022 1488 2019 1489 2017 1489 2015 1490 2014 1491 2014 1493 2014 1494 2015 
1496 2017 1497 2019 1497 2020 1496 2020 1495 2018 1493 2017 1492 2017 1492 2018 1492 2020 1491 2024 1490 2028 1490 2028 1492 2031 1493 2033 1494 2034 
1495 2034 1495 2034 1496 2033 1497 2033 1497 2033 1498 2034 1499 2035 1498 2036 1497 2037 1495 2037 1494 2036 1492 2034 1490 2031 1489 2030 1489 2032 
1488 2034 1488 2036 1487 2037 1486 2037 1484 2037 1482 2036 1480 2035 1480 2034 1482 2035 1482 2035 1483 2035 1484 2035 1485 2033 1485 2031 1486 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1547 2021 _m
_sp 1547 2021 1547 2024 1547 2026 1547 2028 1546 2030 1546 2033 1546 2035 1545 2036 1545 2037 1538 2035 1538 2035 1540 2035 1541 2034 1542 2033 1543 2029 
1543 2026 1543 2022 1544 2018 1544 2014 1545 2014 1555 2031 1557 2014 1558 2014 1560 2017 1563 2020 1565 2023 1567 2026 1569 2029 1570 2031 1570 2032 
1570 2034 1569 2036 1568 2037 1566 2036 1566 2035 1566 2034 1567 2033 1568 2032 1568 2031 1568 2030 1567 2029 1566 2028 1566 2026 1565 2025 1563 2023 
1561 2020 1560 2019 1558 2036 1557 2037 49 _pl _cp 
0 g _f _s _s 
0 g 1654 2025 _m
_sp 1654 2025 1653 2024 1650 2020 1649 2018 1648 2017 1647 2017 1646 2017 1646 2018 1645 2018 1644 2017 1643 2016 1644 2015 1645 2014 1647 2014 1648 2015 
1649 2016 1650 2017 1651 2018 1652 2019 1653 2021 1654 2023 1654 2023 1655 2022 1655 2019 1656 2017 1657 2015 1658 2014 1659 2014 1660 2014 1662 2015 
1663 2017 1665 2019 1665 2020 1664 2020 1662 2018 1661 2017 1660 2017 1660 2018 1659 2020 1658 2024 1657 2028 1658 2028 1660 2031 1661 2033 1661 2034 
1662 2034 1663 2034 1664 2033 1665 2033 1665 2033 1666 2034 1667 2035 1666 2036 1664 2037 1663 2037 1661 2036 1660 2034 1658 2031 1657 2030 1657 2032 
1656 2034 1656 2036 1655 2037 1654 2037 1652 2037 1650 2036 1647 2035 1648 2034 1649 2035 1650 2035 1650 2035 1651 2035 1652 2033 1653 2031 1654 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 1686 2034 _m
_sp 1686 2034 1684 2036 1682 2037 1680 2037 1678 2036 1675 2034 1673 2032 1671 2029 1669 2026 1668 2023 1668 2020 1668 2017 1669 2016 1671 2014 1673 2014 
1675 2014 1676 2014 1677 2015 1679 2016 1680 2018 1682 2020 1679 2009 1678 2006 1676 2006 1674 2006 1674 2005 1686 2005 1686 2006 1684 2006 1683 2006 
1683 2007 1683 2008 1683 2009 1690 2036 1686 2036 35 _pl _cp 1672 2020 _m
_sp 1672 2020 1673 2018 1675 2017 1677 2017 1678 2018 1680 2020 1682 2023 1683 2025 1684 2028 1685 2030 1685 2032 1684 2034 1682 2035 1680 2035 1678 2033 
1675 2030 1674 2027 1672 2024 1672 2021 1672 2021 20 _pl _cp 
0 g _f _s _s 
0 g 1771 2063 _m
_sp 1771 2063 1771 2063 1771 2063 1771 2063 1774 2062 1775 2060 1776 2059 1776 2057 1776 2056 1776 2054 1777 2052 1777 2049 1777 2046 1778 2042 1778 2042 
1779 2043 1780 2043 1782 2045 1783 2046 1785 2048 1786 2050 1787 2052 1789 2053 1790 2055 1791 2056 1792 2058 1792 2059 1793 2061 1793 2062 1792 2064 
1790 2065 1788 2064 1788 2063 1788 2062 1789 2061 1790 2060 1790 2059 1789 2057 1788 2055 1787 2054 1786 2052 1785 2050 1784 2049 1782 2048 1781 2047 
1781 2049 1781 2052 1781 2055 1780 2057 1780 2059 1779 2061 1779 2063 1779 2064 1778 2065 54 _pl _cp 
0 g _f _s _s 
0 g 1876 2053 _m
_sp 1876 2053 1875 2051 1872 2047 1871 2046 1870 2045 1869 2045 1868 2045 1868 2046 1867 2046 1866 2045 1865 2044 1866 2042 1867 2042 1869 2042 1870 2043 
1871 2044 1872 2044 1873 2046 1874 2047 1875 2049 1876 2050 1876 2051 1877 2050 1877 2047 1878 2045 1879 2043 1880 2042 1881 2042 1882 2042 1884 2043 
1885 2045 1887 2047 1887 2047 1886 2048 1884 2045 1883 2045 1882 2045 1882 2046 1881 2048 1880 2051 1879 2055 1880 2056 1882 2059 1883 2061 1883 2062 
1884 2062 1885 2062 1886 2061 1887 2061 1887 2061 1888 2062 1889 2063 1888 2064 1886 2065 1885 2065 1883 2064 1882 2062 1880 2059 1879 2058 1879 2060 
1878 2062 1878 2064 1877 2065 1876 2065 1874 2065 1872 2064 1869 2063 1870 2062 1871 2062 1872 2063 1872 2063 1873 2063 1874 2061 1875 2059 1876 2055 
75 _pl _cp 
0 g _f _s _s 
0 g 1890 2042 _m
_sp 1890 2042 1894 2042 1896 2047 1897 2050 1897 2052 1898 2054 1899 2055 1900 2057 1901 2058 1903 2060 1904 2061 1904 2061 1904 2060 1905 2060 1906 2059 
1908 2060 1909 2062 1908 2064 1906 2065 1904 2064 1902 2062 1901 2061 1899 2058 1899 2057 1898 2056 1900 2065 1892 2064 1892 2063 1894 2063 1895 2062 
1895 2061 1895 2060 1895 2059 33 _pl _cp 
0 g _f _s _s 
0 g 1783 2008 _m
_sp 1783 2008 1783 2006 1784 2006 1785 2006 1786 2004 1786 2004 1786 2003 1785 2001 1783 1991 1782 1988 1781 1986 1781 1984 1781 1983 1782 1979 1784 1977 
1788 1975 1792 1974 1795 1974 1797 1975 1799 1976 1801 1977 1802 1979 1804 1981 1805 1984 1806 1989 1809 2001 1810 2003 1811 2005 1812 2006 1813 2006 
1813 2006 1814 2008 1804 2008 1804 2006 1805 2006 1807 2006 1807 2004 1807 2004 1807 2003 1807 2001 1804 1992 1803 1986 1802 1983 1800 1980 1799 1979 
1798 1978 1796 1977 1795 1976 1793 1976 1790 1977 1788 1978 1787 1980 1786 1982 1786 1983 1786 1985 1787 1987 1788 1990 1791 2001 1792 2003 1793 2005 
1794 2006 1795 2006 1795 2006 1795 2008 64 _pl _cp 
0 g _f _s _s 
0 g 1824 1962 _m
_sp 1824 1962 1823 1961 1822 1960 1820 1959 1819 1959 1817 1960 1816 1963 1817 1967 1818 1970 1820 1972 1822 1973 1823 1973 1824 1972 1824 1972 1824 1972 
1823 1971 1823 1971 1823 1971 1824 1970 1824 1969 1825 1970 1826 1971 1825 1973 1822 1974 1821 1974 1819 1973 1818 1972 1816 1971 1815 1969 1814 1968 
1813 1966 1813 1964 1813 1961 1814 1960 1816 1958 1818 1958 1820 1958 1821 1959 1823 1960 1824 1962 40 _pl _cp 
0 g _f _s _s 
0 g 1831 1972 _m
_sp 1831 1972 1831 1970 1830 1965 1828 1959 1827 1957 1827 1955 1827 1954 1826 1953 1826 1953 1825 1953 1824 1953 1824 1953 1824 1953 1824 1953 1824 1953 
1824 1954 1824 1954 1824 1954 1824 1955 1823 1955 1822 1955 1822 1954 1823 1953 1824 1952 1826 1952 1828 1954 1829 1956 1830 1957 1831 1960 1832 1963 
1834 1972 1838 1972 1838 1973 1834 1973 1835 1974 1836 1976 1836 1978 1838 1980 1839 1980 1839 1980 1839 1980 1839 1980 1839 1980 1839 1979 1839 1979 
1839 1979 1839 1978 1840 1978 1841 1978 1841 1979 1840 1981 1839 1981 1837 1981 1835 1979 1834 1978 1834 1977 1833 1975 1832 1973 1829 1973 1828 1972 
60 _pl _cp 
0 g _f _s _s 
0 g 1874 1985 _m
_sp 1874 1985 1872 1984 1870 1980 1869 1978 1867 1977 1867 1977 1866 1978 1865 1978 1864 1978 1864 1977 1863 1976 1864 1975 1865 1974 1867 1975 1868 1975 
1869 1976 1869 1977 1870 1978 1872 1980 1873 1981 1874 1983 1874 1983 1874 1983 1875 1980 1876 1977 1877 1975 1877 1974 1878 1974 1880 1974 1881 1975 
1883 1977 1884 1979 1885 1980 1884 1980 1882 1978 1880 1977 1879 1977 1879 1978 1879 1980 1878 1984 1877 1988 1877 1988 1879 1991 1880 1993 1881 1994 
1882 1994 1882 1994 1883 1994 1884 1993 1884 1993 1885 1994 1886 1995 1885 1996 1884 1997 1882 1997 1881 1996 1879 1994 1877 1991 1877 1990 1876 1992 
1875 1994 1875 1996 1874 1997 1873 1997 1872 1997 1870 1996 1867 1995 1867 1995 1869 1995 1870 1995 1870 1995 1871 1995 1872 1993 1872 1991 1873 1988 
75 _pl _cp 
0 g _f _s _s 
0 g 1951 2025 _m
_sp 1951 2025 1950 2024 1947 2020 1946 2018 1944 2017 1944 2017 1943 2017 1942 2018 1941 2018 1941 2017 1940 2016 1941 2015 1942 2014 1944 2014 1945 2015 
1946 2016 1947 2017 1948 2018 1949 2019 1950 2021 1951 2023 1951 2023 1951 2022 1952 2019 1953 2017 1954 2015 1955 2014 1956 2014 1957 2014 1958 2015 
1960 2017 1961 2019 1962 2020 1961 2020 1959 2018 1958 2017 1957 2017 1957 2018 1956 2020 1955 2024 1954 2028 1954 2028 1956 2031 1957 2033 1958 2034 
1959 2034 1959 2034 1960 2033 1961 2033 1962 2033 1963 2034 1963 2035 1962 2036 1961 2037 1960 2037 1958 2036 1957 2034 1954 2031 1954 2030 1953 2032 
1952 2036 1951 2037 1949 2037 1947 2036 1944 2035 1944 2034 1946 2035 1947 2035 1947 2035 1948 2035 1949 2033 1950 2031 1950 2028 73 _pl _cp 
0 g _f _s _s 
0 g 1989 2020 _m
_sp 1989 2020 1989 2019 1989 2018 1989 2016 1990 2015 1991 2014 1993 2014 1994 2015 1996 2017 1999 2019 1998 2020 1997 2019 1995 2017 1994 2017 1993 2017 
1993 2018 1993 2019 1994 2020 2001 2049 1993 2048 1993 2047 1995 2047 1996 2046 1996 2045 1996 2044 1996 2043 1994 2035 1992 2036 1990 2037 1988 2037 
1986 2036 1983 2034 1981 2032 1978 2029 1977 2026 1975 2023 1975 2020 1975 2017 1976 2016 1978 2014 1980 2014 1982 2014 1984 2015 1986 2016 1988 2017 
1989 2019 46 _pl _cp 1979 2020 _m
_sp 1979 2020 1980 2017 1983 2016 1985 2016 1986 2018 1988 2019 1989 2022 1990 2024 1991 2025 1992 2027 1992 2029 1993 2031 1993 2032 1992 2035 1990 2036 
1988 2036 1987 2035 1985 2033 1983 2030 1982 2028 1980 2025 1979 2022 1979 2020 1979 2020 24 _pl _cp 
0 g _f _s _s 
0 g 2009 2025 _m
_sp 2009 2025 2008 2024 2005 2020 2004 2018 2003 2017 2002 2017 2001 2017 2001 2018 2000 2018 1999 2017 1998 2016 1999 2015 2000 2014 2002 2014 2003 2015 
2004 2016 2005 2017 2006 2018 2007 2019 2008 2021 2009 2023 2009 2023 2010 2022 2010 2019 2011 2017 2012 2015 2013 2014 2014 2014 2015 2014 2017 2015 
2018 2017 2020 2019 2020 2020 2019 2020 2017 2018 2016 2017 2015 2017 2015 2018 2014 2020 2013 2024 2012 2028 2013 2028 2015 2031 2016 2033 2016 2034 
2017 2034 2018 2034 2019 2033 2020 2033 2020 2033 2021 2034 2022 2035 2021 2036 2019 2037 2018 2037 2016 2036 2015 2034 2013 2031 2012 2030 2012 2032 
2011 2034 2011 2036 2010 2037 2009 2037 2007 2037 2005 2036 2002 2035 2003 2034 2004 2035 2005 2035 2005 2035 2006 2035 2007 2033 2008 2031 2009 2028 
75 _pl _cp 
0 g _f _s _s 
0 g 770 1891 _m
_sp 770 1891 769 1890 767 1886 765 1884 764 1883 763 1883 763 1884 762 1884 761 1884 760 1883 760 1882 761 1881 762 1880 764 1881 765 1881 
766 1882 766 1883 767 1884 768 1886 769 1887 770 1889 771 1889 771 1889 772 1886 773 1883 773 1881 774 1880 775 1880 777 1880 778 1881 
780 1883 781 1885 781 1886 780 1886 779 1884 777 1883 776 1883 776 1884 776 1886 775 1890 774 1894 774 1894 776 1897 777 1899 778 1900 
779 1900 779 1900 780 1900 781 1899 781 1899 782 1900 783 1901 782 1902 781 1903 779 1903 778 1902 776 1900 774 1897 773 1896 773 1898 
772 1900 772 1902 771 1903 770 1903 768 1903 766 1902 764 1901 764 1901 766 1901 766 1901 767 1901 768 1901 769 1899 769 1897 770 1894 
75 _pl _cp 
0 g _f _s _s 
0 g 807 1887 _m
_sp 807 1887 806 1886 805 1886 804 1886 804 1886 804 1886 803 1886 801 1887 799 1887 795 1886 791 1884 789 1881 787 1878 786 1874 787 1870 
788 1867 791 1865 795 1864 797 1864 799 1865 801 1865 803 1866 804 1872 805 1873 805 1873 805 1874 805 1874 806 1875 807 1875 807 1875 
807 1875 808 1875 799 1875 798 1875 799 1875 801 1874 801 1873 801 1873 801 1872 800 1869 799 1866 796 1865 793 1866 791 1867 790 1869 
789 1872 790 1876 791 1880 793 1883 796 1885 799 1886 801 1885 803 1884 804 1882 805 1880 806 1880 807 1887 57 _pl _cp 
0 g _f _s _s 
0 g 827 1890 _m
_sp 827 1890 827 1907 827 1907 827 1907 827 1909 828 1911 829 1912 830 1912 831 1912 831 1914 819 1914 819 1912 819 1912 821 1912 822 1911 
822 1909 822 1907 822 1880 823 1880 837 1902 837 1880 838 1880 855 1907 856 1909 858 1911 859 1912 860 1912 861 1914 852 1914 851 1912 
853 1912 854 1912 854 1911 854 1910 852 1907 842 1890 842 1907 842 1908 842 1908 842 1911 844 1912 845 1912 846 1914 834 1914 834 1912 
834 1912 836 1911 837 1908 837 1907 837 1907 837 1906 51 _pl _cp 
0 g _f _s _s 
0 g 939 1891 _m
_sp 939 1891 938 1890 935 1886 934 1884 932 1883 932 1883 931 1884 930 1884 929 1884 929 1883 928 1882 929 1881 930 1880 932 1881 933 1881 
934 1882 935 1883 936 1884 937 1886 938 1887 939 1889 939 1889 939 1889 940 1886 941 1883 942 1881 943 1880 944 1880 945 1880 946 1881 
948 1883 949 1885 950 1886 949 1886 947 1884 946 1883 945 1883 945 1884 944 1886 943 1890 942 1894 942 1894 944 1897 945 1899 946 1900 
947 1900 947 1900 948 1900 949 1899 950 1899 951 1900 951 1901 950 1902 949 1903 948 1903 946 1902 945 1900 942 1897 942 1896 941 1898 
940 1902 939 1903 937 1903 935 1902 932 1901 932 1901 934 1901 935 1901 935 1901 936 1901 937 1899 938 1897 938 1894 73 _pl _cp 
0 g _f _s _s 
0 g 967 1876 _m
_sp 967 1876 969 1877 971 1878 972 1880 972 1881 972 1883 971 1885 970 1886 969 1886 967 1886 964 1886 958 1886 958 1886 958 1886 959 1885 
960 1884 960 1883 959 1882 956 1869 955 1866 953 1865 953 1865 953 1865 959 1865 962 1865 964 1865 966 1865 967 1865 968 1866 970 1867 
971 1869 971 1871 970 1873 969 1875 968 1876 35 _pl _cp 961 1875 _m
_sp 961 1875 959 1869 959 1868 959 1867 960 1866 961 1866 964 1866 966 1867 967 1869 967 1871 966 1874 963 1875 962 1875 13 _pl _cp 962 1877 _m
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1325 2773 1323 2773 47 _pl _cp 
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1241 1902 1242 1904 1243 1906 1244 1909 1245 1910 1247 1911 1248 1912 1249 1913 38 _pl _cp 
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1290 1884 1289 1882 1288 1881 1288 1880 1287 1878 1286 1877 1284 1875 1282 1873 38 _pl _cp 
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1693 1882 1693 1885 17 _pl _cp 1688 1912 _m
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1706 1882 1706 1885 1706 1897 1707 1899 1709 1900 1710 1901 1711 1901 1713 1901 1714 1899 1715 1897 1715 1894 1715 1885 1714 1882 1712 1882 1711 1882 
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1730 1896 1731 1899 1731 1902 1731 1904 1732 1905 1733 1906 1733 1908 1734 1909 1735 1910 1736 1911 1737 1912 1739 1913 42 _pl _cp 
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788 1668 785 1668 47 _pl _cp 
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823 1687 820 1684 820 1683 833 1683 835 1688 834 1688 834 1688 833 1687 832 1686 831 1686 830 1686 41 _pl _cp 
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1886 2548 1887 2548 1907 2575 1909 2577 1910 2579 1912 2579 1913 2580 1913 2581 1904 2581 1904 2580 1905 2580 1906 2580 1906 2579 1906 2577 1904 2575 
30 _pl _cp 
0 g _f _s _s 
0 g 1941 2543 _m
_sp 1941 2543 1944 2555 1938 2554 1938 2554 1939 2554 1940 2554 1940 2553 1940 2552 1940 2551 1936 2535 1935 2534 1935 2534 1935 2534 1935 2533 1936 2533 
1938 2532 1940 2532 1942 2532 1944 2533 1945 2534 1947 2535 1948 2537 1949 2539 1950 2541 1950 2543 1949 2546 1947 2547 1946 2547 1945 2547 1943 2545 
30 _pl _cp 1938 2534 _m
_sp 1938 2534 1939 2533 1940 2533 1942 2533 1944 2535 1945 2537 1946 2539 1947 2541 1947 2543 1947 2544 1945 2545 1944 2545 1942 2544 1941 2542 1940 2540 
1939 2538 1939 2536 1938 2535 18 _pl _cp 
0 g _f _s _s 
0 g 1952 2537 _m
_sp 1952 2537 1952 2535 1953 2533 1955 2532 1957 2532 1959 2532 1960 2533 1962 2534 1963 2535 1964 2537 1965 2539 1966 2540 1966 2542 1966 2544 1965 2546 
1963 2547 1961 2547 1960 2547 1958 2546 1957 2545 1955 2544 1954 2542 1953 2541 1952 2539 1952 2537 1952 2537 26 _pl _cp 1955 2536 _m
_sp 1955 2536 1956 2534 1958 2533 1960 2534 1961 2536 1962 2538 1963 2540 1963 2541 1963 2543 1962 2545 1961 2546 1960 2546 1959 2545 1957 2544 1956 2542 
1956 2541 1956 2539 1955 2538 1955 2536 1955 2536 20 _pl _cp 
0 g _f _s _s 
0 g 1978 2536 _m
_sp 1978 2536 1977 2535 1977 2534 1977 2533 1978 2532 1979 2532 1980 2532 1981 2532 1982 2533 1984 2535 1983 2536 1983 2535 1981 2534 1981 2534 1980 2534 
1980 2534 1980 2535 1980 2536 1986 2555 1980 2554 1980 2554 1981 2554 1982 2554 1982 2553 1982 2552 1982 2551 1980 2546 1979 2547 1978 2547 1977 2547 
1975 2546 1974 2545 1972 2544 1970 2542 1969 2540 1968 2538 1968 2536 1969 2533 1972 2532 1974 2532 1976 2534 1977 2535 42 _pl _cp 1971 2536 _m
_sp 1971 2536 1972 2534 1973 2533 1975 2534 1977 2537 1978 2538 1978 2539 1979 2542 1980 2544 1979 2545 1978 2546 1977 2546 1976 2545 1974 2544 1973 2543 
1972 2541 1972 2540 1971 2538 1971 2536 1971 2536 20 _pl _cp 
0 g _f _s _s 
0 g 1985 2546 _m
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1987 2527 1987 2527 1987 2528 1986 2528 1986 2528 1986 2528 1985 2528 1984 2528 1984 2527 1984 2526 1985 2525 1987 2526 1988 2526 1990 2528 1991 2530 
1993 2533 1994 2534 1995 2536 1996 2538 1997 2541 1998 2542 1999 2544 1999 2545 1998 2546 1997 2547 1996 2547 1995 2546 1996 2545 1996 2545 1997 2544 
1997 2543 1997 2543 1997 2542 1997 2541 1996 2540 1996 2539 1995 2537 1995 2537 1994 2536 1994 2535 1993 2535 1993 2536 1993 2536 1992 2538 1992 2540 
1992 2542 1991 2544 1990 2546 1990 2547 64 _pl _cp 
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(motion.)_S 2400 8987 _m
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([)_S /Times-BoldItalicR 600 _ff
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(coefficients)_S 67 _t
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(linear)_S 67 _t
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(rotational)_S 67 _t
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6913 8376 _m
7486 8436 _m
67 _t
(on)_S 67 _t
(the)_S gsave 4 4 scale 16 _sr 
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0 g 1794 2109 _m
_sp 1794 2109 1794 2169 1786 2169 1786 2168 1792 2168 1792 2111 1786 2111 1786 2109 8 _pl _cp 
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_sp 1757 2131 1757 2150 1757 2152 1757 2154 1758 2155 1760 2155 1761 2155 1761 2156 1749 2156 1749 2155 1749 2155 1750 2155 1751 2154 1752 2152 1752 2150 
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30 _pl _cp 1804 2109 _m
_sp 1804 2109 1805 2108 1806 2108 1808 2108 1810 2110 1811 2112 1812 2114 1813 2116 1813 2118 1813 2119 1811 2120 1810 2120 1808 2119 1807 2117 1806 2115 
1805 2113 1805 2111 1804 2110 18 _pl _cp 
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0 g 1818 2112 _m
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1829 2122 1827 2122 1826 2122 1824 2121 1823 2120 1821 2119 1820 2117 1819 2116 1818 2114 1818 2112 1818 2112 26 _pl _cp 1821 2111 _m
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1841 2121 1840 2120 1838 2119 1836 2117 1835 2115 1834 2113 1834 2111 1835 2108 1838 2107 1840 2107 1842 2109 1843 2110 42 _pl _cp 1837 2111 _m
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1858 2117 1857 2119 1856 2121 1856 2122 64 _pl _cp 
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_sp 1257 769 1264 769 1264 779 3 _pl _cp 
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1524 736 1522 735 1521 734 1519 733 1518 732 1517 730 1516 729 1516 726 1517 725 1518 728 1519 730 1521 731 1524 732 1527 731 1529 730 
1530 728 1531 725 1531 722 1529 719 1527 716 1524 712 1520 708 1515 703 1515 702 1535 702 1538 709 1537 709 1536 708 1535 707 1535 707 
1533 706 1531 706 47 _pl _cp 
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0 g 1584 775 _m
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1855 728 1856 725 1856 722 1854 719 1852 716 1849 712 1845 708 1840 703 1840 702 1860 702 1863 709 1862 709 1861 708 1860 707 1860 707 
1858 706 1856 706 47 _pl _cp 
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0 g 1909 775 _m
_sp 1909 775 1911 775 1912 775 1914 774 1915 774 1917 773 1918 771 1919 770 1919 768 1919 766 1918 764 1916 763 1915 762 1914 763 1913 763 
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1917 777 1915 778 1912 778 1914 780 1921 780 1922 784 1922 784 1921 783 1920 783 1919 783 1913 783 41 _pl _cp 
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0 g 2174 706 _m
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2188 707 2187 707 2186 706 2184 706 49 _pl _cp 
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0 g 2237 775 _m
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0 g _f _s _s 
0 g 976 1487 _m
_sp 976 1487 977 1486 978 1485 979 1486 980 1487 979 1488 978 1489 977 1488 8 _pl _cp 
0 g _f _s _s 
0 g 1317 1487 _m
_sp 1317 1487 1318 1486 1319 1485 1320 1486 1320 1487 1320 1488 1319 1489 1318 1488 8 _pl _cp 
0 g _f _s _s 
0 g 1642 1487 _m
_sp 1642 1487 1643 1486 1644 1485 1645 1486 1645 1487 1645 1488 1644 1489 1643 1488 8 _pl _cp 
0 g _f _s _s 
0 g 1967 1487 _m
_sp 1967 1487 1968 1486 1969 1485 1970 1486 1970 1487 1970 1488 1969 1489 1968 1488 8 _pl _cp 
0 g _f _s _s 
0 g 2293 1487 _m
_sp 2293 1487 2294 1486 2295 1485 2296 1486 2296 1487 2296 1488 2295 1489 2294 1488 8 _pl _cp 
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0 g 976 1339 _m
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0 g 1317 1339 _m
_sp 1317 1339 1318 1338 1319 1337 1320 1338 1320 1339 1320 1340 1319 1341 1318 1340 8 _pl _cp 
0 g _f _s _s 
0 g 1642 1339 _m
_sp 1642 1339 1643 1338 1644 1337 1645 1338 1645 1339 1645 1340 1644 1341 1643 1340 8 _pl _cp 
0 g _f _s _s 
0 g 1967 1339 _m
_sp 1967 1339 1968 1338 1969 1337 1970 1338 1970 1339 1970 1340 1969 1341 1968 1340 8 _pl _cp 
0 g _f _s _s 
0 g 2293 1339 _m
_sp 2293 1339 2294 1338 2295 1337 2296 1338 2296 1339 2296 1340 2295 1341 2294 1340 8 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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0 g _f _s _s 
0 g 1317 1191 _m
_sp 1317 1191 1318 1189 1319 1188 1320 1189 1320 1190 1320 1192 1319 1192 1318 1192 8 _pl _cp 
0 g _f _s _s 
0 g 1642 1191 _m
_sp 1642 1191 1643 1189 1644 1188 1645 1189 1645 1190 1645 1192 1644 1192 1643 1192 8 _pl _cp 
0 g _f _s _s 
0 g 1967 1191 _m
_sp 1967 1191 1968 1189 1969 1188 1970 1189 1970 1190 1970 1192 1969 1192 1968 1192 8 _pl _cp 
0 g _f _s _s 
0 g 2293 1191 _m
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0 g _f _s _s 
0 g 649 1042 _m
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0 g _f _s _s 
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0 g _f _s _s 
0 g 1317 1042 _m
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0 g _f _s _s 
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0 g _f _s _s 
0 g 1967 1042 _m
_sp 1967 1042 1968 1041 1969 1040 1970 1041 1970 1042 1970 1043 1969 1044 1968 1043 8 _pl _cp 
0 g _f _s _s 
0 g 2293 1042 _m
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0 g _f _s _s 
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0 g _f _s _s 
0 g 1642 894 _m
_sp 1642 894 1643 893 1644 892 1645 893 1645 894 1645 895 1644 896 1643 895 8 _pl _cp 
0 g _f _s _s 
0 g 1967 894 _m
_sp 1967 894 1968 893 1969 892 1970 893 1970 894 1970 895 1969 896 1968 895 8 _pl _cp 
0 g _f _s _s 
0 g 2293 894 _m
_sp 2293 894 2294 893 2295 892 2296 893 2296 894 2296 895 2295 896 2294 895 8 _pl _cp 
0 g _f _s _s 
0 g 649 746 _m
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0 g _f _s _s 
0 g 976 746 _m
_sp 976 746 977 745 978 744 979 745 980 746 979 747 978 748 977 747 8 _pl _cp 
0 g _f _s _s 
0 g 1317 746 _m
_sp 1317 746 1318 745 1319 744 1320 745 1320 746 1320 747 1319 748 1318 747 8 _pl _cp 
0 g _f _s _s 
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_sp 1642 746 1643 745 1644 744 1645 745 1645 746 1645 747 1644 748 1643 747 8 _pl _cp 
0 g _f _s _s 
0 g 1967 746 _m
_sp 1967 746 1968 745 1969 744 1970 745 1970 746 1970 747 1969 748 1968 747 8 _pl _cp 
0 g _f _s _s 
0 g 2293 746 _m
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0 g _f _s 
_s 0 g 0 0 0 0 _cw 
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(151)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
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2400 11855 _m
(The)_S 67 _t
(spatial)_S 67 _t
(distribution)_S 67 _t
(of)_S 67 _t
(mass)_S 67 _t
(within)_S 67 _t
(a)_S 67 _t
(body)_S 67 _t
(has)_S 67 _t
(several)_S 67 _t
(important)_S 67 _t
(effects)_S 1500 11506 _m
(which)_S 67 _t
(are)_S 67 _t
(quantified)_S 67 _t
(as)_S 67 _t
(moments)_S 67 _t
(of)_S 67 _t
(inertia.)_S 134 _t
(Calculation)_S 67 _t
(of)_S 67 _t
(inertial)_S 67 _t
(moments)_S 67 _t
(are)_S 67 _t
(as)_S 1500 11157 _m
(shown)_S 67 _t
(in)_S 67 _t
(Equations)_S 67 _t
(\(6.55\))_S 67 _t
(through)_S 67 _t
(\(6.60\).)_S 134 _t
(In)_S 67 _t
(practice)_S 67 _t
(these)_S 67 _t
(calculations)_S 67 _t
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(weighted)_S 67 _t
(sums,)_S 67 _t
(measured)_S 67 _t
(from)_S 67 _t
(vehicle)_S 67 _t
(origin)_S 67 _t
(to)_S 67 _t
(centers)_S 67 _t
(of)_S 67 _t
(mass)_S 67 _t
(for)_S 67 _t
(individual)_S 1500 10459 _m
(internal)_S 67 _t
(vehicle)_S 67 _t
(components.)_S 134 _t
(If)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(has)_S 67 _t
(a)_S 67 _t
(variable)_S 67 _t
(ballast)_S 67 _t
(system,)_S 67 _t
(changes)_S 67 _t
(of)_S 1500 10110 _m
(mass)_S 67 _t
(and)_S 67 _t
(inertial)_S 67 _t
(moment)_S 67 _t
(must)_S 67 _t
(be)_S 67 _t
(accounted)_S 67 _t
(for)_S 67 _t
(and)_S 67 _t
(then)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(frame)_S 67 _t
(mass)_S 67 _t
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/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(M)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
(becomes)_S 67 _t
(slowly)_S 67 _t
(time-varying.)_S gsave 4 4 scale 16 _sr 
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1081 2290 1081 2291 1080 2291 1079 2292 1078 2293 1078 2294 1078 2296 1084 2316 1085 2318 1086 2320 1087 2321 1088 2321 1088 2321 1089 2323 29 _pl _cp 
0 g _f _s _s 
0 g 1093 2281 _m
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1090 2275 1090 2275 1092 2277 1093 2279 1093 2279 1093 2279 1094 2277 1095 2274 1096 2273 1098 2274 1100 2277 1100 2277 1100 2277 1099 2276 1098 2275 
1097 2276 1096 2280 1095 2282 1095 2283 1097 2286 1098 2286 1099 2286 1099 2286 1100 2286 1100 2286 1101 2287 1101 2287 1101 2288 1100 2289 1099 2289 
1098 2288 1097 2286 1095 2284 1095 2284 1095 2285 1094 2288 1093 2289 1092 2289 1090 2288 1089 2287 1089 2287 1090 2287 1090 2287 1091 2287 1092 2286 
1093 2282 61 _pl _cp 
0 g _f _s _s 
0 g 1234 2306 _m
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1241 2281 1239 2278 1238 2278 1237 2278 1237 2278 1237 2278 1236 2278 1235 2279 1234 2279 1234 2278 1233 2277 1234 2275 1235 2274 1237 2275 1238 2276 
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1250 2305 1250 2304 1251 2303 1253 2302 1253 2301 1253 2301 1253 2300 1252 2299 1252 2297 1251 2296 1251 2295 1250 2293 1249 2292 1249 2291 1248 2290 
1248 2290 1247 2289 1247 2290 1247 2290 1246 2294 1246 2297 1245 2300 1244 2303 1243 2306 1242 2307 70 _pl _cp 
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1369 2286 1368 2285 1368 2285 1368 2284 1369 2284 1369 2283 1369 2283 1368 2283 1367 2283 1366 2283 1365 2284 1363 2286 1362 2287 1361 2288 1359 2289 
1358 2289 1372 2306 1371 2307 1357 2307 1356 2300 1357 2300 1358 2302 1358 2303 1360 2303 1362 2303 1368 2303 1356 2289 1354 2287 43 _pl _cp 
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1438 2288 1438 2289 1439 2290 1447 2319 1438 2318 1438 2317 1440 2317 1441 2317 1441 2316 1441 2315 1441 2313 1439 2305 1437 2307 1435 2307 1433 2307 
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1434 2289 46 _pl _cp 1425 2290 _m
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1433 2306 1432 2305 1430 2303 1428 2301 1427 2298 1426 2295 1425 2292 1425 2290 1425 2290 24 _pl _cp 
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90 _pl _cp 
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_sp 1150 2301 1131 2301 1131 2299 1150 2299 4 _pl _cp 
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0 g 1228 2327 _m
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1398 2327 31 _pl _cp 
0 g _f _s _s 
0 g 1266 2307 _m
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1264 2323 1263 2320 1264 2320 1265 2321 1265 2322 1267 2323 1269 2324 1270 2324 1272 2323 1273 2321 1273 2319 1273 2317 1272 2315 1270 2313 1268 2310 
1266 2308 1263 2305 1263 2304 1276 2304 1278 2309 1277 2309 1277 2308 1276 2308 1276 2307 1275 2307 1273 2307 41 _pl _cp 
0 g _f _s _s 
0 g 1383 2307 _m
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1383 2308 1380 2305 1380 2304 1393 2304 1395 2309 1394 2309 1394 2308 1393 2308 1392 2307 1391 2307 1390 2307 41 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 8117 9204 _m
/Times-BoldR 600 _ff
(\(6.55\))_S /Times-RomanR 600 _ff
gsave 4 4 scale 16 _sr 
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_sp 1076 2061 1076 2059 1077 2059 1079 2059 1079 2057 1079 2057 1079 2056 1079 2054 1073 2034 1072 2032 1071 2030 1070 2029 1069 2029 1069 2029 1069 2028 
1081 2028 1081 2029 1080 2029 1079 2030 1078 2031 1078 2032 1078 2034 1084 2054 1085 2056 1086 2058 1087 2059 1088 2059 1088 2059 1089 2061 29 _pl _cp 
0 g _f _s _s 
0 g 1087 2026 _m
_sp 1087 2026 1087 2025 1088 2025 1088 2025 1090 2025 1091 2023 1091 2021 1092 2020 1092 2018 1093 2016 1093 2014 1093 2012 1093 2010 1092 2009 1091 2008 
1089 2007 1089 2007 1089 2007 1089 2007 1088 2007 1088 2008 1087 2008 1087 2007 1086 2006 1087 2005 1088 2005 1089 2005 1090 2006 1092 2008 1094 2010 
1095 2012 1096 2014 1097 2015 1098 2018 1099 2020 1100 2022 1101 2023 1101 2024 1100 2026 1099 2027 1098 2026 1098 2025 1098 2025 1098 2024 1099 2024 
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1094 2022 1093 2024 1093 2026 1092 2027 64 _pl _cp 
0 g _f _s _s 
0 g 1243 2033 _m
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1252 2042 1252 2042 1253 2042 1254 2041 1254 2041 1255 2042 1256 2043 1255 2044 1254 2045 1252 2045 1251 2044 1249 2042 1247 2039 1246 2038 1246 2040 
1245 2042 1245 2044 1244 2045 1243 2045 1241 2045 1239 2044 1237 2043 1237 2043 1239 2043 1239 2043 1240 2043 1241 2043 1242 2041 1242 2039 1243 2036 
75 _pl _cp 
0 g _f _s _s 
0 g 1353 2023 _m
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(\(6.60\))_S /Times-RomanR 600 _ff
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67 _t
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(mass)_S 67 _t
(matrix)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(M)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
67 _t
(using)_S 67 _t
/Times-BoldR 600 _ff
(equation)_S 67 _t
(\(6.54\))_S /Times-RomanR 600 _ff
1876 9675 _m
(\267)_S 2220 9675 _m
(Initialize)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(variables)_S 67 _t
(for)_S 67 _t
(posture)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(P)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
(,)_S 67 _t
(velocities)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-BoldR 600 _ff
(])_S /Times-RomanR 600 _ff
2220 9442 _m
(and)_S 67 _t
(time)_S 67 _t
(rates)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(velocities)_S 67 _t
(using)_S 67 _t
/Times-BoldR 600 _ff
(Table)_S 67 _t
(6.1)_S /Times-RomanR 600 _ff
1876 8976 _m
(\267)_S 2220 8976 _m
(Loop)_S 67 _t
(until)_S 67 _t
(robot)_S 67 _t
(is)_S 67 _t
(done:)_S 134 _t
2220 8510 _m
(-)_S 2533 8510 _m
(receive)_S 67 _t
(updated)_S 67 _t
(state)_S 67 _t
(vector)_S 67 _t
(from)_S 67 _t
(robot,)_S 67 _t
(including)_S 67 _t
(ordered)_S 67 _t
(effector)_S 2533 8277 _m
(values)_S 67 _t
(for)_S 67 _t
(rudders,)_S 67 _t
(planes,)_S 67 _t
(propellers,)_S 67 _t
(thrusters)_S 67 _t
(and)_S 67 _t
(elapsed)_S 67 _t
(time)_S 2220 7811 _m
(-)_S 2533 7811 _m
(Calculate)_S 67 _t
(new)_S 67 _t
(values)_S 67 _t
(for)_S 67 _t
(time)_S 67 _t
(rate)_S 67 _t
(of)_S 67 _t
(change)_S 67 _t
(of)_S 67 _t
(body)_S 67 _t
(velocities,)_S 67 _t
(using)_S 2533 7578 _m
(the)_S 67 _t
(current)_S 67 _t
(vehicle)_S 67 _t
(state)_S 67 _t
(vector)_S 67 _t
(and)_S 67 _t
(equation)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(right-hand)_S 2533 7345 _m
(sides)_S 67 _t
(using)_S 67 _t
/Times-BoldR 600 _ff
(Table)_S 67 _t
(6.2,)_S 67 _t
(equations)_S 67 _t
(\(6.24\),)_S 67 _t
(\(6.30\),)_S 67 _t
(\(6.35\),)_S 67 _t
(and)_S 2533 7112 _m
(\(6.48\))_S 67 _t
(through)_S 67 _t
(\(6.53\))_S /Times-RomanR 600 _ff
2220 6645 _m
(-)_S 2533 6645 _m
(Update)_S 67 _t
(velocities)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-BoldR 600 _ff
(])_S /Times-BoldItalicR 360 _ff
4278 6600 _m
(body)_S 4511 6600 _m
/Times-BoldR 600 _ff
4511 6645 _m
67 _t
/Times-RomanR 600 _ff
(using)_S 67 _t
/Times-BoldR 600 _ff
(equation)_S 67 _t
(\(6.31\))_S /Times-RomanR 600 _ff
2220 6178 _m
(-)_S 2533 6178 _m
(Perform)_S 67 _t
(transformation)_S 67 _t
(to)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-BoldR 600 _ff
(])_S /Times-BoldItalicR 360 _ff
4989 6133 _m
(world)_S 5269 6133 _m
/Times-RomanR 600 _ff
5269 6178 _m
67 _t
(using)_S 67 _t
/Times-BoldR 600 _ff
(equations)_S 67 _t
(\(6.5\),)_S 67 _t
(\(6.9\),)_S 67 _t
(\(6.10\),)_S 2533 5945 _m
(\(6.11\),)_S 67 _t
(and)_S 67 _t
(\(6.22\))_S /Times-RomanR 600 _ff
2220 5478 _m
(-)_S 2533 5478 _m
(Update)_S 67 _t
(posture)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(P)_S /Times-BoldR 600 _ff
(])_S 67 _t
/Times-RomanR 600 _ff
(using)_S 67 _t
(newly-calculated)_S 67 _t
(velocities)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(V)_S /Times-BoldR 600 _ff
(])_S /Times-BoldItalicR 360 _ff
7190 5433 _m
(world)_S 7470 5433 _m
/Times-RomanR 600 _ff
7470 5478 _m
(,)_S 2533 5245 _m
(ocean)_S 67 _t
(current)_S 67 _t
(estimate)_S 67 _t
(and)_S 67 _t
(previous)_S 67 _t
(posture)_S 67 _t
(using)_S 67 _t
/Times-BoldR 600 _ff
(equation)_S 67 _t
(\(6.33\))_S /Times-RomanR 600 _ff
2220 4779 _m
(-)_S 2533 4779 _m
(Return)_S 67 _t
(newly-calculated)_S 67 _t
(hydrodynamics)_S 67 _t
(values)_S 67 _t
(to)_S 67 _t
(robot)_S 67 _t
(via)_S 67 _t
(telemetry)_S 2533 4546 _m
(update)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(robot)_S 67 _t
(state)_S 67 _t
(vector.)_S 134 _t
(Most)_S 67 _t
(calculated)_S 67 _t
(velocities)_S 67 _t
(and)_S 2533 4313 _m
(accelerations)_S 67 _t
(correspond)_S 67 _t
(to)_S 67 _t
(real-world)_S 67 _t
(values)_S 67 _t
(provided)_S 67 _t
(by)_S 67 _t
(inertial,)_S 2533 4080 _m
(flow)_S 67 _t
(and)_S 67 _t
(pressure)_S 67 _t
(sensors.)_S 2220 3614 _m
(-)_S 2533 3614 _m
(Wait)_S 67 _t
(for)_S 67 _t
(next)_S 67 _t
(updated)_S 67 _t
(state)_S 67 _t
(robot)_S 67 _t
(vector.)_S 134 _t
(Continue)_S 67 _t
(loop)_S 67 _t
(upon)_S 67 _t
(receipt.)_S 67 _t
2533 3381 _m
(Shutdown)_S 67 _t
(when)_S 67 _t
(model)_S 67 _t
(is)_S 67 _t
(no)_S 67 _t
(longer)_S 67 _t
(required)_S 67 _t
(by)_S 67 _t
(robot.)_S 4950 1288 _m
(154)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
/Times-BoldR 600 _ff
(E.)_S 1980 11855 _m
(EULER)_S 67 _t
(ANGLE)_S 67 _t
(METHODS)_S 67 _t
(COMPARED)_S 67 _t
(TO)_S 67 _t
(QUATERNION)_S 67 _t
(METHODS)_S /Times-RomanR 600 _ff
1980 11506 _m
(The)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(presented)_S 67 _t
(here)_S 67 _t
(is)_S 67 _t
(based)_S 67 _t
(on)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(representations)_S 1500 11157 _m
(of)_S 67 _t
(vehicle)_S 67 _t
(orientation.)_S 134 _t
(Another)_S 67 _t
(possible)_S 67 _t
(representation)_S 67 _t
(method)_S 67 _t
(of)_S 67 _t
(interest)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(unit)_S 1500 10808 _m
(quaternion.)_S 134 _t
(The)_S 67 _t
(use)_S 67 _t
(of)_S 67 _t
(quaternions)_S 67 _t
(is)_S 67 _t
(most)_S 67 _t
(notable)_S 67 _t
(for)_S 67 _t
(a)_S 67 _t
(lack)_S 67 _t
(of)_S 67 _t
(singularity)_S 67 _t
(when)_S 1500 10459 _m
(pointing)_S 67 _t
(vertically,)_S 67 _t
(and)_S 67 _t
(also)_S 67 _t
(for)_S 67 _t
(well-developed)_S 67 _t
(mathematics)_S 67 _t
(that)_S 67 _t
(permits)_S 67 _t
(rapid)_S 67 _t
(and)_S 1500 10110 _m
(efficient)_S 67 _t
(orientation)_S 67 _t
(update)_S 67 _t
(rates)_S 67 _t
(\(Cooke)_S 67 _t
(92b\))_S 67 _t
(\(Kolve)_S 67 _t
(93\))_S 67 _t
(\(Chou)_S 67 _t
(92\))_S 67 _t
(\(Funda)_S 67 _t
(90\))_S 1500 9761 _m
(\(Shoemake)_S 67 _t
(85\).)_S 134 _t
(This)_S 67 _t
(section)_S 67 _t
(briefly)_S 67 _t
(describes)_S 67 _t
(quaternion)_S 67 _t
(mathematics)_S 67 _t
(as)_S 67 _t
(a)_S 67 _t
(possible)_S 1500 9412 _m
(alternative)_S 67 _t
(to)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(orientation)_S 67 _t
(calculations)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 1500 9063 _m
(hydrodynamics)_S 67 _t
(model.)_S 1980 8714 _m
(The)_S 67 _t
(underlying)_S 67 _t
(mathematical)_S 67 _t
(reason)_S 67 _t
(that)_S 67 _t
(an)_S 67 _t
(Euler)_S 67 _t
(angle)_S 67 _t
(rotation)_S 67 _t
(matrix)_S 67 _t
(is)_S 67 _t
(unable)_S 1500 8364 _m
(to)_S 67 _t
(satisfactorily)_S 67 _t
(represent)_S 67 _t
(a)_S 67 _t
(vehicle)_S 67 _t
(pointing)_S 67 _t
(vertically)_S 67 _t
(\(along)_S 67 _t
(the)_S 67 _t
/Times-BoldItalicR 600 _ff
(z)_S /Times-RomanR 600 _ff
(-axis\))_S 67 _t
(is)_S 67 _t
(that)_S 1500 7905 _m
(extraction)_S 67 _t
(of)_S 67 _t
(Euler)_S 67 _t
(angles)_S 67 _t
(provides)_S 67 _t
(a)_S 67 _t
(unique)_S 67 _t
(value)_S 67 _t
(for)_S 67 _t
(pitch)_S 67 _t
(\()_S 6536 7833 _m
7261 7905 _m
(\))_S 67 _t
(but)_S 67 _t
(can)_S 67 _t
(only)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 181 1634 1958 _cw 
_s 1663 1994 _m
_sp 1663 1994 1662 1999 1661 2004 1659 2006 1656 2008 1653 2009 1650 2009 1648 2008 1646 2006 1644 2003 1643 2001 1643 1998 1642 1995 1642 1991 1642 1985 
1644 1981 1646 1977 1649 1976 1652 1975 1655 1975 1657 1976 1659 1978 1661 1980 1662 1982 1663 1985 1663 1988 1663 1992 1663 1993 28 _pl _cp 1647 1995 _m
_sp 1647 1995 1647 1998 1647 2000 1648 2003 1649 2005 1651 2006 1652 2007 1655 2006 1657 2004 1658 2000 1659 1995 11 _pl _cp 1659 1993 _m
_sp 1659 1993 1659 1991 1659 1989 1659 1987 1659 1986 1658 1982 1657 1979 1655 1977 1653 1976 1651 1977 1649 1979 1648 1982 1647 1986 1647 1992 1647 1992 
1647 1993 16 _pl _cp 
0 g _f _s _s 
0 g 1797 1993 _m
_sp 1797 1993 1803 1993 1803 1997 1788 1997 1785 1997 1784 1996 1783 1996 1782 1995 1780 1994 1779 1992 1781 1991 1783 1993 1785 1993 1786 1993 1786 1993 
1786 1986 1786 1985 1786 1983 1785 1982 1784 1980 1783 1978 1783 1977 1784 1976 1785 1975 1786 1976 1787 1977 1788 1980 1788 1983 1788 1986 1788 1993 
1795 1993 1795 1983 1795 1979 1796 1977 1797 1975 1799 1975 1800 1975 1802 1977 1803 1978 1803 1981 1801 1981 1800 1979 1799 1978 1797 1979 1797 1983 
45 _pl _cp 
0 g _f _s _s 
0 g 1715 1994 _m
_sp 1715 1994 1696 1994 1696 1993 1715 1993 4 _pl _cp 1715 1987 _m
_sp 1715 1987 1696 1987 1696 1985 1715 1985 4 _pl _cp 
0 g _f _s _s 
0 g 1755 1997 _m
_sp 1755 1997 1755 1989 1746 1989 1746 1987 1755 1987 1755 1979 1757 1979 1757 1987 1765 1987 1765 1989 1757 1989 1757 1997 12 _pl _cp 1765 1977 _m
_sp 1765 1977 1746 1977 1746 1975 1765 1975 4 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 1500 7392 _m
(provide)_S 67 _t
(the)_S 67 _t
(sum)_S 67 _t
(\()_S 2956 7320 _m
3569 7392 _m
(,)_S 67 _t
(nose)_S 67 _t
(up\))_S 67 _t
(or)_S 67 _t
(difference)_S 67 _t
(\()_S 5631 7320 _m
6244 7392 _m
(,)_S 67 _t
(nose)_S 67 _t
(down\))_S 67 _t
(of)_S 67 _t
(roll)_S 67 _t
(and)_S 67 _t
(yaw,)_S gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 153 739 1830 _cw 
_s 762 1871 _m
_sp 762 1871 762 1874 762 1876 763 1877 763 1878 763 1878 762 1880 760 1881 758 1880 757 1879 757 1878 757 1877 758 1876 758 1874 758 1872 
758 1871 755 1870 753 1869 752 1868 750 1867 749 1865 747 1863 746 1861 746 1858 747 1854 748 1851 751 1849 754 1847 758 1847 758 1838 
762 1838 762 1847 766 1847 769 1849 771 1852 772 1855 773 1859 772 1863 771 1866 769 1868 766 1870 41 _pl _cp 758 1869 _m
_sp 758 1869 758 1848 755 1849 753 1852 752 1854 751 1858 751 1862 753 1865 755 1868 9 _pl _cp 762 1869 _m
_sp 762 1869 765 1868 767 1866 768 1863 769 1859 769 1855 767 1852 765 1849 762 1848 9 _pl _cp 
0 g _f _s _s 
0 g 866 1877 _m
_sp 866 1877 866 1849 864 1849 862 1851 861 1853 861 1857 861 1869 859 1869 857 1869 856 1869 854 1869 854 1867 854 1867 854 1867 856 1866 
857 1864 857 1863 857 1857 857 1855 857 1853 857 1851 858 1850 860 1849 861 1848 863 1847 866 1847 866 1837 870 1837 870 1847 874 1848 
877 1849 878 1852 879 1857 879 1863 879 1866 881 1867 881 1867 882 1867 882 1867 882 1867 882 1869 880 1869 879 1869 877 1869 875 1869 
875 1857 875 1854 874 1851 872 1850 870 1849 870 1877 51 _pl _cp 
0 g _f _s _s 
0 g 814 1871 _m
_sp 814 1871 814 1863 805 1863 805 1861 814 1861 814 1852 815 1852 815 1861 824 1861 824 1863 815 1863 815 1871 12 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore gsave 4 4 scale 16 _sr 
_s [] 0 _d 2 _lc 0 g 63 153 1407 1830 _cw 
_s 1430 1871 _m
_sp 1430 1871 1430 1874 1430 1876 1431 1877 1431 1878 1431 1878 1430 1880 1428 1881 1426 1880 1425 1879 1425 1878 1425 1877 1426 1876 1426 1874 1426 1872 
1426 1871 1423 1870 1421 1869 1420 1868 1418 1867 1417 1865 1415 1863 1414 1861 1414 1858 1415 1854 1416 1851 1419 1849 1422 1847 1426 1847 1426 1838 
1430 1838 1430 1847 1434 1847 1437 1849 1439 1852 1440 1855 1441 1859 1440 1863 1439 1866 1437 1868 1434 1870 41 _pl _cp 1426 1869 _m
_sp 1426 1869 1426 1848 1423 1849 1421 1852 1420 1854 1419 1858 1419 1862 1421 1865 1423 1868 9 _pl _cp 1430 1869 _m
_sp 1430 1869 1433 1868 1435 1866 1436 1863 1437 1859 1437 1855 1435 1852 1433 1849 1430 1848 9 _pl _cp 
0 g _f _s _s 
0 g 1534 1877 _m
_sp 1534 1877 1534 1849 1532 1849 1530 1851 1529 1853 1529 1857 1529 1869 1527 1869 1525 1869 1524 1869 1522 1869 1522 1867 1522 1867 1522 1867 1524 1866 
1525 1864 1525 1863 1525 1857 1525 1855 1525 1853 1525 1851 1526 1850 1528 1849 1529 1848 1531 1847 1534 1847 1534 1837 1538 1837 1538 1847 1542 1848 
1545 1849 1546 1852 1547 1857 1547 1863 1547 1866 1549 1867 1549 1867 1550 1867 1550 1867 1550 1867 1550 1869 1548 1869 1547 1869 1545 1869 1543 1869 
1543 1857 1543 1854 1542 1851 1540 1850 1538 1849 1538 1877 51 _pl _cp 
0 g _f _s _s 
0 g 1482 1871 _m
_sp 1482 1871 1482 1863 1473 1863 1473 1861 1482 1861 1482 1852 1483 1852 1483 1861 1492 1861 1492 1863 1483 1863 1483 1871 12 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 1500 6988 _m
(not)_S 67 _t
(unique)_S 67 _t
(values)_S 67 _t
(for)_S 67 _t
(each.)_S 134 _t
(Thus)_S 67 _t
(three)_S 67 _t
(parameters)_S 67 _t
(are)_S 67 _t
(inadequate)_S 67 _t
(to)_S 67 _t
(unambiguously)_S 1500 6639 _m
(represent)_S 67 _t
(all)_S 67 _t
(possible)_S 67 _t
(orientations)_S 67 _t
(as)_S 67 _t
(desired.)_S 134 _t
(Sir)_S 67 _t
(William)_S 67 _t
(Rowan)_S 67 _t
(Hamilton)_S 67 _t
(deduced)_S 1500 6290 _m
(and)_S 67 _t
(developed)_S 67 _t
(quaternion)_S 67 _t
(algebra)_S 67 _t
(in)_S 67 _t
(1843)_S 67 _t
(after)_S 67 _t
(searching)_S 67 _t
(many)_S 67 _t
(years)_S 67 _t
(for)_S 67 _t
(a)_S 1500 5941 _m
(generalization)_S 67 _t
(of)_S 67 _t
(complex)_S 67 _t
(numbers.)_S 134 _t
(He)_S 67 _t
(determined)_S 67 _t
(that)_S 67 _t
(four)_S 67 _t
(parameters)_S 67 _t
(are)_S 67 _t
(necessary)_S 1500 5592 _m
(to)_S 67 _t
(represent)_S 67 _t
(all)_S 67 _t
(possible)_S 67 _t
(orientations)_S 67 _t
(without)_S 67 _t
(potential)_S 67 _t
(mathematical)_S 67 _t
(singularity)_S 1500 5243 _m
(\(Cooke)_S 67 _t
(92b\).)_S 1980 4894 _m
(Consider)_S 67 _t
(the)_S 67 _t
(unit)_S 67 _t
(sphere)_S 67 _t
(as)_S 67 _t
(illustrated)_S 67 _t
(in)_S 67 _t
(Figure)_S 67 _t
(6.6.)_S 134 _t
(Three)_S 67 _t
(parameters)_S 67 _t
(are)_S 1500 4545 _m
(necessary)_S 67 _t
(to)_S 67 _t
(describe)_S 67 _t
(a)_S 67 _t
(unit)_S 67 _t
(vector)_S 67 _t
(directed)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(center)_S 67 _t
(to)_S 67 _t
(any)_S 67 _t
(point)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(sphere)_S 1500 4196 _m
(surface.)_S 134 _t
(A)_S 67 _t
(fourth)_S 67 _t
(parameter)_S 67 _t
(can)_S 67 _t
(then)_S 67 _t
(be)_S 67 _t
(used)_S 67 _t
(to)_S 67 _t
(describe)_S 67 _t
(a)_S 67 _t
(value)_S 67 _t
(for)_S 67 _t
(rotation)_S 67 _t
(about)_S 1500 3847 _m
(this)_S 67 _t
(axis.)_S 134 _t
(This)_S 67 _t
(combination)_S 67 _t
(of)_S 67 _t
(unit)_S 67 _t
(vector)_S 67 _t
(and)_S 67 _t
(axial)_S 67 _t
(rotation)_S 67 _t
(uniquely)_S 67 _t
(defines)_S 67 _t
(all)_S 1500 3497 _m
(possible)_S 67 _t
(orientations,)_S 67 _t
(provided)_S 67 _t
(rotation)_S 67 _t
(values)_S 67 _t
(are)_S 67 _t
(specified)_S 67 _t
(to)_S 67 _t
(have)_S 67 _t
(a)_S 67 _t
(range)_S 67 _t
/Times-BoldR 600 _ff
([)_S /Times-BoldItalicR 600 _ff
(0..2)_S /Symbol 600 _ff
(p)_S /Times-BoldR 600 _ff
(\))_S /Times-RomanR 600 _ff
1500 3147 _m
(\(Euler's)_S 67 _t
(Theorem\).)_S 4950 1288 _m
(155)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 375 1950 _m
_sp 2174 1950 2174 1953 375 1953 3 _pl _pf _np _s _s 2171 1950 _m
_sp 2174 1950 2174 2999 2171 2999 3 _pl _pf _np _s _s 375 2996 _m
_sp 2174 2996 2174 2999 375 2999 3 _pl _pf _np _s _s 375 1950 _m
_sp 378 1950 378 2999 375 2999 3 _pl _pf _np 
_s 0 g 981 1731 409 1984 _cw 
_s 
_s 0 g _s 1255 2449 _m
_sp 1255 2449 1256 2442 1262 2443 1266 2443 1271 2443 1277 2442 1284 2440 1292 2438 1301 2434 1310 2430 1319 2425 1327 2420 1334 2415 1342 2410 1349 2405 
1355 2400 1358 2396 1363 2392 1366 2389 1369 2385 1372 2382 1375 2378 1377 2376 1379 2373 1381 2370 1383 2367 1385 2363 1386 2360 1387 2357 1388 2354 
1388 2352 1395 2352 1398 2356 1399 2357 1399 2359 1399 2360 1399 2361 1399 2363 1399 2364 1398 2367 1397 2369 1396 2372 1394 2375 1391 2379 1388 2383 
1384 2388 1380 2392 1377 2396 1373 2399 1368 2404 1364 2407 1359 2411 1355 2415 1347 2421 1336 2429 1327 2434 1318 2439 1310 2444 1303 2447 1298 2449 
1294 2451 1291 2452 1287 2453 1283 2454 1280 2455 1276 2456 1273 2457 1270 2457 1267 2457 1264 2457 1262 2456 1261 2456 1259 2455 1258 2454 1258 2453 
75 _pl _pf _np _s 
_s 255 g _s 1326 2343 _m
_sp 1326 2343 1328 2342 1331 2340 1335 2338 1339 2337 1346 2335 1351 2333 1357 2332 1362 2331 1365 2331 1368 2331 1371 2331 1374 2331 1376 2332 1378 2332 
1379 2333 1381 2334 1382 2334 1383 2335 1385 2336 1386 2338 1398 2356 1397 2355 1396 2354 1395 2353 1394 2353 1391 2352 1389 2352 1386 2352 1383 2352 
1379 2353 1375 2354 1371 2355 1365 2356 1361 2358 1357 2360 1351 2363 1346 2365 1342 2367 39 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1258 2453 _m
_sp 1258 2453 1257 2452 1256 2451 1256 2450 1256 2449 1256 2448 1256 2445 1257 2443 1258 2440 1259 2437 1261 2434 1262 2432 1264 2429 1266 2427 1268 2424 
1270 2421 1273 2418 1277 2415 1281 2410 1286 2406 1289 2403 1292 2400 1297 2407 1297 2380 1271 2369 1276 2376 1272 2380 1267 2385 1262 2390 1259 2393 
1256 2397 1253 2402 1250 2407 1248 2411 1246 2414 1245 2417 1244 2419 1244 2422 1243 2424 1243 2426 1243 2428 1243 2430 1244 2432 1245 2433 1245 2435 
45 _pl _pf 
0 g _cp _s _s _s 1279 2328 _m
_sp 1279 2328 1284 2328 1281 2328 1432 2496 1459 2478 1442 2566 1354 2549 1379 2531 1282 2333 9 _pl _pf _np _s 
_s 255 g _s 1278 2319 _m
_sp 1278 2319 1281 2318 1281 2317 1438 2504 1465 2486 1448 2573 1360 2556 1387 2538 1276 2320 9 _pl _pf 
0 g _cp _s _s _s 1452 2575 _m
_sp 1452 2575 1452 2576 1452 2576 1451 2577 1450 2577 1450 2578 1449 2578 1448 2578 1448 2578 1447 2578 1446 2578 1446 2577 1445 2576 1445 2576 1444 2575 
1444 2574 1444 2574 1445 2573 1445 2572 1445 2572 1446 2571 1447 2571 1447 2570 1448 2570 1449 2570 1450 2571 1450 2571 1451 2571 1451 2572 1452 2573 
1452 2573 1452 2574 1452 2575 33 _pl _pf 
6 _w 0 g _cp _s 
_s 8 _w 0 g 1725 2474 _m
1725 2474 _l 1725 2474 _m
1725 2463 _l 1725 2463 _m
1725 2451 _l 1725 2451 _m
1724 2439 _l 1724 2439 _m
1723 2428 _l 1723 2428 _m
1722 2416 _l 1722 2416 _m
1720 2405 _l 1720 2405 _m
1718 2393 _l 1718 2393 _m
1716 2382 _l 1716 2382 _m
1714 2371 _l 1714 2371 _m
1711 2360 _l 1711 2360 _m
1708 2349 _l 1708 2349 _m
1705 2338 _l 1705 2338 _m
1701 2327 _l 1701 2327 _m
1698 2317 _l 1698 2317 _m
1694 2306 _l 1694 2306 _m
1690 2296 _l 1690 2296 _m
1685 2286 _l 1685 2286 _m
1680 2275 _l 1680 2275 _m
1676 2265 _l 1676 2265 _m
1670 2256 _l 1670 2256 _m
1665 2246 _l 1665 2246 _m
1659 2236 _l 1659 2236 _m
1654 2227 _l 1654 2227 _m
1648 2217 _l 1648 2217 _m
1641 2208 _l 1641 2208 _m
1635 2199 _l 1635 2199 _m
1628 2191 _l 1628 2191 _m
1621 2182 _l 1621 2182 _m
1614 2173 _l 1614 2173 _m
1607 2165 _l 1607 2165 _m
1600 2157 _l 1600 2157 _m
1592 2149 _l 1592 2149 _m
1584 2141 _l 1584 2141 _m
1576 2133 _l 1576 2133 _m
1568 2126 _l 1568 2126 _m
1560 2119 _l 1560 2119 _m
1552 2112 _l 1552 2112 _m
1543 2105 _l 1543 2105 _m
1534 2098 _l 1534 2098 _m
1525 2092 _l 1525 2092 _m
1516 2086 _l 1516 2086 _m
1507 2080 _l 1507 2080 _m
1497 2074 _l 1497 2074 _m
1488 2069 _l 1488 2069 _m
1478 2063 _l 1478 2063 _m
1468 2058 _l 1468 2058 _m
1459 2054 _l 1459 2054 _m
1449 2049 _l 1449 2049 _m
1438 2045 _l 1438 2045 _m
1428 2041 _l 1428 2041 _m
1418 2037 _l 1418 2037 _m
1407 2033 _l 1407 2033 _m
1397 2030 _l 1397 2030 _m
1386 2027 _l 1386 2027 _m
1375 2024 _l 1375 2024 _m
1364 2022 _l 1364 2022 _m
1354 2020 _l 1354 2020 _m
1342 2018 _l 1342 2018 _m
1331 2016 _l 1331 2016 _m
1320 2015 _l 1320 2015 _m
1309 2014 _l 1309 2014 _m
1297 2013 _l 1297 2013 _m
1286 2012 _l 1286 2012 _m
1274 2012 _l 1274 2012 _m
1263 2012 _l 1263 2012 _m
1252 2013 _l 1252 2013 _m
1240 2014 _l 1240 2014 _m
1229 2015 _l 1229 2015 _m
1218 2016 _l 1218 2016 _m
1207 2018 _l 1207 2018 _m
1196 2020 _l 1196 2020 _m
1185 2022 _l 1185 2022 _m
1174 2024 _l 1174 2024 _m
1163 2027 _l 1163 2027 _m
1152 2030 _l 1152 2030 _m
1142 2033 _l 1142 2033 _m
1131 2037 _l 1131 2037 _m
1121 2041 _l 1121 2041 _m
1111 2045 _l 1111 2045 _m
1100 2049 _l 1100 2049 _m
1090 2054 _l 1090 2054 _m
1080 2058 _l 1080 2058 _m
1071 2063 _l 1071 2063 _m
1061 2069 _l 1061 2069 _m
1052 2074 _l 1052 2074 _m
1042 2080 _l 1042 2080 _m
1033 2086 _l 1033 2086 _m
1024 2092 _l 1024 2092 _m
1015 2098 _l 1015 2098 _m
1006 2105 _l 1006 2105 _m
998 2112 _l 998 2112 _m
989 2119 _l 989 2119 _m
981 2126 _l 981 2126 _m
973 2133 _l 973 2133 _m
965 2141 _l 965 2141 _m
957 2149 _l 957 2149 _m
949 2157 _l 949 2157 _m
942 2165 _l 942 2165 _m
935 2173 _l 935 2173 _m
928 2182 _l 928 2182 _m
921 2191 _l 921 2191 _m
914 2199 _l 914 2199 _m
908 2208 _l 908 2208 _m
901 2217 _l 901 2217 _m
895 2227 _l 895 2227 _m
890 2236 _l 890 2236 _m
884 2246 _l 884 2246 _m
879 2256 _l 879 2256 _m
873 2265 _l 873 2265 _m
869 2275 _l 869 2275 _m
864 2286 _l 864 2286 _m
859 2296 _l 859 2296 _m
855 2306 _l 855 2306 _m
851 2317 _l 851 2317 _m
848 2327 _l 848 2327 _m
844 2338 _l 844 2338 _m
841 2349 _l 841 2349 _m
838 2360 _l 838 2360 _m
835 2371 _l 835 2371 _m
833 2382 _l 833 2382 _m
831 2393 _l 831 2393 _m
829 2405 _l 829 2405 _m
827 2416 _l 827 2416 _m
826 2428 _l 826 2428 _m
825 2439 _l 825 2439 _m
824 2451 _l 824 2451 _m
824 2463 _l 824 2463 _m
824 2474 _l 824 2474 _m
824 2486 _l 824 2486 _m
824 2498 _l 824 2498 _m
825 2509 _l 825 2509 _m
826 2521 _l 826 2521 _m
827 2532 _l 827 2532 _m
829 2544 _l 829 2544 _m
831 2555 _l 831 2555 _m
833 2566 _l 833 2566 _m
835 2578 _l 835 2578 _m
838 2589 _l 838 2589 _m
841 2600 _l 841 2600 _m
844 2611 _l 844 2611 _m
848 2621 _l 848 2621 _m
851 2632 _l 851 2632 _m
855 2642 _l 855 2642 _m
859 2653 _l 859 2653 _m
864 2663 _l 864 2663 _m
869 2673 _l 869 2673 _m
873 2683 _l 873 2683 _m
879 2693 _l 879 2693 _m
884 2703 _l 884 2703 _m
890 2712 _l 890 2712 _m
895 2722 _l 895 2722 _m
901 2731 _l 901 2731 _m
908 2740 _l 908 2740 _m
914 2749 _l 914 2749 _m
921 2758 _l 921 2758 _m
928 2767 _l 928 2767 _m
935 2775 _l 935 2775 _m
942 2784 _l 942 2784 _m
949 2792 _l 949 2792 _m
957 2800 _l 957 2800 _m
965 2808 _l 965 2808 _m
973 2815 _l 973 2815 _m
981 2823 _l 981 2823 _m
989 2830 _l 989 2830 _m
998 2837 _l 998 2837 _m
1006 2844 _l 1006 2844 _m
1015 2850 _l 1015 2850 _m
1024 2857 _l 1024 2857 _m
1033 2863 _l 1033 2863 _m
1042 2869 _l 1042 2869 _m
1052 2874 _l 1052 2874 _m
1061 2880 _l 1061 2880 _m
1071 2885 _l 1071 2885 _m
1080 2890 _l 1080 2890 _m
1090 2895 _l 1090 2895 _m
1100 2900 _l 1100 2900 _m
1111 2904 _l 1111 2904 _m
1121 2908 _l 1121 2908 _m
1131 2912 _l 1131 2912 _m
1142 2915 _l 1142 2915 _m
1152 2919 _l 1152 2919 _m
1163 2922 _l 1163 2922 _m
1174 2924 _l 1174 2924 _m
1185 2927 _l 1185 2927 _m
1196 2929 _l 1196 2929 _m
1207 2931 _l 1207 2931 _m
1218 2933 _l 1218 2933 _m
1229 2934 _l 1229 2934 _m
1240 2935 _l 1240 2935 _m
1252 2936 _l 1252 2936 _m
1263 2936 _l 1263 2936 _m
1274 2936 _l 1274 2936 _m
1286 2936 _l 1286 2936 _m
1297 2936 _l 1297 2936 _m
1309 2935 _l 1309 2935 _m
1320 2934 _l 1320 2934 _m
1331 2933 _l 1331 2933 _m
1342 2931 _l 1342 2931 _m
1354 2929 _l 1354 2929 _m
1364 2927 _l 1364 2927 _m
1375 2924 _l 1375 2924 _m
1386 2922 _l 1386 2922 _m
1397 2919 _l 1397 2919 _m
1407 2915 _l 1407 2915 _m
1418 2912 _l 1418 2912 _m
1428 2908 _l 1428 2908 _m
1438 2904 _l 1438 2904 _m
1449 2900 _l 1449 2900 _m
1459 2895 _l 1459 2895 _m
1468 2890 _l 1468 2890 _m
1478 2885 _l 1478 2885 _m
1488 2880 _l 1488 2880 _m
1497 2874 _l 1497 2874 _m
1507 2869 _l 1507 2869 _m
1516 2863 _l 1516 2863 _m
1525 2857 _l 1525 2857 _m
1534 2850 _l 1534 2850 _m
1543 2844 _l 1543 2844 _m
1552 2837 _l 1552 2837 _m
1560 2830 _l 1560 2830 _m
1568 2823 _l 1568 2823 _m
1576 2815 _l 1576 2815 _m
1584 2808 _l 1584 2808 _m
1592 2800 _l 1592 2800 _m
1600 2792 _l 1600 2792 _m
1607 2784 _l 1607 2784 _m
1614 2775 _l 1614 2775 _m
1621 2767 _l 1621 2767 _m
1628 2758 _l 1628 2758 _m
1635 2749 _l 1635 2749 _m
1641 2740 _l 1641 2740 _m
1648 2731 _l 1648 2731 _m
1654 2722 _l 1654 2722 _m
1659 2712 _l 1659 2712 _m
1665 2703 _l 1665 2703 _m
1670 2693 _l 1670 2693 _m
1676 2683 _l 1676 2683 _m
1680 2673 _l 1680 2673 _m
1685 2663 _l 1685 2663 _m
1690 2653 _l 1690 2653 _m
1694 2642 _l 1694 2642 _m
1698 2632 _l 1698 2632 _m
1701 2621 _l 1701 2621 _m
1705 2611 _l 1705 2611 _m
1708 2600 _l 1708 2600 _m
1711 2589 _l 1711 2589 _m
1714 2578 _l 1714 2578 _m
1716 2566 _l 1716 2566 _m
1718 2555 _l 1718 2555 _m
1720 2544 _l 1720 2544 _m
1722 2532 _l 1722 2532 _m
1723 2521 _l 1723 2521 _m
1724 2509 _l 1724 2509 _m
1725 2498 _l 1725 2498 _m
1725 2486 _l 1725 2486 _m
1725 2474 _l 
_s 1 _w 0 g 1418 2803 _m
1418 2803 _l 1418 2803 _m
1417 2799 _l 1417 2799 _m
1417 2795 _l 1417 2795 _m
1416 2790 _l 1416 2790 _m
1415 2786 _l 1415 2786 _m
1413 2782 _l 1413 2782 _m
1411 2778 _l 1411 2778 _m
1409 2774 _l 1409 2774 _m
1406 2770 _l 1406 2770 _m
1403 2767 _l 1403 2767 _m
1400 2763 _l 1400 2763 _m
1396 2759 _l 1396 2759 _m
1392 2756 _l 1392 2756 _m
1388 2753 _l 1388 2753 _m
1384 2750 _l 1384 2750 _m
1379 2747 _l 1379 2747 _m
1375 2744 _l 1375 2744 _m
1369 2741 _l 1369 2741 _m
1364 2738 _l 1364 2738 _m
1358 2736 _l 1358 2736 _m
1353 2733 _l 1353 2733 _m
1347 2731 _l 1347 2731 _m
1341 2729 _l 1341 2729 _m
1335 2727 _l 1335 2727 _m
1328 2725 _l 1328 2725 _m
1321 2724 _l 1321 2724 _m
1315 2722 _l 1315 2722 _m
1308 2721 _l 1308 2721 _m
1301 2720 _l 1301 2720 _m
1294 2720 _l 1294 2720 _m
1286 2719 _l 1286 2719 _m
1279 2719 _l 1279 2719 _m
1272 2719 _l 1272 2719 _m
1264 2719 _l 1264 2719 _m
1257 2719 _l 1257 2719 _m
1250 2720 _l 1250 2720 _m
1242 2720 _l 1242 2720 _m
1235 2721 _l 1235 2721 _m
1229 2722 _l 1229 2722 _m
1222 2724 _l 1222 2724 _m
1215 2725 _l 1215 2725 _m
1209 2727 _l 1209 2727 _m
1202 2729 _l 1202 2729 _m
1196 2731 _l 1196 2731 _m
1190 2733 _l 1190 2733 _m
1185 2736 _l 1185 2736 _m
1179 2738 _l 1179 2738 _m
1174 2741 _l 1174 2741 _m
1169 2744 _l 1169 2744 _m
1164 2747 _l 1164 2747 _m
1159 2750 _l 1159 2750 _m
1155 2753 _l 1155 2753 _m
1151 2756 _l 1151 2756 _m
1147 2759 _l 1147 2759 _m
1143 2763 _l 1143 2763 _m
1140 2767 _l 1140 2767 _m
1137 2770 _l 1137 2770 _m
1134 2774 _l 1134 2774 _m
1132 2778 _l 1132 2778 _m
1130 2782 _l 1130 2782 _m
1128 2786 _l 1128 2786 _m
1127 2790 _l 1127 2790 _m
1126 2795 _l 1126 2795 _m
1126 2799 _l 1126 2799 _m
1125 2803 _l 1125 2803 _m
1126 2807 _l 1126 2807 _m
1126 2812 _l 1126 2812 _m
1127 2816 _l 1127 2816 _m
1128 2820 _l 1128 2820 _m
1130 2824 _l 1130 2824 _m
1132 2828 _l 1132 2828 _m
1134 2832 _l 1134 2832 _m
1137 2836 _l 1137 2836 _m
1140 2839 _l 1140 2839 _m
1143 2843 _l 1143 2843 _m
1147 2847 _l 1147 2847 _m
1151 2850 _l 1151 2850 _m
1155 2853 _l 1155 2853 _m
1159 2856 _l 1159 2856 _m
1164 2860 _l 1164 2860 _m
1169 2862 _l 1169 2862 _m
1174 2865 _l 1174 2865 _m
1179 2868 _l 1179 2868 _m
1185 2871 _l 1185 2871 _m
1190 2873 _l 1190 2873 _m
1196 2875 _l 1196 2875 _m
1202 2877 _l 1202 2877 _m
1209 2879 _l 1209 2879 _m
1215 2881 _l 1215 2881 _m
1222 2882 _l 1222 2882 _m
1229 2884 _l 1229 2884 _m
1235 2885 _l 1235 2885 _m
1242 2886 _l 1242 2886 _m
1250 2886 _l 1250 2886 _m
1257 2887 _l 1257 2887 _m
1264 2887 _l 1264 2887 _m
1272 2887 _l 1272 2887 _m
1279 2887 _l 1279 2887 _m
1286 2887 _l 1286 2887 _m
1294 2886 _l 1294 2886 _m
1301 2886 _l 1301 2886 _m
1308 2885 _l 1308 2885 _m
1315 2884 _l 1315 2884 _m
1321 2882 _l 1321 2882 _m
1328 2881 _l 1328 2881 _m
1335 2879 _l 1335 2879 _m
1341 2877 _l 1341 2877 _m
1347 2875 _l 1347 2875 _m
1353 2873 _l 1353 2873 _m
1358 2871 _l 1358 2871 _m
1364 2868 _l 1364 2868 _m
1369 2865 _l 1369 2865 _m
1375 2862 _l 1375 2862 _m
1379 2860 _l 1379 2860 _m
1384 2856 _l 1384 2856 _m
1388 2853 _l 1388 2853 _m
1392 2850 _l 1392 2850 _m
1396 2847 _l 1396 2847 _m
1400 2843 _l 1400 2843 _m
1403 2839 _l 1403 2839 _m
1406 2836 _l 1406 2836 _m
1409 2832 _l 1409 2832 _m
1411 2828 _l 1411 2828 _m
1413 2824 _l 1413 2824 _m
1415 2820 _l 1415 2820 _m
1416 2816 _l 1416 2816 _m
1417 2812 _l 1417 2812 _m
1417 2807 _l 1417 2807 _m
1418 2803 _l 1240 2871 _m
1238 2871 _l 1232 2872 _m
1232 2872 _l 1246 2865 _m
1244 2866 _l 1244 2866 _m
1244 2862 _l 1244 2862 _m
1246 2863 _l 1246 2863 _m
1246 2864 _l 1401 2919 _m
1432 2904 _l 1432 2904 _m
1461 2884 _l 1461 2884 _m
1479 2865 _l 1479 2865 _m
1493 2839 _l 1493 2839 _m
1512 2808 _l 1512 2808 _m
1516 2785 _l 1516 2785 _m
1517 2761 _l 1517 2761 _m
1512 2735 _l 1512 2735 _m
1507 2718 _l 1507 2718 _m
1496 2694 _l 1496 2694 _m
1483 2673 _l 1483 2673 _m
1464 2655 _l 1464 2655 _m
1438 2635 _l 1438 2635 _m
1411 2620 _l 1411 2620 _m
1379 2606 _l 1379 2606 _m
1346 2597 _l 1346 2597 _m
1315 2591 _l 1315 2591 _m
1281 2592 _l 1281 2592 _m
1233 2591 _l 1233 2591 _m
1203 2591 _l 1203 2591 _m
1171 2596 _l 1171 2596 _m
1139 2606 _l 1139 2606 _m
1114 2615 _l 1114 2615 _m
1085 2631 _l 1085 2631 _m
1068 2645 _l 1068 2645 _m
1049 2667 _l 1049 2667 _m
1035 2682 _l 1035 2682 _m
1022 2709 _l 1022 2709 _m
1016 2727 _l 1016 2727 _m
1010 2754 _l 1010 2754 _m
1012 2774 _l 1012 2774 _m
1017 2798 _l 1017 2798 _m
1026 2817 _l 1026 2817 _m
1042 2841 _l 1042 2841 _m
1053 2853 _l 1053 2853 _m
1075 2871 _l 1075 2871 _m
1108 2896 _l 1108 2896 _m
1123 2905 _l 1123 2905 _m
1150 2919 _l 1558 2831 _m
1583 2789 _l 1583 2789 _m
1595 2769 _l 1595 2769 _m
1606 2735 _l 1606 2735 _m
1609 2695 _l 1609 2695 _m
1607 2662 _l 1607 2662 _m
1596 2624 _l 1596 2624 _m
1581 2595 _l 1581 2595 _m
1561 2565 _l 1561 2565 _m
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1508 2518 _l 1508 2518 _m
1470 2495 _l 1470 2495 _m
1428 2479 _l 1428 2479 _m
1381 2467 _l 1381 2467 _m
1340 2460 _l 1340 2460 _m
1277 2451 _l 1277 2451 _m
1234 2449 _l 1234 2449 _m
1179 2453 _l 1179 2453 _m
1135 2461 _l 1135 2461 _m
1088 2469 _l 1088 2469 _m
1051 2483 _l 1051 2483 _m
1014 2505 _l 1014 2505 _m
989 2527 _l 989 2527 _m
959 2557 _l 959 2557 _m
943 2580 _l 943 2580 _m
925 2619 _l 925 2619 _m
916 2645 _l 916 2645 _m
915 2687 _l 915 2687 _m
922 2719 _l 922 2719 _m
940 2764 _l 940 2764 _m
956 2794 _l 956 2794 _m
965 2811 _l 1672 2692 _m
1679 2657 _l 1679 2657 _m
1679 2618 _l 1679 2618 _m
1674 2568 _l 1674 2568 _m
1660 2519 _l 1660 2519 _m
1632 2470 _l 1632 2470 _m
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1568 2403 _l 1568 2403 _m
1555 2393 _l 1555 2393 _m
1515 2368 _l 1515 2368 _m
1489 2355 _l 1489 2355 _m
1456 2341 _l 1456 2341 _m
1415 2328 _l 1415 2328 _m
1378 2318 _l 1378 2318 _m
1344 2314 _l 1344 2314 _m
1287 2307 _l 1287 2307 _m
1217 2306 _l 1217 2306 _m
1164 2311 _l 1164 2311 _m
1127 2315 _l 1127 2315 _m
1096 2323 _l 1096 2323 _m
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1026 2349 _l 1026 2349 _m
1007 2360 _l 1007 2360 _m
967 2383 _l 967 2383 _m
943 2406 _l 943 2406 _m
910 2440 _l 910 2440 _m
891 2469 _l 891 2469 _m
872 2507 _l 872 2507 _m
855 2556 _l 855 2556 _m
849 2594 _l 849 2594 _m
850 2631 _l 1719 2535 _m
1715 2498 _l 1715 2498 _m
1707 2457 _l 1707 2457 _m
1695 2413 _l 1695 2413 _m
1678 2380 _l 1678 2380 _m
1656 2348 _l 1656 2348 _m
1636 2326 _l 1636 2326 _m
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1563 2261 _l _s 1563 2261 _m
1518 2233 _l 1518 2233 _m
1468 2213 _l 1468 2213 _m
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1320 2180 _l 1320 2180 _m
1230 2179 _l 1230 2179 _m
1140 2187 _l 1140 2187 _m
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965 2262 _l 965 2262 _m
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826 2472 _l 826 2472 _m
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1431 2100 _l 1431 2100 _m
1380 2089 _l 1380 2089 _m
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1186 2078 _l 1186 2078 _m
1121 2088 _l 1121 2088 _m
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1548 2785 _l 1548 2785 _m
1604 2756 _l 1604 2756 _m
1636 2736 _l 1636 2736 _m
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1470 2639 1468 2640 1465 2641 1463 2642 1461 2643 1460 2644 1460 2645 1460 2646 1461 2648 1463 2649 1465 2649 1467 2649 1469 2648 1470 2646 1471 2643 
1472 2643 1472 2650 1471 2650 1471 2649 1470 2649 1470 2649 1469 2649 1467 2650 1466 2650 1464 2650 1461 2650 1459 2649 1457 2647 1456 2644 1456 2642 
1458 2640 1460 2639 1463 2637 1466 2635 1469 2633 1470 2631 1469 2629 1466 2628 1465 2628 1463 2628 1462 2628 1460 2629 1459 2630 1459 2631 1458 2633 
1457 2635 1456 2635 62 _pl _cp 
0 g _f _s _s 
0 g 1483 2650 _m
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1492 2626 1493 2626 1500 2628 1500 2629 1497 2630 1497 2633 1497 2650 1489 2650 1489 2649 1489 2649 1492 2648 1492 2645 1492 2632 1491 2631 1490 2630 
1488 2629 1487 2629 1486 2629 1484 2631 1483 2632 1483 2635 36 _pl _cp 
0 g _f _s _s 
0 g 1509 2651 _m
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1510 2629 1509 2632 1509 2643 1511 2646 1512 2647 1513 2647 1513 2646 1515 2645 1516 2645 1517 2646 1518 2647 1517 2649 1515 2650 1514 2650 1512 2649 
1511 2648 1509 2646 32 _pl _cp 
0 g _f _s _s 
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1534 2648 1534 2650 1527 2650 1527 2651 1527 2656 1528 2659 1530 2660 1532 2660 1533 2659 1534 2657 1535 2657 1537 2657 1537 2659 1537 2660 1536 2661 
1534 2662 1532 2662 1528 2661 1525 2659 1524 2656 1523 2651 36 _pl _cp 
0 g _f _s _s 
0 g 1549 2642 _m
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1549 2630 1551 2627 1552 2626 1553 2626 1555 2627 1556 2628 1557 2629 1557 2630 1556 2629 1555 2629 1554 2629 1554 2631 1554 2642 1554 2643 1554 2644 
1554 2645 1553 2646 1552 2648 1550 2649 1548 2650 1546 2650 1542 2650 1540 2649 1538 2647 1537 2645 1538 2643 1540 2642 1541 2643 1542 2644 1542 2645 
1542 2645 1542 2646 1542 2646 1542 2646 1543 2648 1545 2649 1547 2649 1548 2648 1549 2646 1549 2643 55 _pl _cp 1549 2640 _m
_sp 1549 2640 1546 2639 1544 2638 1542 2636 1541 2635 1541 2633 1542 2630 1544 2629 1547 2630 1549 2631 10 _pl _cp 
0 g _f _s _s 
0 g 1579 2635 _m
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1575 2644 1576 2643 1578 2643 1578 2645 1577 2647 1576 2649 1574 2650 1571 2650 1567 2649 1564 2648 1561 2645 1560 2642 1559 2638 1560 2633 1562 2629 
1565 2627 1569 2626 1571 2626 1573 2627 1574 2628 1576 2629 1577 2630 1578 2631 1578 2632 1579 2634 40 _pl _cp 
0 g _f _s _s 
0 g 1586 2641 _m
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1595 2627 1598 2628 1601 2631 1603 2635 1602 2635 1601 2633 1599 2631 1597 2630 1594 2629 1591 2630 1588 2632 1587 2636 1586 2640 1586 2641 29 _pl _cp 1596 2642 _m
_sp 1596 2642 1596 2645 1595 2647 1593 2648 1591 2648 1589 2648 1588 2647 1587 2645 1586 2642 9 _pl _cp 
0 g _f _s _s 
0 g 1485 2592 _m
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1488 2562 1485 2563 1485 2566 1485 2573 1488 2572 1490 2572 1493 2572 1496 2574 1499 2577 1500 2580 1501 2585 1500 2589 1498 2593 1496 2595 1492 2596 
1490 2596 1489 2595 1487 2593 33 _pl _cp 1485 2589 _m
_sp 1485 2589 1485 2576 1486 2575 1487 2574 1489 2573 1490 2573 1493 2574 1495 2576 1496 2579 1496 2583 1496 2587 1495 2590 1493 2592 1490 2593 1489 2593 
1487 2592 1486 2591 17 _pl _cp 
0 g _f _s _s 
0 g 1503 2583 _m
_sp 1503 2583 1504 2579 1505 2576 1508 2574 1511 2572 1515 2572 1519 2572 1522 2574 1525 2577 1526 2580 1527 2584 1526 2588 1525 2591 1522 2594 1519 2595 
1515 2596 1511 2595 1508 2594 1505 2591 1504 2587 20 _pl _cp 1508 2585 _m
_sp 1508 2585 1509 2580 1510 2576 1513 2574 1516 2573 1518 2574 1520 2576 1521 2578 1522 2582 1521 2587 1520 2591 1517 2593 1514 2594 1512 2593 1510 2592 
1509 2589 1508 2586 1508 2585 18 _pl _cp 
0 g _f _s _s 
0 g 1537 2596 _m
_sp 1537 2596 1536 2596 1529 2593 1529 2592 1530 2592 1532 2591 1533 2588 1533 2577 1532 2574 1530 2573 1529 2573 1529 2572 1541 2572 1541 2573 1540 2573 
1538 2574 1537 2577 17 _pl _cp 1532 2605 _m
_sp 1532 2605 1533 2603 1535 2602 1537 2603 1538 2605 1537 2607 1535 2608 1533 2607 8 _pl _cp 
0 g _f _s _s 
0 g 1550 2596 _m
_sp 1550 2596 1550 2596 1542 2593 1542 2592 1543 2592 1545 2591 1546 2588 1546 2577 1545 2574 1543 2573 1542 2573 1542 2572 1554 2572 1554 2573 1553 2573 
1551 2574 1550 2577 1550 2589 1552 2591 1553 2592 1555 2593 1556 2593 1558 2593 1559 2591 1559 2589 1559 2586 1559 2577 1559 2574 1556 2573 1556 2573 
1556 2572 1568 2572 1568 2573 1567 2573 1564 2574 1564 2577 1564 2589 1564 2592 1563 2594 1561 2595 1558 2596 1556 2596 1554 2595 1552 2594 1550 2592 
45 _pl _cp 
0 g _f _s _s 
0 g 1568 2594 _m
_sp 1568 2594 1568 2593 1571 2593 1571 2578 1571 2575 1572 2574 1574 2572 1576 2572 1578 2572 1579 2573 1581 2574 1582 2576 1581 2576 1580 2575 1578 2574 
1577 2575 1576 2578 1576 2593 1581 2593 1581 2595 1576 2595 1576 2602 1575 2602 1574 2600 1573 2599 1572 2598 1571 2597 1570 2596 28 _pl _cp 
0 g _f _s _s _s 1281 2318 _m
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1276 2318 1276 2317 1276 2316 1276 2316 1276 2316 1277 2315 1277 2315 1278 2315 1278 2315 1278 2315 1279 2315 1279 2315 1280 2316 1280 2316 1280 2316 
1281 2317 1281 2317 1281 2318 33 _pl _pf _np _s _s 1255 2449 _m
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1355 2400 1358 2396 1363 2392 1366 2389 1369 2385 1372 2382 1375 2378 1377 2376 1379 2373 1381 2370 1383 2367 1385 2363 1386 2360 1387 2357 1388 2354 
1388 2352 1395 2352 1398 2356 1399 2357 1399 2359 1399 2360 1399 2361 1399 2363 1399 2364 1398 2367 1397 2369 1396 2372 1394 2375 1391 2379 1388 2383 
1384 2388 1380 2392 1377 2396 1373 2399 1368 2404 1364 2407 1359 2411 1355 2415 1347 2421 1336 2429 1327 2434 1318 2439 1310 2444 1303 2447 1298 2449 
1294 2451 1291 2452 1287 2453 1283 2454 1280 2455 1276 2456 1273 2457 1270 2457 1267 2457 1264 2457 1262 2456 1261 2456 1259 2455 1258 2454 1258 2453 
75 _pl _pf _np _s 
_s 255 g _s 1326 2343 _m
_sp 1326 2343 1328 2342 1331 2340 1335 2338 1339 2337 1346 2335 1351 2333 1357 2332 1362 2331 1365 2331 1368 2331 1371 2331 1374 2331 1376 2332 1378 2332 
1379 2333 1381 2334 1382 2334 1383 2335 1385 2336 1386 2338 1398 2356 1397 2355 1396 2354 1395 2353 1394 2353 1391 2352 1389 2352 1386 2352 1383 2352 
1379 2353 1375 2354 1371 2355 1365 2356 1361 2358 1357 2360 1351 2363 1346 2365 1342 2367 39 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1258 2453 _m
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1270 2421 1273 2418 1277 2415 1281 2410 1286 2406 1289 2403 1292 2400 1297 2407 1297 2380 1271 2369 1276 2376 1272 2380 1267 2385 1262 2390 1259 2393 
1256 2397 1253 2402 1250 2407 1248 2411 1246 2414 1245 2417 1244 2419 1244 2422 1243 2424 1243 2426 1243 2428 1243 2430 1244 2432 1245 2433 1245 2435 
45 _pl _pf 
0 g _cp _s _s _s 1279 2328 _m
_sp 1279 2328 1284 2328 1281 2328 1432 2496 1459 2478 1442 2566 1354 2549 1379 2531 1282 2333 9 _pl _pf _np _s 
_s 255 g _s 1278 2319 _m
_sp 1278 2319 1281 2318 1281 2317 1438 2504 1465 2486 1448 2573 1360 2556 1387 2538 1276 2320 9 _pl _pf 
0 g _cp _s _s _s 1452 2575 _m
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1444 2574 1444 2574 1445 2573 1445 2572 1445 2572 1446 2571 1447 2571 1447 2570 1448 2570 1449 2570 1450 2571 1450 2571 1451 2571 1451 2572 1452 2573 
1452 2573 1452 2574 1452 2575 33 _pl _pf 
6 _w 0 g _cp _s 
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1185 2280 1183 2280 1181 2281 1178 2283 1177 2285 1178 2287 1181 2288 1182 2288 1184 2287 1185 2285 1186 2283 1187 2283 1187 2288 1186 2288 1186 2288 
1185 2288 1185 2288 1184 2288 1183 2289 1182 2289 1181 2289 1178 2289 1176 2288 1175 2286 1174 2284 1174 2282 1175 2281 1177 2279 1179 2278 1182 2277 
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0 g _f _s _s 
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1198 2262 1196 2263 1196 2265 1196 2271 1198 2270 1200 2270 1204 2271 1206 2273 1208 2276 1209 2280 1208 2284 1207 2286 1205 2288 1202 2289 1201 2289 
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1217 2271 1216 2274 1216 2284 1218 2286 1220 2287 1222 2287 1223 2286 1223 2284 1223 2281 1223 2274 1223 2271 1221 2271 1221 2271 1221 2270 1230 2270 
1230 2271 1230 2271 1228 2271 1227 2274 1227 2282 1227 2285 1226 2287 1224 2289 1222 2289 1221 2289 1219 2288 1218 2287 1216 2286 43 _pl _cp 
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1244 2272 1246 2273 1248 2276 1247 2277 1246 2275 1245 2274 1243 2272 1241 2272 1238 2273 1236 2275 1235 2277 1234 2281 1234 2281 28 _pl _cp 1243 2282 _m
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1256 2271 1255 2274 1255 2283 1256 2285 1257 2286 1258 2286 1259 2285 1260 2285 1260 2285 1261 2285 1262 2286 1261 2288 1260 2289 1259 2289 1258 2288 
1256 2287 1255 2286 32 _pl _cp 
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1276 2272 1278 2273 1280 2276 1279 2277 1278 2275 1277 2274 1275 2272 1273 2272 1270 2273 1268 2275 1267 2277 1266 2281 1266 2281 28 _pl _cp 1275 2282 _m
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1190 2240 1191 2239 1192 2240 1193 2241 1192 2242 1191 2244 1189 2245 1187 2245 1183 2244 1181 2242 1179 2239 1178 2235 1179 2231 1180 2229 1183 2227 
1186 2226 1189 2227 1191 2228 1193 2230 1194 2232 35 _pl _cp 
0 g _f _s _s 
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1209 2228 1211 2230 1213 2233 1212 2233 1211 2231 1209 2230 1207 2229 1205 2228 1203 2229 1201 2231 1200 2233 1199 2237 1199 2237 28 _pl _cp 1207 2239 _m
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1220 2228 1220 2230 1220 2240 1222 2242 1224 2243 1225 2243 1226 2242 1227 2240 1227 2237 1227 2230 1227 2228 1225 2227 1224 2227 1224 2226 1234 2226 
1234 2227 1233 2227 1231 2228 1231 2230 1231 2239 1231 2242 1230 2244 1228 2245 1226 2245 1225 2245 1223 2244 1222 2243 1220 2242 43 _pl _cp 
0 g _f _s _s 
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1241 2229 1240 2231 1240 2243 1244 2243 1244 2245 1240 2245 1240 2250 1239 2250 1238 2248 1236 2246 1235 2245 26 _pl _cp 
0 g _f _s _s 
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0 g _f _s _s 
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1271 2228 1270 2230 1270 2239 1271 2241 1272 2242 1273 2242 1274 2242 1275 2241 1275 2241 1276 2242 1277 2243 1276 2244 1275 2245 1274 2245 1273 2244 
1271 2243 1270 2242 32 _pl _cp 
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1231 2556 1233 2554 1234 2553 18 _pl _cp 
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1275 2514 1273 2515 17 _pl _cp 
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(Figure)_S 67 _t
(6.6)_S /Times-RomanR 600 _ff
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(Quaternion)_S 67 _t
(representation.)_S 1980 6613 _m
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(\(Cooke)_S 67 _t
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(\(Kolve)_S 67 _t
(93\))_S 67 _t
(\(Chou)_S 67 _t
(92\))_S 67 _t
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(90\))_S 67 _t
(\(Maillot)_S 67 _t
(90\))_S 67 _t
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(\(Shoemake)_S 67 _t
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0 g 1259 1129 _m
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1265 1119 1267 1117 1268 1116 1267 1115 1265 1114 1264 1114 1264 1113 1278 1113 1278 1114 1276 1115 1275 1115 1273 1117 1271 1119 1263 1131 1270 1140 
1272 1142 1274 1144 1275 1144 1277 1145 1277 1146 1266 1146 1266 1145 1267 1145 1269 1145 1270 1144 1269 1142 1267 1140 1262 1133 1258 1140 1256 1142 
1256 1144 1256 1145 1258 1145 1259 1145 1259 1146 1244 1146 1244 1145 1247 1144 1248 1144 1250 1142 1251 1140 56 _pl _cp 
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1400 1119 1400 1117 1400 1115 1398 1114 1396 1114 1395 1114 1395 1113 1410 1113 1410 1114 1409 1114 1407 1114 1406 1115 1406 1117 1406 1119 1406 1128 
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1535 1137 1537 1137 1537 1140 1538 1142 1539 1143 1541 1143 1543 1144 1545 1144 1555 1144 24 _pl _cp 
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67 _t
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67 _t
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67 _t
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67 _t
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1070 2782 1067 2778 1064 2774 1063 2769 1062 2764 1063 2760 1064 2757 1066 2755 1069 2753 1070 2752 1071 2750 1073 2749 1074 2748 1076 2747 1077 2746 
1079 2745 1082 2745 1084 2744 1086 2744 1087 2744 1088 2744 1089 2746 1088 2746 1088 2746 1085 2747 1082 2748 1079 2750 42 _pl _cp 1083 2785 _m
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1072 2755 1075 2754 1077 2754 1080 2755 1082 2757 1084 2759 1086 2762 1088 2765 1089 2769 1090 2773 1090 2776 1090 2780 1088 2783 1086 2784 29 _pl _cp 
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1193 2753 1194 2753 1196 2754 1197 2755 1199 2757 1200 2759 1197 2748 1196 2745 1194 2744 1193 2744 1192 2743 1204 2743 1204 2744 1202 2744 1201 2745 
1201 2746 1201 2747 1201 2748 1209 2775 1205 2775 35 _pl _cp 1190 2759 _m
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1194 2769 1192 2766 1191 2763 1190 2760 1190 2760 20 _pl _cp 
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1283 2746 1283 2747 1283 2748 1290 2775 1286 2775 35 _pl _cp 1272 2759 _m
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1275 2769 1274 2766 1272 2763 1272 2760 1272 2760 20 _pl _cp 
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1364 2746 1365 2747 1365 2748 1372 2775 1368 2775 35 _pl _cp 1354 2759 _m
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1357 2769 1355 2766 1354 2763 1354 2760 1354 2760 20 _pl _cp 
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1439 2753 1440 2753 1441 2754 1442 2755 1444 2757 1446 2759 1443 2748 1442 2745 1440 2744 1438 2744 1438 2743 1449 2743 1450 2744 1448 2744 1447 2745 
1446 2746 1446 2747 1447 2748 1454 2775 1450 2775 35 _pl _cp 1436 2759 _m
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1221 2759 1218 2760 1215 2759 1213 2757 1211 2753 20 _pl _cp 1214 2749 _m
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1216 2757 1215 2756 1214 2753 18 _pl _cp 
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1238 2758 1236 2757 1235 2755 1236 2754 1237 2753 1239 2753 21 _pl _cp 
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1302 2738 1302 2741 1302 2759 18 _pl _cp 
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1375 2756 1374 2753 1375 2753 1376 2754 1376 2755 1378 2756 1380 2757 1381 2757 1383 2756 1384 2754 1384 2752 1384 2750 1383 2748 1381 2746 1379 2743 
1377 2741 1374 2738 1374 2737 1387 2737 1389 2742 1388 2742 1388 2741 1387 2741 1387 2740 1386 2740 1384 2740 41 _pl _cp 
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1401 2758 1399 2757 1398 2755 1399 2754 1401 2753 1402 2753 21 _pl _cp 
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1461 2748 1461 2748 1463 2748 1465 2747 1466 2745 1467 2743 1467 2741 1466 2739 1464 2738 1463 2738 1462 2738 1460 2739 1459 2740 1458 2740 1457 2740 
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/Times-BoldR 600 _ff
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1073 2434 1074 2435 1075 2436 1077 2437 1078 2439 1080 2441 1077 2430 1076 2427 1074 2426 1072 2426 1072 2425 1084 2425 1084 2426 1082 2426 1081 2426 
1081 2427 1081 2428 1081 2430 1088 2457 1084 2457 35 _pl _cp 1070 2441 _m
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1073 2450 1072 2447 1070 2444 1070 2441 1070 2441 20 _pl _cp 
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1456 2495 1454 2495 1452 2495 1449 2495 1437 2495 35 _pl _cp 1440 2470 _m
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1073 2301 1074 2302 1075 2303 1077 2304 1078 2306 1080 2308 1077 2297 1076 2294 1074 2293 1072 2293 1072 2292 1084 2292 1084 2293 1082 2293 1081 2293 
1081 2294 1081 2295 1081 2297 1088 2324 1084 2324 35 _pl _cp 1070 2308 _m
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1073 2317 1072 2314 1070 2311 1070 2308 1070 2308 20 _pl _cp 
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1288 2313 1288 2308 1289 2307 1289 2306 1289 2306 1289 2306 1288 2304 1286 2303 1285 2303 1284 2302 1297 2302 1297 2303 1297 2303 1295 2304 1294 2306 
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1453 2359 1449 2360 1448 2360 1446 2360 1446 2360 1446 2360 1446 2360 1446 2359 1446 2358 1445 2355 25 _pl _cp 
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1073 2168 1074 2169 1075 2170 1077 2171 1078 2173 1080 2175 1077 2164 1076 2161 1074 2160 1072 2160 1072 2159 1084 2159 1084 2160 1082 2160 1081 2160 
1081 2161 1081 2162 1081 2164 1088 2191 1084 2191 35 _pl _cp 1070 2175 _m
_sp 1070 2175 1071 2172 1073 2171 1075 2171 1076 2173 1078 2174 1080 2177 1081 2180 1082 2182 1083 2185 1083 2187 1082 2189 1080 2190 1078 2189 1076 2187 
1073 2184 1072 2181 1070 2178 1070 2175 1070 2175 20 _pl _cp 
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1279 2200 1280 2200 1281 2198 1281 2197 1280 2195 1275 2175 1274 2173 1273 2171 1272 2170 1271 2170 1270 2170 1270 2169 1279 2169 1284 2169 1287 2169 
1289 2169 1291 2170 1294 2171 1296 2173 1297 2176 1297 2178 1297 2180 1296 2182 1296 2183 1295 2184 1294 2185 41 _pl _cp 1283 2185 _m
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15 _pl _cp 1283 2187 _m
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1286 2199 1286 2196 17 _pl _cp 
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1456 2229 1454 2229 1452 2229 1449 2229 1437 2229 35 _pl _cp 1440 2204 _m
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1073 2035 1074 2036 1075 2037 1077 2038 1078 2040 1080 2042 1077 2031 1076 2028 1074 2027 1072 2027 1072 2026 1084 2026 1084 2027 1082 2027 1081 2027 
1081 2028 1081 2029 1081 2031 1088 2058 1084 2058 35 _pl _cp 1070 2042 _m
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1073 2051 1072 2048 1070 2045 1070 2042 1070 2042 20 _pl _cp 
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1282 2061 1285 2064 1288 2066 1292 2067 1294 2067 1295 2066 1297 2066 1298 2065 1299 2064 1299 2063 1300 2061 1300 2059 1301 2059 1303 2069 1302 2069 
1301 2068 1300 2068 1300 2068 1299 2068 1297 2069 1295 2069 1294 2069 1292 2069 1287 2068 1283 2067 1279 2065 1276 2061 1274 2058 1272 2053 1272 2049 
1272 2046 1273 2043 1274 2041 1276 2039 1278 2037 1280 2036 1283 2035 1286 2035 1289 2036 1291 2036 1293 2037 1295 2038 1297 2040 1299 2042 59 _pl _cp 
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1458 2096 1457 2096 1455 2096 1452 2096 1440 2096 35 _pl _cp 1443 2071 _m
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1456 2093 1452 2094 1451 2094 1449 2094 1449 2094 1449 2094 1449 2094 1448 2093 1448 2092 1447 2089 25 _pl _cp 
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1101 2440 1098 2441 1095 2440 1092 2438 1091 2434 20 _pl _cp 1094 2430 _m
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1096 2439 1095 2438 1094 2435 18 _pl _cp 
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1347 2451 1348 2450 1349 2451 1350 2452 1349 2454 1348 2456 1346 2457 1343 2457 1339 2456 1336 2455 1334 2452 1332 2449 1332 2445 1333 2441 1335 2437 
1337 2435 1341 2434 1343 2434 1345 2435 1346 2436 1348 2437 1349 2438 1350 2439 1350 2440 1351 2442 40 _pl _cp 
0 g _f _s _s 
0 g 1354 2445 _m
_sp 1354 2445 1355 2441 1357 2437 1361 2435 1365 2434 1368 2434 1371 2436 1374 2439 1375 2442 1376 2446 1375 2451 1373 2454 1370 2456 1365 2457 1361 2456 
1358 2455 1356 2452 1355 2449 18 _pl _cp 1358 2447 _m
_sp 1358 2447 1359 2442 1361 2439 1363 2437 1366 2436 1368 2437 1370 2438 1371 2441 1372 2444 1371 2449 1370 2453 1367 2455 1364 2456 1362 2455 1360 2454 
1359 2451 1358 2448 1358 2447 18 _pl _cp 
0 g _f _s _s 
0 g 1379 2435 _m
_sp 1379 2435 1380 2435 1380 2435 1381 2435 1382 2435 1383 2435 1386 2434 1388 2434 1391 2435 1394 2436 1395 2438 1396 2440 1395 2443 1394 2445 1393 2446 
1392 2446 1390 2447 1387 2448 1385 2449 1383 2451 1382 2452 1382 2453 1382 2454 1383 2455 1385 2456 1387 2456 1389 2456 1391 2455 1392 2453 1393 2450 
1394 2450 1394 2457 1393 2457 1393 2457 1392 2456 1392 2457 1391 2457 1389 2457 1388 2457 1387 2457 1384 2457 1381 2456 1380 2454 1379 2451 1379 2449 
1380 2448 1382 2446 1385 2445 1388 2443 1391 2441 1392 2439 1391 2436 1388 2435 1385 2436 1383 2437 1382 2438 1381 2439 1381 2440 1380 2442 1379 2442 
60 _pl _cp 
0 g _f _s _s 
0 g 1441 2399 _m
_sp 1441 2399 1443 2402 1446 2405 1447 2406 1449 2408 1450 2409 1451 2410 1453 2413 1454 2415 1455 2418 1455 2420 1454 2424 1452 2426 1450 2428 1446 2429 
1444 2429 1442 2428 1441 2427 1439 2426 1438 2424 1437 2423 1436 2421 1435 2419 1436 2418 1438 2420 1439 2422 1441 2424 1444 2424 1447 2424 1449 2423 
1450 2421 1451 2418 1450 2415 1449 2412 1447 2408 1444 2404 1440 2400 1435 2396 1435 2395 1455 2395 1458 2402 1457 2402 1456 2401 1455 2400 1454 2399 
1453 2399 1451 2399 47 _pl _cp 
0 g _f _s _s 
0 g 1093 2305 _m
_sp 1093 2305 1093 2304 1095 2305 1095 2305 1096 2305 1097 2304 1097 2303 1097 2290 1096 2287 1094 2286 1094 2286 1094 2286 1103 2286 1103 2286 1102 2286 
1100 2287 1100 2290 1100 2308 18 _pl _cp 
0 g _f _s _s 
0 g 1201 2309 _m
_sp 1201 2309 1199 2307 1197 2306 1195 2305 1193 2305 1190 2306 1188 2308 1187 2310 1186 2314 1186 2318 1188 2320 1189 2322 1192 2323 1194 2322 1195 2320 
1197 2318 1198 2317 1199 2318 1200 2319 1199 2321 1198 2323 1196 2324 1193 2324 1189 2323 1186 2322 1184 2319 1182 2316 1182 2312 1183 2308 1185 2304 
1187 2302 1191 2301 1193 2301 1195 2302 1196 2303 1198 2304 1199 2305 1200 2306 1200 2307 1201 2309 40 _pl _cp 
0 g _f _s _s 
0 g 1204 2312 _m
_sp 1204 2312 1205 2308 1207 2304 1211 2302 1215 2301 1218 2301 1221 2303 1224 2306 1225 2309 1226 2313 1225 2318 1223 2321 1220 2323 1215 2324 1211 2323 
1208 2322 1206 2319 1205 2316 18 _pl _cp 1208 2314 _m
_sp 1208 2314 1209 2309 1211 2306 1213 2304 1216 2303 1218 2304 1220 2305 1221 2308 1222 2311 1221 2316 1220 2320 1217 2322 1214 2323 1212 2322 1210 2321 
1209 2318 1208 2315 1208 2314 18 _pl _cp 
0 g _f _s _s 
0 g 1229 2302 _m
_sp 1229 2302 1230 2302 1230 2302 1231 2302 1232 2302 1233 2302 1236 2301 1238 2301 1241 2302 1244 2303 1245 2305 1246 2307 1245 2310 1244 2312 1243 2313 
1242 2313 1240 2314 1237 2315 1235 2316 1233 2318 1232 2319 1232 2320 1232 2321 1233 2322 1235 2323 1237 2323 1239 2323 1241 2322 1242 2320 1243 2317 
1244 2317 1244 2324 1243 2324 1243 2324 1242 2323 1242 2324 1241 2324 1239 2324 1238 2324 1237 2324 1234 2324 1231 2323 1230 2321 1229 2318 1229 2316 
1230 2315 1232 2313 1235 2312 1238 2310 1241 2308 1242 2306 1241 2303 1238 2302 1235 2303 1233 2304 1232 2305 1231 2306 1231 2307 1230 2309 1229 2309 
60 _pl _cp 
0 g _f _s _s 
0 g 1268 2335 _m
_sp 1268 2335 1265 2333 1263 2332 1261 2330 1260 2328 1258 2325 1256 2322 1255 2318 1255 2314 1255 2310 1256 2306 1258 2303 1260 2300 1261 2298 1263 2296 
1265 2295 1268 2293 1268 2294 1266 2296 1264 2298 1263 2299 1263 2301 1262 2302 1261 2303 1260 2305 1260 2308 1260 2311 1260 2314 1260 2317 1260 2320 
1260 2323 1261 2325 1262 2326 1263 2327 1263 2329 1264 2330 1266 2332 1268 2334 38 _pl _cp 
0 g _f _s _s 
0 g 1301 2293 _m
_sp 1301 2293 1304 2295 1306 2296 1308 2298 1309 2300 1311 2303 1313 2306 1314 2310 1314 2314 1314 2318 1313 2322 1311 2325 1309 2328 1308 2330 1306 2332 
1304 2333 1301 2335 1301 2334 1303 2332 1305 2330 1306 2329 1307 2327 1307 2326 1308 2325 1309 2323 1309 2320 1309 2317 1309 2314 1309 2311 1309 2308 
1309 2305 1308 2303 1307 2302 1307 2301 1306 2299 1305 2298 1303 2296 1301 2294 38 _pl _cp 
0 g _f _s _s 
0 g 1340 2302 _m
_sp 1340 2302 1341 2302 1341 2302 1342 2302 1343 2302 1344 2302 1347 2301 1349 2301 1352 2302 1355 2303 1356 2305 1357 2307 1356 2310 1355 2312 1354 2313 
1353 2313 1351 2314 1348 2315 1346 2316 1344 2318 1343 2319 1343 2320 1343 2321 1344 2322 1346 2323 1348 2323 1350 2323 1352 2322 1353 2320 1354 2317 
1355 2317 1355 2324 1354 2324 1354 2324 1353 2323 1353 2324 1352 2324 1350 2324 1349 2324 1348 2324 1345 2324 1342 2323 1341 2321 1340 2318 1340 2316 
1341 2315 1343 2313 1346 2312 1349 2310 1352 2308 1353 2306 1352 2303 1349 2302 1346 2303 1344 2304 1343 2305 1342 2306 1342 2307 1341 2309 1340 2309 
60 _pl _cp 
0 g _f _s _s 
0 g 1367 2325 _m
_sp 1367 2325 1366 2325 1359 2322 1359 2321 1360 2321 1362 2320 1363 2317 1363 2306 1362 2303 1360 2303 1359 2303 1359 2302 1371 2302 1371 2303 1370 2303 
1368 2303 1367 2306 17 _pl _cp 1362 2333 _m
_sp 1362 2333 1363 2331 1365 2330 1367 2331 1368 2333 1367 2335 1365 2336 1363 2335 8 _pl _cp 
0 g _f _s _s 
0 g 1380 2325 _m
_sp 1380 2325 1379 2325 1372 2322 1372 2321 1373 2321 1375 2320 1376 2317 1376 2306 1375 2303 1373 2303 1372 2303 1372 2302 1383 2302 1383 2303 1383 2303 
1381 2303 1380 2306 1380 2318 1381 2320 1383 2321 1384 2322 1385 2322 1387 2322 1388 2320 1389 2318 1389 2315 1389 2306 1389 2303 1386 2303 1386 2303 
1386 2302 1397 2302 1397 2303 1396 2303 1394 2303 1393 2306 1393 2317 1393 2320 1392 2322 1390 2324 1387 2324 1385 2324 1384 2323 1382 2322 1380 2320 
45 _pl _cp 
0 g _f _s _s 
0 g 1441 2266 _m
_sp 1441 2266 1443 2269 1446 2272 1447 2273 1449 2275 1450 2276 1451 2277 1453 2280 1454 2282 1455 2285 1455 2287 1454 2291 1452 2293 1450 2295 1446 2296 
1444 2296 1442 2295 1441 2294 1439 2293 1438 2291 1437 2290 1436 2288 1435 2286 1436 2285 1438 2287 1439 2289 1441 2291 1444 2291 1447 2291 1449 2290 
1450 2288 1451 2285 1450 2282 1449 2279 1447 2275 1444 2271 1440 2267 1435 2263 1435 2262 1455 2262 1458 2269 1457 2269 1456 2268 1455 2267 1454 2266 
1453 2266 1451 2266 47 _pl _cp 
0 g _f _s _s 
0 g 1094 2155 _m
_sp 1094 2155 1095 2157 1098 2159 1100 2161 1101 2163 1102 2165 1103 2166 1103 2168 1103 2169 1103 2172 1102 2174 1100 2175 1097 2175 1095 2174 1093 2173 
1092 2172 1091 2171 1091 2170 1090 2168 1091 2168 1092 2170 1093 2171 1094 2172 1096 2172 1099 2171 1100 2168 1100 2166 1099 2164 1098 2161 1096 2159 
1093 2156 1090 2153 1090 2153 1103 2153 1105 2157 1105 2157 1104 2157 1103 2156 1103 2156 1102 2155 1100 2155 41 _pl _cp 
0 g _f _s _s 
0 g 1201 2176 _m
_sp 1201 2176 1199 2174 1197 2173 1195 2172 1193 2172 1190 2173 1188 2175 1187 2177 1186 2181 1186 2185 1188 2187 1189 2189 1192 2190 1194 2189 1195 2187 
1197 2185 1198 2184 1199 2185 1200 2186 1199 2188 1198 2190 1196 2191 1193 2191 1189 2190 1186 2189 1184 2186 1182 2183 1182 2179 1183 2175 1185 2171 
1187 2169 1191 2168 1193 2168 1195 2169 1196 2170 1198 2171 1199 2172 1200 2173 1200 2174 1201 2176 40 _pl _cp 
0 g _f _s _s 
0 g 1204 2179 _m
_sp 1204 2179 1205 2175 1207 2171 1211 2169 1215 2168 1218 2168 1221 2170 1224 2173 1225 2176 1226 2180 1225 2185 1223 2188 1220 2190 1215 2191 1211 2190 
1208 2189 1206 2186 1205 2183 18 _pl _cp 1208 2181 _m
_sp 1208 2181 1209 2176 1211 2173 1213 2171 1216 2170 1218 2171 1220 2172 1221 2175 1222 2178 1221 2183 1220 2187 1217 2189 1214 2190 1212 2189 1210 2188 
1209 2185 1208 2182 1208 2181 18 _pl _cp 
0 g _f _s _s 
0 g 1229 2169 _m
_sp 1229 2169 1230 2169 1230 2169 1231 2169 1232 2169 1233 2169 1236 2168 1238 2168 1241 2169 1244 2170 1245 2172 1246 2174 1245 2177 1244 2179 1243 2180 
1242 2180 1240 2181 1237 2182 1235 2183 1233 2185 1232 2186 1232 2187 1232 2188 1233 2189 1235 2190 1237 2190 1239 2190 1241 2189 1242 2187 1243 2184 
1244 2184 1244 2191 1243 2191 1243 2191 1242 2190 1242 2191 1241 2191 1239 2191 1238 2191 1237 2191 1234 2191 1231 2190 1230 2188 1229 2185 1229 2183 
1230 2182 1232 2180 1235 2179 1238 2177 1241 2175 1242 2173 1241 2170 1238 2169 1235 2170 1233 2171 1232 2172 1231 2173 1231 2174 1230 2176 1229 2176 
60 _pl _cp 
0 g _f _s _s 
0 g 1268 2202 _m
_sp 1268 2202 1265 2200 1263 2199 1261 2197 1260 2195 1258 2192 1256 2189 1255 2185 1255 2181 1255 2177 1256 2173 1258 2170 1260 2167 1261 2165 1263 2163 
1265 2162 1268 2160 1268 2161 1266 2163 1264 2165 1263 2166 1263 2168 1262 2169 1261 2170 1260 2172 1260 2175 1260 2178 1260 2181 1260 2184 1260 2187 
1260 2190 1261 2192 1262 2193 1263 2194 1263 2196 1264 2197 1266 2199 1268 2201 38 _pl _cp 
0 g _f _s _s 
0 g 1301 2160 _m
_sp 1301 2160 1304 2162 1306 2163 1308 2165 1309 2167 1311 2170 1313 2173 1314 2177 1314 2181 1314 2185 1313 2189 1311 2192 1309 2195 1308 2197 1306 2199 
1304 2200 1301 2202 1301 2201 1303 2199 1305 2197 1306 2196 1307 2194 1307 2193 1308 2192 1309 2190 1309 2187 1309 2184 1309 2181 1309 2178 1309 2175 
1309 2172 1308 2170 1307 2169 1307 2168 1306 2166 1305 2165 1303 2163 1301 2161 38 _pl _cp 
0 g _f _s _s 
0 g 1340 2169 _m
_sp 1340 2169 1341 2169 1341 2169 1342 2169 1343 2169 1344 2169 1347 2168 1349 2168 1352 2169 1355 2170 1356 2172 1357 2174 1356 2177 1355 2179 1354 2180 
1353 2180 1351 2181 1348 2182 1346 2183 1344 2185 1343 2186 1343 2187 1343 2188 1344 2189 1346 2190 1348 2190 1350 2190 1352 2189 1353 2187 1354 2184 
1355 2184 1355 2191 1354 2191 1354 2191 1353 2190 1353 2191 1352 2191 1350 2191 1349 2191 1348 2191 1345 2191 1342 2190 1341 2188 1340 2185 1340 2183 
1341 2182 1343 2180 1346 2179 1349 2177 1352 2175 1353 2173 1352 2170 1349 2169 1346 2170 1344 2171 1343 2172 1342 2173 1342 2174 1341 2176 1340 2176 
60 _pl _cp 
0 g _f _s _s 
0 g 1367 2192 _m
_sp 1367 2192 1366 2192 1359 2189 1359 2188 1360 2188 1362 2187 1363 2184 1363 2173 1362 2170 1360 2170 1359 2170 1359 2169 1371 2169 1371 2170 1370 2170 
1368 2170 1367 2173 17 _pl _cp 1362 2200 _m
_sp 1362 2200 1363 2198 1365 2197 1367 2198 1368 2200 1367 2202 1365 2203 1363 2202 8 _pl _cp 
0 g _f _s _s 
0 g 1380 2192 _m
_sp 1380 2192 1379 2192 1372 2189 1372 2188 1373 2188 1375 2187 1376 2184 1376 2173 1375 2170 1373 2170 1372 2170 1372 2169 1383 2169 1383 2170 1383 2170 
1381 2170 1380 2173 1380 2185 1381 2187 1383 2188 1384 2189 1385 2189 1387 2189 1388 2187 1389 2185 1389 2182 1389 2173 1389 2170 1386 2170 1386 2170 
1386 2169 1397 2169 1397 2170 1396 2170 1394 2170 1393 2173 1393 2184 1393 2187 1392 2189 1390 2191 1387 2191 1385 2191 1384 2190 1382 2189 1380 2187 
45 _pl _cp 
0 g _f _s _s 
0 g 1441 2133 _m
_sp 1441 2133 1443 2136 1446 2139 1447 2140 1449 2142 1450 2143 1451 2144 1453 2147 1454 2149 1455 2152 1455 2154 1454 2158 1452 2160 1450 2162 1446 2163 
1444 2163 1442 2162 1441 2161 1439 2160 1438 2158 1437 2157 1436 2155 1435 2153 1436 2152 1438 2154 1439 2156 1441 2158 1444 2158 1447 2158 1449 2157 
1450 2155 1451 2152 1450 2149 1449 2146 1447 2142 1444 2138 1440 2134 1435 2130 1435 2129 1455 2129 1458 2136 1457 2136 1456 2135 1455 2134 1454 2133 
1453 2133 1451 2133 47 _pl _cp 
0 g _f _s _s 
0 g 1091 2036 _m
_sp 1091 2036 1092 2036 1094 2039 1096 2040 1099 2039 1100 2036 1100 2035 1100 2034 1099 2033 1098 2033 1096 2032 1095 2031 1095 2030 1095 2030 1095 2030 
1097 2030 1099 2030 1101 2028 1101 2025 1100 2022 1097 2021 1096 2021 1094 2022 1094 2022 1093 2022 1092 2022 1091 2021 1092 2020 1095 2019 1099 2020 
1101 2021 1103 2024 1104 2027 1104 2029 1103 2031 1102 2032 1100 2033 1101 2034 1102 2035 1103 2037 1103 2038 1103 2039 1102 2041 1100 2042 1098 2042 
1096 2042 1094 2041 1093 2040 1093 2039 1092 2038 50 _pl _cp 
0 g _f _s _s 
0 g 1201 2043 _m
_sp 1201 2043 1199 2041 1197 2040 1195 2039 1193 2039 1190 2040 1188 2042 1187 2044 1186 2048 1186 2052 1188 2054 1189 2056 1192 2057 1194 2056 1195 2054 
1197 2052 1198 2051 1199 2052 1200 2053 1199 2055 1198 2057 1196 2058 1193 2058 1189 2057 1186 2056 1184 2053 1182 2050 1182 2046 1183 2042 1185 2038 
1187 2036 1191 2035 1193 2035 1195 2036 1196 2037 1198 2038 1199 2039 1200 2040 1200 2041 1201 2043 40 _pl _cp 
0 g _f _s _s 
0 g 1204 2046 _m
_sp 1204 2046 1205 2042 1207 2038 1211 2036 1215 2035 1218 2035 1221 2037 1224 2040 1225 2043 1226 2047 1225 2052 1223 2055 1220 2057 1215 2058 1211 2057 
1208 2056 1206 2053 1205 2050 18 _pl _cp 1208 2048 _m
_sp 1208 2048 1209 2043 1211 2040 1213 2038 1216 2037 1218 2038 1220 2039 1221 2042 1222 2045 1221 2050 1220 2054 1217 2056 1214 2057 1212 2056 1210 2055 
1209 2052 1208 2049 1208 2048 18 _pl _cp 
0 g _f _s _s 
0 g 1229 2036 _m
_sp 1229 2036 1230 2036 1230 2036 1231 2036 1232 2036 1233 2036 1236 2035 1238 2035 1241 2036 1244 2037 1245 2039 1246 2041 1245 2044 1244 2046 1243 2047 
1242 2047 1240 2048 1237 2049 1235 2050 1233 2052 1232 2053 1232 2054 1232 2055 1233 2056 1235 2057 1237 2057 1239 2057 1241 2056 1242 2054 1243 2051 
1244 2051 1244 2058 1243 2058 1243 2058 1242 2057 1242 2058 1241 2058 1239 2058 1238 2058 1237 2058 1234 2058 1231 2057 1230 2055 1229 2052 1229 2050 
1230 2049 1232 2047 1235 2046 1238 2044 1241 2042 1242 2040 1241 2037 1238 2036 1235 2037 1233 2038 1232 2039 1231 2040 1231 2041 1230 2043 1229 2043 
60 _pl _cp 
0 g _f _s _s 
0 g 1268 2069 _m
_sp 1268 2069 1265 2067 1263 2066 1261 2064 1260 2062 1258 2059 1256 2056 1255 2052 1255 2048 1255 2044 1256 2040 1258 2037 1260 2034 1261 2032 1263 2030 
1265 2029 1268 2027 1268 2028 1266 2030 1264 2032 1263 2033 1263 2035 1262 2036 1261 2037 1260 2039 1260 2042 1260 2045 1260 2048 1260 2051 1260 2054 
1260 2057 1261 2059 1262 2060 1263 2061 1263 2063 1264 2064 1266 2066 1268 2068 38 _pl _cp 
0 g _f _s _s 
0 g 1310 2027 _m
_sp 1310 2027 1313 2029 1314 2030 1316 2032 1318 2034 1320 2037 1321 2040 1322 2044 1322 2048 1322 2052 1321 2056 1320 2059 1318 2062 1316 2064 1314 2066 
1313 2067 1310 2069 1309 2068 1311 2066 1313 2064 1314 2063 1315 2061 1315 2060 1316 2059 1317 2057 1317 2054 1317 2051 1317 2048 1317 2045 1317 2042 
1317 2039 1316 2037 1315 2036 1315 2035 1314 2033 1313 2032 1311 2030 1309 2028 38 _pl _cp 
0 g _f _s _s 
0 g 1343 2036 _m
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1355 2047 1354 2048 1351 2049 1349 2050 1347 2052 1346 2053 1346 2054 1347 2056 1350 2057 1353 2057 1355 2056 1356 2054 1357 2051 1358 2051 1358 2058 
1357 2058 1357 2058 1356 2057 1356 2058 1355 2058 1353 2058 1352 2058 1350 2058 1347 2058 1345 2057 1344 2055 1343 2052 1343 2050 1344 2049 1346 2047 
1348 2046 1352 2044 1355 2042 1356 2040 1356 2039 1355 2037 1353 2036 1351 2036 1349 2037 1346 2038 1345 2040 1344 2043 1343 2043 58 _pl _cp 
0 g _f _s _s 
0 g 1370 2059 _m
_sp 1370 2059 1369 2059 1362 2056 1362 2055 1363 2055 1365 2054 1366 2051 1366 2040 1365 2037 1363 2037 1362 2037 1362 2036 1374 2036 1374 2037 1373 2037 
1370 2037 1370 2040 17 _pl _cp 1365 2067 _m
_sp 1365 2067 1366 2065 1367 2064 1369 2065 1370 2067 1369 2069 1367 2070 1366 2069 8 _pl _cp 
0 g _f _s _s 
0 g 1383 2059 _m
_sp 1383 2059 1382 2059 1375 2056 1375 2055 1376 2055 1378 2054 1378 2051 1378 2040 1378 2037 1376 2037 1375 2037 1375 2036 1386 2036 1386 2037 1386 2037 
1383 2037 1383 2040 1383 2052 1384 2054 1386 2055 1387 2056 1388 2056 1390 2056 1391 2054 1392 2052 1392 2049 1392 2040 1391 2037 1389 2037 1388 2037 
1388 2036 1400 2036 1400 2037 1399 2037 1397 2037 1396 2040 1396 2051 1396 2054 1395 2056 1393 2058 1390 2058 1388 2058 1387 2057 1385 2056 1383 2054 
45 _pl _cp 
0 g _f _s _s 
0 g 1443 2000 _m
_sp 1443 2000 1446 2003 1449 2006 1450 2007 1452 2009 1453 2010 1454 2011 1456 2014 1457 2016 1458 2019 1458 2021 1457 2025 1455 2027 1453 2029 1449 2030 
1447 2030 1445 2029 1443 2028 1442 2027 1441 2025 1440 2024 1439 2022 1438 2020 1439 2019 1441 2021 1442 2023 1444 2025 1447 2025 1450 2025 1452 2024 
1453 2022 1453 2019 1453 2016 1451 2013 1449 2009 1446 2005 1442 2001 1438 1997 1438 1996 1457 1996 1460 2003 1460 2003 1459 2002 1458 2001 1457 2000 
1456 2000 1453 2000 47 _pl _cp 
0 g _f _s _s 
0 g 1155 2454 _m
_sp 1155 2454 1136 2454 1136 2452 1155 2452 4 _pl _cp 1155 2446 _m
_sp 1155 2446 1136 2446 1136 2444 1155 2444 4 _pl _cp 
0 g _f _s _s 
0 g 1155 2321 _m
_sp 1155 2321 1136 2321 1136 2319 1155 2319 4 _pl _cp 1155 2313 _m
_sp 1155 2313 1136 2313 1136 2311 1155 2311 4 _pl _cp 
0 g _f _s _s 
0 g 1155 2188 _m
_sp 1155 2188 1136 2188 1136 2186 1155 2186 4 _pl _cp 1155 2180 _m
_sp 1155 2180 1136 2180 1136 2178 1155 2178 4 _pl _cp 
0 g _f _s _s 
0 g 1155 2055 _m
_sp 1155 2055 1136 2055 1136 2053 1155 2053 4 _pl _cp 1155 2047 _m
_sp 1155 2047 1136 2047 1136 2045 1155 2045 4 _pl _cp 
0 g _f _s _s 
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1412 2437 1413 2432 1413 2428 1414 2422 1415 2417 1416 2411 1418 2405 1420 2399 1419 2399 1417 2403 1416 2406 1415 2411 1413 2415 1412 2419 1411 2423 
1410 2428 1410 2432 1409 2437 1409 2441 1409 2446 1409 2450 1409 2455 1410 2459 1410 2464 1411 2469 1412 2473 1413 2478 1414 2482 1415 2486 1417 2490 
1418 2494 46 _pl _cp 
0 g _f _s _s 
0 g 1424 2446 _m
_sp 1424 2446 1424 2445 1466 2445 1466 2446 4 _pl _cp 
0 g _f _s _s 
0 g 1473 2494 _m
_sp 1473 2494 1473 2494 1474 2488 1475 2483 1476 2477 1477 2472 1478 2467 1478 2463 1478 2459 1479 2455 1479 2451 1479 2448 1479 2446 1479 2443 1479 2440 
1479 2437 1478 2432 1478 2428 1477 2422 1476 2417 1475 2411 1474 2405 1472 2399 1472 2399 1474 2403 1475 2406 1476 2411 1478 2415 1479 2419 1480 2423 
1480 2428 1481 2432 1482 2437 1482 2441 1482 2446 1482 2450 1482 2455 1481 2459 1480 2464 1480 2469 1479 2473 1478 2478 1477 2482 1476 2486 1474 2490 
1473 2494 46 _pl _cp 
0 g _f _s _s 
0 g 1419 2361 _m
_sp 1419 2361 1419 2361 1417 2355 1416 2350 1415 2344 1414 2339 1413 2334 1413 2330 1413 2326 1412 2322 1412 2318 1412 2315 1412 2313 1412 2310 1412 2307 
1412 2304 1413 2299 1413 2295 1414 2289 1415 2284 1416 2278 1418 2272 1420 2266 1419 2266 1417 2270 1416 2273 1415 2278 1413 2282 1412 2286 1411 2290 
1410 2295 1410 2300 1409 2304 1409 2308 1409 2313 1409 2317 1409 2322 1410 2326 1410 2331 1411 2336 1412 2340 1413 2345 1414 2349 1415 2353 1417 2357 
1418 2361 46 _pl _cp 
0 g _f _s _s 
0 g 1424 2313 _m
_sp 1424 2313 1424 2312 1466 2312 1466 2313 4 _pl _cp 
0 g _f _s _s 
0 g 1473 2361 _m
_sp 1473 2361 1473 2361 1474 2355 1475 2350 1476 2344 1477 2339 1478 2334 1478 2330 1478 2326 1479 2322 1479 2318 1479 2315 1479 2313 1479 2310 1479 2307 
1479 2304 1478 2299 1478 2295 1477 2289 1476 2284 1475 2278 1474 2272 1472 2266 1472 2266 1474 2270 1475 2273 1476 2278 1478 2282 1479 2286 1480 2290 
1480 2295 1481 2300 1482 2304 1482 2308 1482 2313 1482 2317 1482 2322 1481 2326 1480 2331 1480 2336 1479 2340 1478 2345 1477 2349 1476 2353 1474 2357 
1473 2361 46 _pl _cp 
0 g _f _s _s 
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(requires)_S 67 _t
(that)_S 67 _t
(entities)_S 67 _t
(announce)_S 67 _t
(their)_S 67 _t
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(intervals)_S 67 _t
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(5)_S 67 _t
(seconds)_S 67 _t
(so)_S 67 _t
(that)_S 67 _t
(other)_S 67 _t
(entities)_S 67 _t
(are)_S 67 _t
(aware)_S 67 _t
(of)_S 67 _t
(their)_S 67 _t
("live")_S 67 _t
(presence)_S 67 _t
(\(IEEE)_S 67 _t
(93\).)_S 67 _t
1500 7667 _m
(In)_S 67 _t
(practice)_S 67 _t
(an)_S 67 _t
(interval)_S 67 _t
(of)_S 67 _t
(one)_S 67 _t
(to)_S 67 _t
(three)_S 67 _t
(seconds)_S 67 _t
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(typically)_S 67 _t
(used)_S 67 _t
(for)_S 67 _t
(entities)_S 67 _t
(such)_S 67 _t
(as)_S 1500 7318 _m
(ground)_S 67 _t
(vehicles)_S 67 _t
(which)_S 67 _t
(usually)_S 67 _t
(move)_S 67 _t
(with)_S 67 _t
(constant)_S 67 _t
(linear)_S 67 _t
(velocity.)_S 134 _t
(Highly)_S 67 _t
(dynamic)_S 1500 6969 _m
(vehicles)_S 67 _t
(such)_S 67 _t
(as)_S 67 _t
(jet)_S 67 _t
(aircraft)_S 67 _t
(may)_S 67 _t
(announce)_S 67 _t
(posture)_S 67 _t
(data)_S 67 _t
(many)_S 67 _t
(times)_S 67 _t
(per)_S 67 _t
(second)_S 67 _t
(in)_S 1500 6620 _m
(order)_S 67 _t
(to)_S 67 _t
(permit)_S 67 _t
(smooth)_S 67 _t
(refresh)_S 67 _t
(rates)_S 67 _t
(of)_S 67 _t
(rapidly)_S 67 _t
(varying)_S 67 _t
(postures)_S 67 _t
(\(Towers)_S 67 _t
(94\).)_S 134 _t
(In)_S 67 _t
(order)_S 1500 6271 _m
(to)_S 67 _t
(reduce)_S 67 _t
(unnecessary)_S 67 _t
(network)_S 67 _t
(traffic,)_S 67 _t
(adaptive)_S 67 _t
(time)_S 67 _t
(steps)_S 67 _t
(between)_S 67 _t
(PDUs)_S 67 _t
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(recommended)_S 67 _t
(which)_S 67 _t
(only)_S 67 _t
(broadcast)_S 67 _t
(new)_S 67 _t
(values)_S 67 _t
(when)_S 67 _t
(predicted)_S 67 _t
(dead-reckoning)_S 67 _t
(error)_S 1500 5573 _m
(exceeds)_S 67 _t
(a)_S 67 _t
(reasonable)_S 67 _t
(threshold)_S 67 _t
(\(or)_S 67 _t
(when)_S 67 _t
(the)_S 67 _t
(5)_S 67 _t
(second)_S 67 _t
(keep-alive)_S 67 _t
(deadline)_S 67 _t
(is)_S 67 _t
(reached\).)_S 67 _t
1500 5224 _m
(Choice)_S 67 _t
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(dead)_S 67 _t
(reckoning)_S 67 _t
(algorithm)_S 67 _t
(and)_S 67 _t
(other)_S 67 _t
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(reduce)_S 67 _t
(network)_S 1500 4875 _m
(loading)_S 67 _t
(\(Lin)_S 67 _t
(94\).)_S 134 _t
(In)_S 67 _t
(general,)_S 67 _t
(minimizing)_S 67 _t
(PDU)_S 67 _t
(traffic)_S 67 _t
(is)_S 67 _t
(important)_S 67 _t
(to)_S 67 _t
(reduce)_S 67 _t
(network)_S 1500 4526 _m
(bandwidth,)_S 67 _t
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(also)_S 67 _t
(to)_S 67 _t
(reduce)_S 67 _t
(the)_S 67 _t
(processing)_S 67 _t
(load)_S 67 _t
(on)_S 67 _t
(each)_S 67 _t
(DIS)_S 67 _t
(receiver.)_S 134 _t
(These)_S 1500 4177 _m
(bandwidth)_S 67 _t
(considerations)_S 67 _t
(grow)_S 67 _t
(in)_S 67 _t
(importance)_S 67 _t
(when)_S 67 _t
(the)_S 67 _t
(number)_S 67 _t
(of)_S 67 _t
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(participating)_S 67 _t
(entities)_S 67 _t
(becomes)_S 67 _t
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(also)_S 67 _t
(when)_S 67 _t
(using)_S 67 _t
(multicast)_S 67 _t
(DIS)_S 67 _t
(which)_S 67 _t
(can)_S 1500 3479 _m
(have)_S 67 _t
(world-wide)_S 67 _t
(Internet)_S 67 _t
(scope)_S 67 _t
(\(Macedonia,)_S 67 _t
(Brutzman)_S 67 _t
(94\).)_S 1980 3130 _m
(Although)_S 67 _t
(linear)_S 67 _t
(and)_S 67 _t
(rotational)_S 67 _t
(velocities)_S 67 _t
(and)_S 67 _t
(accelerations)_S 67 _t
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(an)_S 67 _t
(underwater)_S 1500 2781 _m
(vehicle)_S 67 _t
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(orders)_S 67 _t
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(magnitude)_S 67 _t
(lower)_S 67 _t
(than)_S 67 _t
(jet)_S 67 _t
(aircraft,)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(behavior)_S 67 _t
(is)_S 1500 2432 _m
(highly)_S 67 _t
(dynamic)_S 67 _t
(nevertheless.)_S 134 _t
(Example)_S 67 _t
(missions)_S 67 _t
(demonstrating)_S 67 _t
(highly)_S 67 _t
(complex)_S 1500 2083 _m
(interrelationships)_S 67 _t
(among)_S 67 _t
(vehicle)_S 67 _t
(state)_S 67 _t
(variables)_S 67 _t
(appear)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(experimental)_S 67 _t
(results)_S 4950 1288 _m
(160)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1500 11855 _m
(chapter)_S 67 _t
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(distribution)_S 67 _t
(\(Brutzman)_S 67 _t
(94e\).)_S 134 _t
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(missions,)_S 67 _t
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(posture)_S 67 _t
(updates)_S 67 _t
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(closely)_S 67 _t
(evaluate)_S 67 _t
(vehicle)_S 67 _t
(interaction)_S 67 _t
(with)_S 67 _t
(hazardous)_S 1500 11157 _m
(environments)_S 67 _t
(in)_S 67 _t
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(\(such)_S 67 _t
(as)_S 67 _t
(a)_S 67 _t
(minefield\).)_S 134 _t
(Precise)_S 67 _t
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(information)_S 67 _t
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(also)_S 67 _t
(necessary)_S 67 _t
(to)_S 67 _t
(indicate)_S 67 _t
(interactions)_S 67 _t
(of)_S 67 _t
(propulsor)_S 67 _t
(flow)_S 67 _t
(and)_S 67 _t
(sonar)_S 67 _t
(sensors)_S 67 _t
(with)_S 67 _t
(the)_S 1500 10459 _m
(environment.)_S 134 _t
(Currently)_S 67 _t
(thrust,)_S 67 _t
(control)_S 67 _t
(plane)_S 67 _t
(and)_S 67 _t
(sonar)_S 67 _t
(values)_S 67 _t
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(embedded)_S 67 _t
(as)_S 1500 10110 _m
("articulated)_S 67 _t
(parameters")_S 67 _t
(within)_S 67 _t
(individual)_S 67 _t
(DIS)_S 67 _t
(entity)_S 67 _t
(state)_S 67 _t
(PDUs)_S 67 _t
(for)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV.)_S 67 _t
1500 9761 _m
(Future)_S 67 _t
(versions)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(DIS)_S 67 _t
(standard)_S 67 _t
(are)_S 67 _t
(expected)_S 67 _t
(to)_S 67 _t
(provide)_S 67 _t
(new)_S 67 _t
(PDU)_S 67 _t
(types)_S 1500 9412 _m
(specifically)_S 67 _t
(designed)_S 67 _t
(for)_S 67 _t
(announcing)_S 67 _t
(sonar)_S 67 _t
(transmissions,)_S 67 _t
(but)_S 67 _t
(hydrodynamics)_S 67 _t
(flow)_S 1500 9063 _m
(vectors)_S 67 _t
(\(proportional)_S 67 _t
(to)_S 67 _t
(propulsor)_S 67 _t
(values\))_S 67 _t
(will)_S 67 _t
(continue)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(inferred)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(vehicle)_S 1500 8714 _m
(entity)_S 67 _t
(state)_S 67 _t
(PDU)_S 67 _t
(articulated)_S 67 _t
(parameter)_S 67 _t
(values.)_S 1980 8365 _m
(Entity)_S 67 _t
(state)_S 67 _t
(PDUs)_S 67 _t
(must)_S 67 _t
(contain)_S 67 _t
(posture)_S 67 _t
(values)_S 67 _t
(and)_S 67 _t
(can)_S 67 _t
(optionally)_S 67 _t
(include)_S 67 _t
(linear)_S 1500 8016 _m
(velocity,)_S 67 _t
(angular)_S 67 _t
(velocity,)_S 67 _t
(and)_S 67 _t
(linear)_S 67 _t
(acceleration.)_S 134 _t
(Dead)_S 67 _t
(reckoning)_S 67 _t
(algorithm)_S 67 _t
(velocities)_S 1500 7667 _m
(and)_S 67 _t
(accelerations)_S 67 _t
(may)_S 67 _t
(be)_S 67 _t
(in)_S 67 _t
(world)_S 67 _t
(or)_S 67 _t
(body)_S 67 _t
(coordinates.)_S 134 _t
(Body)_S 67 _t
(accelerations)_S 67 _t
(are)_S 67 _t
(not)_S 1500 7318 _m
(explicitly)_S 67 _t
(defined,)_S 67 _t
(but)_S 67 _t
(\(Towers)_S 67 _t
(94\))_S 67 _t
(presents)_S 67 _t
(two)_S 67 _t
(dead)_S 67 _t
(reckoning)_S 67 _t
(algorithms)_S 67 _t
(pertaining)_S 1500 6969 _m
(to)_S 67 _t
(each)_S 67 _t
(of)_S 67 _t
(two)_S 67 _t
(possible)_S 67 _t
(body)_S 67 _t
(acceleration)_S 67 _t
(definitions.)_S 134 _t
(Of)_S 67 _t
(particular)_S 67 _t
(note)_S 67 _t
(are)_S 1500 6620 _m
(experimental)_S 67 _t
(results)_S 67 _t
(which)_S 67 _t
(show)_S 67 _t
(that)_S 67 _t
(average)_S 67 _t
(processing)_S 67 _t
(time)_S 67 _t
(of)_S 67 _t
(world)_S 67 _t
(coordinate)_S 1500 6271 _m
(frame)_S 67 _t
(PDUs)_S 67 _t
(is)_S 67 _t
(only)_S 67 _t
(80%)_S 67 _t
(relative)_S 67 _t
(to)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(PDUs)_S 67 _t
(\(Towers)_S 67 _t
(94\).)_S 134 _t
(On)_S 1500 5922 _m
(the)_S 67 _t
(other)_S 67 _t
(hand,)_S 67 _t
(a)_S 67 _t
(computational)_S 67 _t
(drawback)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(use)_S 67 _t
(of)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(PDUs)_S 1500 5573 _m
(here)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(fact)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(does)_S 67 _t
(not)_S 67 _t
(directly)_S 1500 5224 _m
(provide)_S 67 _t
(accelerations)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame.)_S 134 _t
(The)_S 67 _t
(current)_S 67 _t
(DIS)_S 67 _t
(implementation)_S 1500 4875 _m
(in)_S 67 _t
(the)_S 67 _t
(underwater)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(utilizes)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(PDUs)_S 67 _t
(because)_S 67 _t
(they)_S 67 _t
(are)_S 1500 4526 _m
(more)_S 67 _t
(efficient)_S 67 _t
(for)_S 67 _t
(receivers)_S 67 _t
(and)_S 67 _t
(less)_S 67 _t
(expensive)_S 67 _t
(to)_S 67 _t
(render.)_S 134 _t
(Future)_S 67 _t
(work)_S 67 _t
(of)_S 67 _t
(interest)_S 1500 4177 _m
(includes)_S 67 _t
(implementing)_S 67 _t
(a)_S 67 _t
(selectable)_S 67 _t
(alternative)_S 67 _t
(encoding)_S 67 _t
(of)_S 67 _t
(entity)_S 67 _t
(state)_S 67 _t
(velocities)_S 67 _t
(and)_S 1500 3828 _m
(accelerations)_S 67 _t
(in)_S 67 _t
(body)_S 67 _t
(frame)_S 67 _t
(coordinates,)_S 67 _t
(and)_S 67 _t
(then)_S 67 _t
(empirically)_S 67 _t
(evaluating)_S 67 _t
(whether)_S 1500 3479 _m
(virtual)_S 67 _t
(world)_S 67 _t
(efficiency)_S 67 _t
(is)_S 67 _t
(degraded)_S 67 _t
(by)_S 67 _t
(shifting)_S 67 _t
(PDUs)_S 67 _t
(to)_S 67 _t
(body)_S 67 _t
(coordinates.)_S 134 _t
(Dead)_S 1500 3130 _m
(reckoning)_S 67 _t
(algorithm)_S 67 _t
(efficiency)_S 67 _t
(and)_S 67 _t
(evaluation)_S 67 _t
(is)_S 67 _t
(further)_S 67 _t
(discussed)_S 67 _t
(in)_S 67 _t
(\(Lin)_S 67 _t
(94\).)_S 4950 1288 _m
(161)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
/Times-BoldR 600 _ff
(G.)_S 1980 11855 _m
(OBJECT-ORIENTED)_S 67 _t
(NETWORKED)_S 67 _t
(RIGID)_S 67 _t
(BODY)_S 67 _t
(DYNAMICS)_S 67 _t
(CLASS)_S 1980 11506 _m
(HIERARCHY)_S /Times-RomanR 600 _ff
1980 11157 _m
(Physically)_S 67 _t
(based)_S 67 _t
(modeling)_S 67 _t
(includes)_S 67 _t
(dynamics)_S 67 _t
(\(modeling)_S 67 _t
(forces)_S 67 _t
(and)_S 1500 10808 _m
(accelerations\))_S 67 _t
(as)_S 67 _t
(well)_S 67 _t
(as)_S 67 _t
(kinematics)_S 67 _t
(\(modeling)_S 67 _t
(velocity)_S 67 _t
(effects)_S 67 _t
(only\).)_S 134 _t
(Dynamics)_S 1500 10459 _m
(considerations)_S 67 _t
(are)_S 67 _t
(a)_S 67 _t
(superset)_S 67 _t
(of)_S 67 _t
(kinematics.)_S 134 _t
(The)_S 67 _t
(implementation)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(underwater)_S 1500 10110 _m
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(was)_S 67 _t
(designed)_S 67 _t
(to)_S 67 _t
(incorporate)_S 67 _t
(the)_S 67 _t
(principles)_S 67 _t
(of)_S 1500 9761 _m
(object-oriented)_S 67 _t
(programming)_S 67 _t
(\(encapsulation,)_S 67 _t
(inheritance)_S 67 _t
(and)_S 67 _t
(polymorphism\))_S 67 _t
(and)_S 1500 9412 _m
(structured)_S 67 _t
(programming)_S 67 _t
(\(top-down)_S 67 _t
(design,)_S 67 _t
(modularity)_S 67 _t
(and)_S 67 _t
(data)_S 67 _t
(abstraction\))_S 67 _t
(as)_S 1500 9063 _m
(appropriate)_S 67 _t
(\(Booch)_S 67 _t
(91\))_S 67 _t
(\(Barr)_S 67 _t
(91\))_S 67 _t
(\(Stroustrup)_S 67 _t
(91\))_S 67 _t
(\(Frakes)_S 67 _t
(91\))_S 67 _t
(\(Barzel)_S 67 _t
(92\))_S 67 _t
(\(Pohl)_S 67 _t
(93\))_S 1500 8714 _m
(\(Bailey)_S 67 _t
(94\).)_S 134 _t
(The)_S 67 _t
(many)_S 67 _t
(good)_S 67 _t
(design)_S 67 _t
(and)_S 67 _t
(software)_S 67 _t
(engineering)_S 67 _t
(principles)_S 67 _t
(found)_S 67 _t
(in)_S 1500 8365 _m
(these)_S 67 _t
(references)_S 67 _t
(were)_S 67 _t
(valuable)_S 67 _t
(in)_S 67 _t
(managing)_S 67 _t
(the)_S 67 _t
(complexity)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 1500 8016 _m
(model,)_S 67 _t
(and)_S 67 _t
(also)_S 67 _t
(in)_S 67 _t
(building)_S 67 _t
(a)_S 67 _t
(general)_S 67 _t
(dynamics)_S 67 _t
(model)_S 67 _t
(that)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(easily)_S 67 _t
(adapted)_S 67 _t
(to)_S 1500 7667 _m
(other)_S 67 _t
(underwater)_S 67 _t
(vehicles)_S 67 _t
(\(or)_S 67 _t
(even)_S 67 _t
(other)_S 67 _t
(vehicle)_S 67 _t
(types\).)_S 134 _t
(Although)_S 67 _t
(no)_S 67 _t
(single)_S 67 _t
(software)_S 1500 7318 _m
(engineering)_S 67 _t
(methodology)_S 67 _t
(was)_S 67 _t
(rigidly)_S 67 _t
(adhered)_S 67 _t
(to,)_S 67 _t
(the)_S 67 _t
(resulting)_S 67 _t
(model)_S 67 _t
(implementation)_S 1500 6968 _m
(\(written)_S 67 _t
(in)_S 67 _t
/Times-BoldItalicR 600 _ff
(C++)_S /Times-RomanR 600 _ff
(\))_S 67 _t
(enjoys)_S 67 _t
(most)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(benefits)_S 67 _t
(which)_S 67 _t
(motivate)_S 67 _t
(these)_S 67 _t
(various)_S 67 _t
(references.)_S 67 _t
1500 6618 _m
(Model)_S 67 _t
(structure)_S 67 _t
(is)_S 67 _t
(briefly)_S 67 _t
(presented)_S 67 _t
(here)_S 67 _t
(and)_S 67 _t
(further)_S 67 _t
(described)_S 67 _t
(in)_S 67 _t
(\(Brutzman)_S 67 _t
(94e\).)_S 1980 6269 _m
(Structuring)_S 67 _t
(the)_S 67 _t
(model)_S 67 _t
(design)_S 67 _t
(problem)_S 67 _t
(was)_S 67 _t
(the)_S 67 _t
(key)_S 67 _t
(to)_S 67 _t
(comprehensible)_S 1500 5920 _m
(implementation.)_S 134 _t
(A)_S 67 _t
(straightforward)_S 67 _t
(hierarchy)_S 67 _t
(follows.)_S 134 _t
(Posture)_S 67 _t
(is)_S 67 _t
(common)_S 67 _t
(to)_S 67 _t
(all)_S 1500 5571 _m
(vehicles)_S 67 _t
(and)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(represented)_S 67 _t
(either)_S 67 _t
(by)_S 67 _t
(Euler)_S 67 _t
(angles,)_S 67 _t
(by)_S 67 _t
(Euler)_S 67 _t
(angles)_S 67 _t
(embedded)_S 67 _t
(in)_S 67 _t
(a)_S 1500 5222 _m
(homogenous)_S 67 _t
(transformation)_S 67 _t
(matrix)_S 67 _t
(\(Fu)_S 67 _t
(87\))_S 67 _t
(\(Foley,)_S 67 _t
(van)_S 67 _t
(Dam)_S 67 _t
(90\),)_S 67 _t
(or)_S 67 _t
(by)_S 1500 4873 _m
(quaternions)_S 67 _t
(\(Cooke)_S 67 _t
(92b\).)_S 134 _t
(A)_S 67 _t
(rigid)_S 67 _t
(body)_S 67 _t
(is)_S 67 _t
(subject)_S 67 _t
(to)_S 67 _t
(kinematics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 1500 4524 _m
(which)_S 67 _t
(combine)_S 67 _t
(velocities)_S 67 _t
(with)_S 67 _t
(postures)_S 67 _t
(in)_S 67 _t
(strictly)_S 67 _t
(defined)_S 67 _t
(ways)_S 67 _t
(regardless)_S 67 _t
(of)_S 67 _t
(vehicle)_S 1500 4175 _m
(type)_S 67 _t
(or)_S 67 _t
(environmental)_S 67 _t
(dimensionality.)_S 134 _t
(A)_S 67 _t
(networked)_S 67 _t
(rigid)_S 67 _t
(body)_S 67 _t
(which)_S 67 _t
(communicates)_S 1500 3826 _m
(with)_S 67 _t
(other)_S 67 _t
(entities)_S 67 _t
(via)_S 67 _t
(DIS)_S 67 _t
(needs)_S 67 _t
(to)_S 67 _t
(calculate)_S 67 _t
(postures,)_S 67 _t
(optional)_S 67 _t
(linear)_S 67 _t
(and)_S 67 _t
(rotational)_S 1500 3477 _m
(velocities,)_S 67 _t
(and)_S 67 _t
(\(again)_S 67 _t
(optional\))_S 67 _t
(linear)_S 67 _t
(accelerations.)_S 134 _t
(Such)_S 67 _t
(a)_S 67 _t
(DIS-networked)_S 67 _t
(rigid)_S 67 _t
(body)_S 1500 3128 _m
(has)_S 67 _t
(identical)_S 67 _t
(capabilities)_S 67 _t
(regardless)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(type.)_S 134 _t
(An)_S 67 _t
(entity)_S 67 _t
(dynamics)_S 67 _t
(component)_S 1500 2779 _m
(for)_S 67 _t
(a)_S 67 _t
(real-time)_S 67 _t
(networked)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(combines)_S 67 _t
(the)_S 67 _t
(functionality)_S 67 _t
(of)_S 67 _t
(rigid)_S 67 _t
(bodies)_S 67 _t
(and)_S 1500 2430 _m
(DIS)_S 67 _t
(networking)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(\(forces)_S 67 _t
(and)_S 67 _t
(accelerations\))_S 1500 2081 _m
(unique)_S 67 _t
(to)_S 67 _t
(a)_S 67 _t
(specific)_S 67 _t
(vehicle)_S 67 _t
(type.)_S 134 _t
(This)_S 67 _t
(structured)_S 67 _t
(hierarchy)_S 67 _t
(of)_S 67 _t
(relationships)_S 67 _t
(between)_S 4950 1288 _m
(162)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(posture)_S 67 _t
(representations,)_S 67 _t
(rigid)_S 67 _t
(bodies,)_S 67 _t
(DIS)_S 67 _t
(networking)_S 67 _t
(and)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 1500 11506 _m
(motion)_S 67 _t
(led)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(general)_S 67 _t
(model)_S 67 _t
(class)_S 67 _t
(diagram)_S 67 _t
(which)_S 67 _t
(appears)_S 67 _t
(in)_S 67 _t
(Figure)_S 67 _t
(6.7.)_S 1980 11157 _m
(The)_S 67 _t
(compartment)_S 67 _t
(boxes)_S 67 _t
(in)_S 67 _t
(Figure)_S 67 _t
(6.7)_S 67 _t
(delineate)_S 67 _t
(the)_S 67 _t
(functionality)_S 67 _t
(of)_S 67 _t
(class)_S 1500 10808 _m
(components.)_S 134 _t
(The)_S 67 _t
(first)_S 67 _t
(compartment)_S 67 _t
(is)_S 67 _t
(class)_S 67 _t
(name.)_S 134 _t
(The)_S 67 _t
(second)_S 67 _t
(compartment)_S 67 _t
(indicates)_S 1500 10459 _m
(member)_S 67 _t
(data)_S 67 _t
(fields,)_S 67 _t
(which)_S 67 _t
(are)_S 67 _t
(the)_S 67 _t
(data)_S 67 _t
(structures)_S 67 _t
(encapsulated)_S 67 _t
(by)_S 67 _t
(the)_S 67 _t
(object.)_S 134 _t
(The)_S 1500 10110 _m
(third)_S 67 _t
(compartment)_S 67 _t
(indicates)_S 67 _t
(object)_S 67 _t
(methods)_S 67 _t
(\(functions\))_S 67 _t
(which)_S 67 _t
(effectively)_S 67 _t
(occur)_S 1500 9761 _m
(instantaneously.)_S 134 _t
(The)_S 67 _t
(fourth)_S 67 _t
(compartment)_S 67 _t
(includes)_S 67 _t
(methods)_S 67 _t
(\(functions\))_S 67 _t
(which)_S 67 _t
(are)_S 1500 9412 _m
(time-consuming,)_S 67 _t
(either)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(perspective)_S 67 _t
(of)_S 67 _t
(simulation)_S 67 _t
(clock)_S 67 _t
(duration)_S 67 _t
(or)_S 67 _t
(actual)_S 1500 9063 _m
(delay)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(network)_S 67 _t
(latency.)_S 134 _t
(Adapted)_S 67 _t
(from)_S 67 _t
(the)_S 67 _t
(Object-Oriented)_S 67 _t
(Simulation)_S 67 _t
(Pictures)_S 1500 8714 _m
(\(OOSPICs\))_S 67 _t
(design)_S 67 _t
(and)_S 67 _t
(testing)_S 67 _t
(methodology)_S 67 _t
(\(Bailey)_S 67 _t
(94\),)_S 67 _t
(this)_S 67 _t
(diagraming)_S 67 _t
(approach)_S 67 _t
(is)_S 1500 8365 _m
(very)_S 67 _t
(useful)_S 67 _t
(because)_S 67 _t
(it)_S 67 _t
(simplifies)_S 67 _t
(presentation)_S 67 _t
(of)_S 67 _t
(key)_S 67 _t
(object)_S 67 _t
(relationships)_S 67 _t
(and)_S 67 _t
(clarifies)_S 1500 8016 _m
(hierarchy)_S 67 _t
(design.)_S 134 _t
(Of)_S 67 _t
(particularly)_S 67 _t
(value)_S 67 _t
(is)_S 67 _t
(the)_S 67 _t
(explicit)_S 67 _t
(specification)_S 67 _t
(of)_S 67 _t
(temporal)_S 1500 7667 _m
(relationships,)_S 67 _t
(which)_S 67 _t
(are)_S 67 _t
(critical)_S 67 _t
(to)_S 67 _t
(success)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(real-time)_S 67 _t
(system)_S 67 _t
(and)_S 67 _t
(are)_S 67 _t
(often)_S 1500 7318 _m
(overlooked)_S 67 _t
(in)_S 67 _t
(complex)_S 67 _t
(system)_S 67 _t
(design.)_S 134 _t
(An)_S 67 _t
(example)_S 67 _t
(object)_S 67 _t
(template)_S 67 _t
(which)_S 67 _t
(adapts)_S 67 _t
(the)_S 1500 6968 _m
(OOSPICs)_S 67 _t
(methodology)_S 67 _t
(from)_S 67 _t
/Times-BoldItalicR 600 _ff
(MODSIM)_S /Times-RomanR 600 _ff
67 _t
(programming)_S 67 _t
(language)_S 67 _t
(to)_S 67 _t
/Times-BoldItalicR 600 _ff
(C++)_S /Times-RomanR 600 _ff
67 _t
(appears)_S 67 _t
(as)_S 1500 6618 _m
(Figure)_S 67 _t
(6.8.)_S 134 _t
(A)_S 67 _t
(key)_S 67 _t
(for)_S 67 _t
(OOSPIC)_S 67 _t
(arrow)_S 67 _t
(conventions)_S 67 _t
(is)_S 67 _t
(included)_S 67 _t
(in)_S 67 _t
(Figure)_S 67 _t
(6.9)_S 1500 6269 _m
(\(Bailey)_S 67 _t
(94\).)_S 134 _t
(Software)_S 67 _t
(source)_S 67 _t
(code)_S 67 _t
(throughout)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(class)_S 67 _t
(library)_S 1500 5920 _m
(implementation)_S 67 _t
(\(Brutzman)_S 67 _t
(94e\))_S 67 _t
(follows)_S 67 _t
(the)_S 67 _t
(structural)_S 67 _t
(layout)_S 67 _t
(presented)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(OOSPIC)_S 1500 5571 _m
(diagram)_S 67 _t
(of)_S 67 _t
(Figure)_S 67 _t
(6.8.)_S 4950 1288 _m
(163)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 375 652 _m
_sp 2174 652 2174 655 375 655 3 _pl _pf _np _s _s 2171 652 _m
_sp 2174 652 2174 2999 2171 2999 3 _pl _pf _np _s _s 375 2996 _m
_sp 2174 2996 2174 2999 375 2999 3 _pl _pf _np _s _s 375 652 _m
_sp 378 652 378 2999 375 2999 3 _pl _pf _np 
_s 0 g 2279 1731 409 686 _cw 
_s 
_s 255 g _s 517 2741 _m
_sp 517 2741 517 2254 1058 2254 1058 2741 4 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 517 1496 _m
_sp 517 1496 517 793 1058 793 1058 1496 4 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 517 2146 _m
_sp 517 2146 517 1605 1058 1605 1058 2146 4 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1383 2471 _m
_sp 1383 2471 1383 2254 1816 2254 1816 2471 4 _pl _pf 
0 g _cp _s _s 
_s 255 g _s 1383 2092 _m
_sp 1383 2092 1383 1821 1816 1821 1816 2092 4 _pl _pf 
0 g _cp _s 517 2687 _m
1058 2687 _l 517 2092 _m
1058 2092 _l 517 1442 _m
1058 1442 _l 1166 1334 _m
1599 1334 _l 1599 1334 _m
1599 793 _l 1599 793 _m
1166 793 _l 1166 793 _m
1166 1334 _l 1653 1334 _m
2086 1334 _l 2086 1334 _m
2086 793 _l 2086 793 _m
1653 793 _l 1653 793 _m
1653 1334 _l 1166 1280 _m
1599 1280 _l 1653 1280 _m
2086 1280 _l _s 
_s 255 g _s 1383 2741 _m
_sp 1383 2741 1383 2525 1816 2525 1816 2741 4 _pl _pf 
0 g _cp _s _s 
0 g 574 2729 _m
_sp 574 2729 574 2728 574 2728 576 2727 578 2726 578 2725 578 2722 578 2707 579 2703 580 2700 583 2698 587 2696 591 2696 594 2696 597 2697 
599 2699 601 2700 602 2702 602 2704 603 2706 603 2709 603 2722 603 2724 603 2725 603 2726 604 2727 605 2728 606 2728 607 2728 607 2729 
596 2729 596 2728 598 2728 600 2727 601 2726 601 2725 601 2722 601 2709 601 2707 601 2705 600 2703 600 2702 598 2701 597 2700 595 2699 
593 2699 590 2700 587 2701 586 2703 585 2706 585 2722 585 2724 586 2725 586 2726 586 2727 587 2728 589 2728 590 2728 590 2729 59 _pl _cp 
0 g _f _s _s 
0 g 608 2729 _m
_sp 608 2729 608 2728 609 2728 611 2727 612 2726 612 2725 612 2722 612 2707 613 2703 614 2700 617 2698 621 2696 625 2696 629 2696 632 2697 
634 2699 636 2700 637 2702 637 2704 637 2706 637 2709 637 2722 637 2724 638 2725 638 2726 638 2727 639 2728 641 2728 641 2728 641 2729 
631 2729 631 2728 632 2728 634 2727 635 2726 636 2725 636 2722 636 2709 636 2707 635 2705 635 2703 634 2702 633 2701 631 2700 629 2699 
627 2699 624 2700 622 2701 621 2703 620 2706 620 2722 620 2724 620 2725 620 2726 621 2727 622 2728 624 2728 625 2728 625 2729 59 _pl _cp 
0 g _f _s _s 
0 g 663 2707 _m
_sp 663 2707 657 2722 656 2724 655 2725 655 2726 655 2726 656 2727 657 2728 660 2728 660 2729 643 2729 643 2728 645 2727 646 2726 647 2725 
648 2722 659 2696 661 2696 671 2722 672 2725 672 2725 673 2726 674 2727 675 2728 676 2728 676 2729 665 2729 665 2728 668 2728 669 2727 
670 2726 670 2725 670 2724 669 2722 34 _pl _cp 
0 g _f _s _s 
0 g 698 2714 _m
_sp 698 2714 700 2715 701 2716 703 2716 704 2717 705 2719 706 2722 706 2723 705 2725 704 2726 703 2727 701 2728 699 2729 697 2729 695 2729 
678 2729 678 2728 679 2728 681 2727 682 2726 683 2725 683 2722 683 2704 683 2702 683 2701 682 2700 682 2699 681 2699 679 2698 678 2698 
678 2697 695 2697 697 2697 699 2697 702 2698 704 2699 705 2701 706 2702 707 2704 707 2706 707 2708 706 2709 705 2711 704 2712 703 2713 
701 2713 700 2714 47 _pl _cp 690 2713 _m
_sp 690 2713 692 2713 694 2713 695 2713 696 2712 697 2711 698 2710 699 2708 699 2705 699 2703 698 2701 696 2699 693 2699 691 2699 690 2702 
15 _pl _cp 690 2715 _m
_sp 690 2715 690 2726 691 2727 693 2728 695 2727 696 2726 697 2724 698 2721 697 2719 696 2716 694 2715 692 2715 12 _pl _cp 
0 g _f _s _s 
0 g 710 2708 _m
_sp 710 2708 710 2704 712 2701 714 2698 717 2696 721 2696 724 2696 727 2698 730 2701 731 2704 732 2708 731 2712 729 2716 725 2718 721 2719 
717 2718 713 2716 711 2712 18 _pl _cp 717 2709 _m
_sp 717 2709 717 2713 718 2716 719 2717 721 2718 723 2717 724 2716 725 2713 725 2708 725 2705 725 2702 724 2700 724 2699 723 2698 721 2698 
720 2698 719 2698 718 2699 718 2700 718 2702 717 2704 717 2707 22 _pl _cp 
0 g _f _s _s 
0 g 749 2716 _m
_sp 749 2716 748 2717 747 2718 745 2719 744 2719 740 2718 737 2716 735 2712 734 2708 735 2703 737 2699 739 2697 743 2696 745 2696 747 2697 
748 2698 749 2700 749 2696 751 2697 754 2697 756 2697 758 2698 758 2699 756 2699 756 2702 756 2729 745 2729 745 2728 747 2728 748 2728 
749 2727 749 2726 749 2724 33 _pl _cp 749 2714 _m
_sp 749 2714 749 2702 747 2700 745 2699 744 2699 743 2700 742 2701 742 2703 741 2705 741 2708 741 2710 742 2712 742 2714 742 2715 744 2716 
746 2717 748 2716 17 _pl _cp 
0 g _f _s _s 
0 g 774 2706 _m
_sp 774 2706 771 2713 770 2715 770 2716 770 2716 771 2717 772 2718 773 2718 773 2719 760 2719 760 2718 760 2717 762 2716 763 2715 764 2713 
771 2697 770 2693 769 2691 768 2689 767 2689 766 2689 766 2690 765 2692 763 2693 761 2692 760 2690 760 2689 761 2687 763 2686 765 2686 
767 2686 769 2688 770 2690 772 2693 779 2713 780 2715 780 2715 781 2716 781 2717 782 2717 783 2718 783 2719 776 2719 776 2718 777 2718 
778 2717 778 2716 778 2715 777 2713 49 _pl _cp 
0 g _f _s _s 
0 g 518 2105 _m
_sp 518 2105 531 2105 535 2105 538 2105 541 2106 543 2107 546 2110 548 2113 549 2117 550 2121 549 2125 548 2128 546 2131 544 2134 542 2135 
539 2136 536 2137 532 2137 518 2137 518 2136 519 2136 521 2135 522 2134 522 2133 522 2130 522 2112 522 2110 522 2109 522 2108 521 2107 
520 2106 519 2106 518 2106 33 _pl _cp 530 2132 _m
_sp 530 2132 530 2135 533 2135 535 2135 537 2134 538 2133 539 2131 540 2129 540 2127 541 2124 541 2121 541 2118 541 2116 541 2114 540 2112 
539 2110 538 2108 537 2107 536 2107 534 2106 532 2106 530 2107 530 2108 23 _pl _cp 
0 g _f _s _s 
0 g 552 2137 _m
_sp 552 2137 552 2136 553 2136 555 2135 556 2134 557 2133 557 2130 557 2112 557 2110 557 2109 557 2108 556 2107 555 2106 553 2106 552 2106 
552 2105 569 2105 569 2106 568 2106 566 2107 565 2108 565 2109 565 2112 565 2130 565 2132 565 2133 565 2134 565 2135 567 2136 568 2136 
569 2136 569 2137 32 _pl _cp 
0 g _f _s _s 
0 g 572 2116 _m
_sp 572 2116 572 2104 574 2104 574 2105 575 2106 576 2106 576 2105 579 2104 580 2104 582 2104 583 2104 588 2105 592 2107 594 2110 595 2114 
595 2116 594 2118 593 2119 592 2121 591 2122 590 2123 589 2123 587 2124 582 2126 580 2128 579 2129 578 2131 578 2132 578 2133 579 2135 
581 2136 583 2136 586 2135 589 2134 591 2131 592 2127 594 2127 594 2138 592 2138 592 2137 591 2136 589 2137 587 2137 585 2138 583 2138 
579 2137 576 2135 574 2132 573 2128 573 2126 574 2125 574 2123 575 2122 576 2121 577 2121 579 2120 580 2119 585 2116 587 2115 588 2114 
589 2112 589 2111 589 2109 588 2107 586 2106 584 2106 581 2106 579 2107 578 2109 576 2110 575 2112 574 2113 574 2115 574 2116 74 _pl _cp 
0 g _f _s _s 
0 g 598 2119 _m
_sp 598 2119 598 2113 611 2113 611 2119 4 _pl _cp 
0 g _f _s _s 
0 g 624 2137 _m
_sp 624 2137 613 2137 613 2136 615 2136 617 2135 618 2134 618 2133 618 2130 618 2112 618 2110 618 2109 618 2108 617 2107 616 2106 615 2106 
613 2106 613 2105 624 2105 624 2106 623 2106 621 2107 620 2108 620 2109 620 2112 620 2130 641 2104 642 2104 642 2130 642 2132 642 2133 
643 2134 643 2135 644 2136 645 2136 646 2136 646 2137 635 2137 635 2136 637 2136 639 2135 640 2134 640 2133 640 2130 640 2117 44 _pl _cp 
0 g _f _s _s 
0 g 655 2116 _m
_sp 655 2116 667 2116 667 2119 667 2121 666 2122 665 2124 664 2125 662 2126 660 2127 658 2127 654 2126 652 2124 650 2120 649 2116 650 2111 
652 2107 655 2105 659 2104 661 2104 664 2106 666 2107 668 2110 667 2111 666 2110 664 2109 663 2108 661 2108 660 2108 658 2109 657 2110 
656 2111 656 2113 32 _pl _cp 655 2118 _m
_sp 655 2118 655 2122 656 2124 657 2126 659 2126 660 2126 661 2125 662 2123 662 2120 662 2118 10 _pl _cp 
0 g _f _s _s 
0 g 669 2126 _m
_sp 669 2126 669 2124 672 2124 672 2110 672 2107 673 2106 675 2105 677 2104 679 2104 681 2106 683 2107 684 2110 683 2110 682 2108 680 2107 
679 2108 678 2110 678 2124 683 2124 683 2126 678 2126 678 2135 677 2135 675 2132 673 2130 672 2128 26 _pl _cp 
0 g _f _s _s 
0 g 699 2113 _m
_sp 699 2113 695 2121 695 2123 694 2124 694 2124 695 2125 696 2125 696 2125 696 2127 685 2127 685 2125 687 2124 689 2121 696 2104 696 2104 
703 2119 708 2104 709 2104 716 2121 716 2123 718 2124 719 2125 719 2127 712 2127 712 2125 713 2125 714 2125 715 2124 715 2123 714 2121 
711 2113 708 2121 708 2123 708 2124 708 2125 709 2125 710 2125 710 2127 699 2127 699 2125 699 2125 700 2125 701 2123 702 2121 44 _pl _cp 
0 g _f _s _s 
0 g 721 2116 _m
_sp 721 2116 722 2111 724 2107 727 2105 731 2104 735 2104 738 2106 740 2109 741 2112 742 2116 741 2120 739 2124 736 2126 731 2127 727 2126 
724 2124 722 2120 17 _pl _cp 727 2117 _m
_sp 727 2117 727 2121 728 2124 730 2125 731 2126 733 2125 734 2124 735 2120 735 2115 735 2112 735 2110 735 2108 734 2107 733 2106 731 2106 
730 2106 729 2106 728 2107 728 2108 728 2110 728 2112 727 2115 22 _pl _cp 
0 g _f _s _s 
0 g 754 2126 _m
_sp 754 2126 745 2126 745 2125 745 2125 746 2125 747 2124 747 2123 747 2121 747 2110 747 2108 747 2108 747 2107 747 2107 746 2106 745 2106 
745 2106 745 2105 757 2105 757 2106 756 2106 755 2106 754 2107 754 2108 754 2110 754 2117 754 2119 755 2121 756 2122 757 2123 758 2123 
759 2122 760 2121 762 2120 764 2121 765 2123 764 2126 761 2127 759 2127 758 2126 756 2124 754 2122 41 _pl _cp 
0 g _f _s _s 
0 g 775 2137 _m
_sp 775 2137 766 2137 766 2136 766 2136 767 2136 768 2134 768 2134 768 2132 768 2110 768 2108 768 2108 768 2107 768 2107 767 2106 766 2106 
766 2106 766 2105 777 2105 777 2106 777 2106 776 2106 775 2107 775 2108 775 2110 775 2114 776 2115 779 2110 781 2108 781 2108 781 2107 
781 2106 780 2106 780 2106 780 2105 791 2105 791 2106 790 2107 788 2108 787 2110 781 2119 782 2121 784 2123 786 2124 789 2125 789 2125 
789 2126 779 2126 779 2125 781 2125 782 2125 783 2124 782 2124 781 2123 780 2121 775 2116 55 _pl _cp 
0 g _f _s _s 
0 g 799 2116 _m
_sp 799 2116 811 2116 811 2119 811 2121 810 2122 809 2124 808 2125 806 2126 804 2127 802 2127 798 2126 796 2124 794 2120 793 2116 794 2111 
796 2107 799 2105 803 2104 805 2104 808 2106 810 2107 812 2110 811 2111 810 2110 808 2109 807 2108 805 2108 804 2108 802 2109 801 2110 
800 2111 800 2113 32 _pl _cp 799 2118 _m
_sp 799 2118 799 2122 800 2124 801 2126 803 2126 804 2126 805 2125 806 2123 806 2120 806 2118 10 _pl _cp 
0 g _f _s _s 
0 g 829 2124 _m
_sp 829 2124 828 2125 826 2126 825 2127 823 2127 819 2126 817 2124 815 2120 814 2115 815 2111 817 2107 819 2105 823 2104 825 2104 826 2105 
828 2106 829 2108 829 2104 831 2105 833 2105 835 2105 838 2106 838 2107 836 2107 836 2110 836 2137 825 2137 825 2136 827 2136 828 2136 
829 2134 829 2134 829 2132 33 _pl _cp 829 2122 _m
_sp 829 2122 829 2110 827 2108 825 2107 824 2107 822 2108 821 2109 821 2111 821 2113 821 2116 821 2118 821 2120 821 2121 822 2123 824 2124 
825 2124 827 2124 17 _pl _cp 
0 g _f _s _s 
0 g 862 2121 _m
_sp 862 2121 865 2122 867 2123 868 2124 868 2125 869 2127 869 2129 869 2131 868 2133 866 2135 863 2136 862 2137 860 2137 858 2137 855 2137 
840 2137 840 2136 842 2136 844 2135 845 2134 845 2133 845 2130 845 2112 845 2110 845 2109 845 2108 844 2107 843 2106 842 2106 840 2106 
840 2105 857 2105 857 2106 856 2106 854 2107 853 2108 853 2109 853 2112 853 2120 854 2120 864 2105 873 2105 873 2106 872 2107 870 2109 
869 2110 868 2112 47 _pl _cp 853 2121 _m
_sp 853 2121 853 2133 853 2135 855 2136 858 2135 860 2134 861 2132 861 2129 861 2127 860 2125 860 2124 859 2123 858 2122 857 2122 855 2121 
15 _pl _cp 
0 g _f _s _s 
0 g 884 2126 _m
_sp 884 2126 875 2126 875 2125 875 2125 877 2125 877 2124 878 2123 878 2121 878 2110 878 2108 878 2108 878 2107 877 2107 876 2106 875 2106 
875 2106 875 2105 887 2105 887 2106 886 2106 885 2106 884 2107 884 2108 884 2110 24 _pl _cp 885 2134 _m
_sp 885 2134 884 2137 881 2138 878 2137 877 2134 878 2132 881 2131 884 2132 8 _pl _cp 
0 g _f _s _s 
0 g 893 2103 _m
_sp 893 2103 890 2101 889 2099 890 2097 891 2095 894 2094 898 2094 901 2094 904 2095 906 2096 908 2097 909 2098 910 2099 911 2101 911 2102 
910 2105 909 2107 906 2108 903 2108 897 2108 896 2108 895 2109 896 2111 897 2112 899 2112 902 2112 904 2112 905 2113 906 2114 907 2115 
908 2116 909 2118 909 2119 908 2122 907 2124 910 2124 910 2126 904 2126 902 2127 900 2127 895 2126 892 2125 890 2123 889 2120 889 2117 
891 2115 892 2114 895 2112 893 2111 891 2109 890 2108 890 2106 891 2105 53 _pl _cp 895 2102 _m
_sp 895 2102 899 2102 903 2102 906 2101 907 2099 906 2098 905 2097 903 2096 900 2096 897 2096 895 2097 893 2098 893 2099 894 2101 14 _pl _cp 899 2113 _m
_sp 899 2113 898 2113 897 2115 896 2117 896 2120 896 2123 897 2125 898 2126 899 2126 900 2126 901 2124 902 2122 902 2119 902 2116 901 2115 
900 2114 16 _pl _cp 
0 g _f _s _s 
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1485 1954 1494 1954 1494 1955 1494 1955 1492 1956 1491 1958 1491 1969 1492 1970 1494 1971 1495 1972 1496 1972 1497 1972 1498 1971 1499 1969 1499 1967 
1499 1958 1498 1956 1496 1955 1496 1955 1496 1954 1505 1954 1505 1955 1505 1955 1503 1956 1502 1958 1502 1967 1502 1970 1501 1972 1499 1973 1497 1973 
1496 1973 1494 1973 1493 1972 1491 1970 1490 1971 1489 1972 1487 1973 1486 1973 1485 1973 1483 1973 1482 1972 1480 1970 72 _pl _cp 
0 g _f _s _s 
0 g 1510 1966 _m
_sp 1510 1966 1523 1966 1522 1969 1521 1971 1518 1972 1515 1973 1512 1972 1509 1970 1508 1967 1507 1963 1508 1959 1509 1956 1512 1955 1515 1954 1518 1954 
1520 1956 1522 1958 1524 1961 1523 1961 1522 1960 1520 1958 1518 1957 1516 1956 1514 1957 1512 1959 1511 1961 1510 1965 1510 1966 28 _pl _cp 1518 1967 _m
_sp 1518 1967 1518 1969 1517 1971 1516 1972 1514 1972 1513 1972 1511 1971 1510 1969 1510 1967 9 _pl _cp 
0 g _f _s _s 
0 g 1525 1972 _m
_sp 1525 1972 1525 1971 1527 1971 1527 1959 1527 1957 1528 1955 1529 1954 1531 1954 1532 1954 1534 1955 1535 1956 1536 1957 1535 1958 1534 1956 1533 1956 
1532 1957 1531 1959 1531 1971 1535 1971 1535 1973 1531 1973 1531 1979 1530 1979 1529 1977 1529 1976 1528 1975 1527 1974 1526 1973 28 _pl _cp 
0 g _f _s _s 
0 g 1543 1974 _m
_sp 1543 1974 1542 1974 1536 1972 1536 1971 1537 1971 1539 1970 1539 1968 1539 1958 1539 1956 1537 1955 1536 1955 1536 1954 1547 1954 1547 1955 1545 1955 
1543 1956 1543 1958 1543 1967 1544 1970 1545 1971 1546 1971 1546 1970 1547 1969 1548 1969 1549 1970 1550 1971 1549 1973 1547 1973 1545 1973 1543 1970 
30 _pl _cp 
0 g _f _s _s 
0 g 1562 1960 _m
_sp 1562 1960 1558 1969 1557 1970 1557 1970 1557 1971 1557 1971 1558 1972 1559 1972 1559 1972 1559 1973 1551 1973 1551 1972 1553 1971 1554 1969 1560 1956 
1558 1952 1558 1950 1557 1949 1556 1949 1556 1949 1555 1949 1554 1949 1554 1950 1553 1950 1552 1949 1551 1948 1552 1946 1554 1945 1555 1945 1557 1946 
1558 1947 1559 1948 1567 1969 1569 1971 1570 1972 1570 1973 1564 1973 1564 1972 1564 1972 1566 1972 1566 1971 1566 1971 1566 1971 1566 1971 1566 1970 
1566 1970 1565 1969 47 _pl _cp 
0 g _f _s _s 
0 g 1586 1954 _m
_sp 1586 1954 1587 1954 1588 1955 1588 1955 1589 1955 1590 1954 1592 1954 1594 1954 1597 1954 1599 1955 1600 1957 1601 1959 1600 1961 1599 1963 1598 1964 
1597 1964 1595 1965 1593 1966 1590 1968 1589 1970 1590 1971 1593 1972 1595 1972 1597 1971 1598 1969 1599 1967 1599 1967 1599 1973 1599 1973 1598 1973 
1598 1973 1597 1973 1597 1973 1595 1973 1594 1973 1593 1973 1590 1973 1588 1972 1587 1970 1586 1968 1586 1967 1587 1965 1589 1964 1591 1963 1594 1961 
1597 1960 1598 1958 1597 1956 1594 1955 1592 1956 1590 1956 1589 1957 1588 1958 1588 1959 1587 1961 1586 1961 56 _pl _cp 
0 g _f _s _s 
0 g 1602 1972 _m
_sp 1602 1972 1602 1971 1604 1971 1604 1959 1604 1957 1605 1955 1607 1954 1608 1954 1609 1954 1611 1955 1612 1956 1613 1957 1613 1958 1612 1956 1610 1956 
1609 1957 1608 1959 1608 1971 1612 1971 1612 1973 1608 1973 1608 1979 1608 1979 1607 1977 1606 1976 1605 1975 1604 1974 1603 1973 28 _pl _cp 
0 g _f _s _s 
0 g 1625 1967 _m
_sp 1625 1967 1623 1966 1621 1965 1619 1964 1617 1963 1616 1962 1615 1960 1615 1958 1616 1955 1619 1954 1620 1954 1622 1954 1623 1955 1625 1957 1626 1955 
1628 1954 1630 1954 1632 1956 1632 1957 1631 1956 1630 1956 1629 1957 1629 1958 1629 1967 1629 1968 1629 1968 1628 1969 1628 1970 1627 1971 1626 1972 
1624 1973 1622 1973 1619 1973 1617 1972 1616 1971 1615 1969 1616 1968 1617 1967 1618 1968 1619 1969 1619 1969 1619 1969 1619 1970 1619 1970 1619 1970 
1620 1971 1622 1972 1624 1971 1625 1968 49 _pl _cp 1625 1965 _m
_sp 1625 1965 1623 1964 1621 1963 1619 1962 1618 1960 1618 1959 1619 1957 1621 1956 1623 1957 1625 1958 10 _pl _cp 
0 g _f _s _s 
0 g 1633 1972 _m
_sp 1633 1972 1633 1971 1635 1971 1635 1959 1635 1957 1636 1955 1637 1954 1639 1954 1640 1954 1642 1955 1643 1956 1644 1957 1643 1958 1642 1956 1641 1956 
1639 1957 1639 1959 1639 1971 1643 1971 1643 1973 1639 1973 1639 1979 1638 1979 1637 1977 1637 1976 1636 1975 1635 1974 1634 1973 28 _pl _cp 
0 g _f _s _s 
0 g 1648 1966 _m
_sp 1648 1966 1661 1966 1660 1969 1659 1971 1657 1972 1654 1973 1650 1972 1648 1970 1646 1967 1645 1963 1646 1959 1647 1956 1650 1955 1653 1954 1656 1954 
1658 1956 1660 1958 1662 1961 1661 1961 1660 1960 1659 1958 1657 1957 1655 1956 1652 1957 1650 1959 1649 1961 1648 1965 1648 1966 28 _pl _cp 1657 1967 _m
_sp 1657 1967 1656 1969 1655 1971 1654 1972 1653 1972 1651 1972 1650 1971 1649 1969 1648 1967 9 _pl _cp 
0 g _f _s _s 
0 g 1688 1959 _m
_sp 1688 1959 1685 1969 1684 1970 1684 1970 1684 1971 1684 1971 1684 1972 1685 1972 1686 1972 1686 1973 1677 1973 1677 1972 1679 1972 1680 1969 1687 1954 
1688 1954 1694 1969 1696 1971 1697 1972 1697 1973 1691 1973 1691 1972 1693 1972 1693 1971 1693 1971 1693 1971 1693 1971 1693 1970 1693 1970 1692 1969 
30 _pl _cp 
0 g _f _s _s 
0 g 1702 1966 _m
_sp 1702 1966 1715 1966 1714 1969 1713 1971 1711 1972 1708 1973 1704 1972 1702 1970 1700 1967 1699 1963 1700 1959 1701 1956 1704 1955 1707 1954 1710 1954 
1712 1956 1714 1958 1716 1961 1715 1961 1714 1960 1713 1958 1711 1957 1709 1956 1706 1957 1704 1959 1703 1961 1702 1965 1702 1966 28 _pl _cp 1711 1967 _m
_sp 1711 1967 1710 1969 1709 1971 1708 1972 1707 1972 1705 1972 1704 1971 1703 1969 1702 1967 9 _pl _cp 
0 g _f _s _s 
0 g 1734 1961 _m
_sp 1734 1961 1733 1959 1731 1958 1730 1957 1728 1957 1725 1958 1723 1959 1722 1962 1721 1965 1722 1968 1723 1970 1725 1971 1727 1972 1728 1972 1729 1970 
1730 1968 1731 1967 1733 1968 1733 1969 1733 1971 1732 1972 1730 1973 1727 1973 1723 1972 1721 1970 1719 1967 1718 1963 1719 1959 1720 1957 1723 1955 
1726 1954 1729 1955 1731 1956 1733 1958 1734 1960 35 _pl _cp 
0 g _f _s _s 
0 g 1736 1972 _m
_sp 1736 1972 1736 1971 1738 1971 1738 1959 1738 1957 1739 1955 1740 1954 1742 1954 1743 1954 1745 1955 1746 1956 1747 1957 1746 1958 1745 1956 1744 1956 
1743 1957 1742 1959 1742 1971 1746 1971 1746 1973 1742 1973 1742 1979 1741 1979 1740 1977 1740 1976 1739 1975 1738 1974 1737 1973 28 _pl _cp 
0 g _f _s _s 
0 g 1748 1963 _m
_sp 1748 1963 1749 1959 1751 1957 1754 1955 1758 1954 1762 1955 1764 1957 1766 1960 1767 1964 1766 1968 1764 1971 1762 1972 1758 1973 1754 1972 1751 1970 
1749 1967 16 _pl _cp 1752 1965 _m
_sp 1752 1965 1753 1961 1754 1958 1756 1956 1758 1955 1760 1956 1762 1957 1763 1959 1763 1962 1763 1966 1762 1969 1760 1971 1757 1972 1755 1971 1753 1970 
1752 1968 1752 1965 1752 1965 18 _pl _cp 
0 g _f _s _s 
0 g 1775 1974 _m
_sp 1775 1974 1775 1974 1768 1972 1768 1971 1769 1971 1771 1970 1771 1968 1771 1958 1771 1956 1769 1955 1768 1955 1768 1954 1779 1954 1779 1955 1778 1955 
1776 1956 1775 1958 1775 1967 1777 1970 1778 1971 1778 1971 1779 1970 1780 1969 1780 1969 1781 1970 1782 1971 1781 1973 1780 1973 1779 1973 1778 1973 
1776 1972 1775 1970 32 _pl _cp 
0 g _f _s _s 
0 g 1423 1922 _m
_sp 1423 1922 1421 1921 1419 1920 1417 1920 1416 1919 1415 1918 1414 1916 1413 1914 1413 1912 1414 1910 1416 1909 1417 1909 1419 1909 1420 1910 1422 1911 
1423 1912 1425 1910 1426 1909 1428 1910 1430 1911 1430 1913 1429 1912 1428 1911 1427 1912 1427 1914 1427 1922 1427 1923 1427 1924 1427 1925 1427 1926 
1426 1927 1425 1928 1423 1929 1421 1929 1418 1929 1416 1928 1415 1926 1414 1924 1415 1923 1416 1922 1417 1923 1418 1924 1418 1924 1418 1924 1418 1926 
1418 1926 1417 1926 1418 1927 1420 1928 1422 1928 1423 1927 1423 1925 1423 1923 53 _pl _cp 1423 1921 _m
_sp 1423 1921 1421 1920 1419 1919 1418 1918 1417 1916 1417 1915 1418 1913 1420 1912 1422 1912 1423 1914 10 _pl _cp 
0 g _f _s _s 
0 g 1438 1939 _m
_sp 1438 1939 1438 1939 1431 1937 1431 1936 1432 1936 1434 1935 1435 1933 1435 1914 1434 1911 1432 1911 1431 1911 1431 1910 1442 1910 1442 1911 1441 1911 
1439 1911 1438 1914 17 _pl _cp 
0 g _f _s _s 
0 g 1443 1928 _m
_sp 1443 1928 1443 1927 1445 1927 1445 1915 1445 1912 1446 1911 1447 1909 1449 1909 1450 1909 1452 1910 1453 1911 1454 1913 1453 1913 1452 1912 1451 1911 
1450 1912 1449 1915 1449 1927 1453 1927 1453 1928 1449 1928 1449 1934 1448 1934 1447 1932 1445 1930 1444 1929 26 _pl _cp 
0 g _f _s _s 
0 g 1458 1921 _m
_sp 1458 1921 1471 1921 1470 1924 1469 1927 1467 1928 1464 1929 1460 1928 1458 1926 1456 1923 1455 1919 1456 1915 1457 1912 1460 1910 1463 1909 1466 1910 
1468 1911 1470 1913 1472 1916 1471 1917 1470 1915 1469 1913 1467 1912 1465 1912 1462 1913 1460 1915 1459 1917 1458 1921 1458 1921 28 _pl _cp 1467 1922 _m
_sp 1467 1922 1467 1924 1466 1926 1464 1927 1463 1927 1462 1927 1460 1926 1459 1924 1458 1922 9 _pl _cp 
0 g _f _s _s 
0 g 1480 1929 _m
_sp 1480 1929 1479 1929 1473 1927 1473 1926 1474 1926 1476 1925 1476 1923 1476 1914 1476 1911 1474 1911 1473 1911 1473 1910 1484 1910 1484 1911 1482 1911 
1480 1911 1480 1914 1480 1923 1481 1925 1482 1926 1483 1926 1483 1925 1484 1925 1485 1925 1486 1925 1487 1927 1486 1928 1484 1929 1482 1928 1480 1926 
30 _pl _cp 
0 g _f _s _s 
0 g 1494 1929 _m
_sp 1494 1929 1493 1929 1487 1927 1487 1926 1488 1926 1490 1925 1490 1923 1490 1914 1490 1911 1488 1911 1487 1911 1487 1910 1497 1910 1497 1911 1496 1911 
1494 1911 1494 1914 1494 1924 1496 1926 1498 1927 1500 1927 1501 1926 1501 1924 1501 1921 1501 1914 1501 1911 1499 1911 1498 1911 1498 1910 1508 1910 
1508 1911 1507 1911 1505 1911 1505 1914 1505 1923 1505 1926 1504 1928 1502 1929 1500 1929 1499 1929 1497 1928 1496 1927 1494 1926 43 _pl _cp 
0 g _f _s _s 
0 g 1520 1922 _m
_sp 1520 1922 1517 1921 1515 1920 1513 1920 1512 1919 1511 1918 1510 1916 1509 1914 1509 1912 1510 1910 1512 1909 1514 1909 1515 1909 1517 1910 1518 1911 
1520 1912 1521 1910 1522 1909 1524 1910 1526 1911 1526 1913 1525 1912 1524 1911 1524 1912 1523 1914 1523 1922 1523 1923 1523 1924 1523 1925 1523 1926 
1522 1927 1521 1928 1519 1929 1517 1929 1514 1929 1512 1928 1511 1926 1510 1924 1511 1923 1512 1922 1513 1923 1514 1924 1514 1924 1514 1924 1514 1926 
1514 1926 1514 1926 1515 1927 1516 1928 1518 1928 1519 1927 1520 1925 1520 1923 53 _pl _cp 1520 1921 _m
_sp 1520 1921 1517 1920 1516 1919 1514 1918 1513 1916 1513 1915 1514 1913 1516 1912 1518 1912 1520 1914 10 _pl _cp 
0 g _f _s _s 
0 g 1527 1928 _m
_sp 1527 1928 1527 1927 1530 1927 1530 1915 1530 1912 1531 1911 1532 1909 1533 1909 1534 1909 1536 1910 1537 1911 1538 1913 1538 1913 1537 1912 1536 1911 
1534 1912 1533 1915 1533 1927 1537 1927 1537 1928 1533 1928 1533 1934 1533 1934 1531 1932 1529 1930 1528 1929 26 _pl _cp 
0 g _f _s _s 
0 g 1543 1921 _m
_sp 1543 1921 1556 1921 1555 1924 1554 1927 1551 1928 1548 1929 1545 1928 1542 1926 1541 1923 1540 1919 1541 1915 1542 1912 1545 1910 1548 1909 1551 1910 
1553 1911 1555 1913 1557 1916 1556 1917 1555 1915 1553 1913 1551 1912 1549 1912 1547 1913 1545 1915 1544 1917 1543 1921 1543 1921 28 _pl _cp 1551 1922 _m
_sp 1551 1922 1551 1924 1550 1926 1549 1927 1547 1927 1546 1927 1544 1926 1543 1924 1543 1922 9 _pl _cp 
0 g _f _s _s 
0 g 1565 1939 _m
_sp 1565 1939 1564 1939 1558 1937 1558 1936 1559 1936 1561 1935 1561 1933 1561 1914 1561 1911 1559 1911 1558 1911 1558 1910 1568 1910 1568 1911 1567 1911 
1566 1911 1565 1914 17 _pl _cp 
0 g _f _s _s 
0 g 1581 1916 _m
_sp 1581 1916 1577 1924 1576 1925 1576 1925 1576 1926 1576 1927 1577 1928 1578 1928 1578 1928 1578 1928 1569 1928 1569 1928 1571 1927 1573 1924 1579 1912 
1577 1907 1577 1905 1576 1905 1575 1904 1575 1904 1574 1904 1573 1905 1573 1905 1572 1905 1571 1904 1570 1903 1571 1901 1573 1900 1574 1900 1576 1901 
1577 1903 1578 1904 1586 1924 1588 1927 1589 1928 1589 1928 1583 1928 1583 1928 1583 1928 1584 1927 1585 1926 1585 1926 1585 1926 1585 1926 1585 1925 
1585 1925 1584 1924 47 _pl _cp 
0 g _f _s _s 
0 g 1611 1928 _m
_sp 1611 1928 1604 1928 1604 1928 1605 1928 1607 1927 1607 1924 1607 1916 1607 1913 1609 1911 1610 1909 1613 1909 1614 1909 1616 1910 1617 1911 1618 1912 
1618 1909 1619 1909 1625 1911 1625 1912 1622 1912 1622 1915 1622 1928 1615 1928 1615 1928 1616 1928 1618 1927 1618 1924 1618 1914 1616 1912 1614 1911 
1613 1911 1612 1912 1611 1914 1611 1916 34 _pl _cp 
0 g _f _s _s 
0 g 1632 1926 _m
_sp 1632 1926 1632 1929 1632 1929 1626 1927 1626 1926 1626 1926 1628 1925 1629 1923 1629 1905 1628 1902 1626 1902 1625 1902 1625 1901 1636 1901 1636 1902 
1635 1902 1633 1902 1632 1905 1632 1911 1634 1910 1636 1909 1640 1910 1642 1912 1644 1916 1645 1920 1644 1924 1643 1926 1641 1928 1638 1929 1637 1929 
1635 1928 1634 1927 32 _pl _cp 1632 1924 _m
_sp 1632 1924 1632 1913 1634 1911 1636 1911 1638 1912 1640 1913 1641 1915 1641 1918 1641 1922 1640 1924 1638 1926 1636 1927 1634 1926 13 _pl _cp 
0 g _f _s _s 
0 g 1665 1939 _m
_sp 1665 1939 1664 1939 1658 1937 1658 1936 1658 1936 1660 1935 1661 1933 1661 1927 1659 1929 1656 1929 1653 1928 1651 1926 1649 1922 1648 1918 1649 1914 
1650 1912 1652 1910 1655 1909 1657 1909 1658 1910 1660 1911 1661 1912 1661 1909 1661 1909 1667 1911 1667 1912 1667 1912 1665 1913 1665 1915 29 _pl _cp 1661 1914 _m
_sp 1661 1914 1661 1922 1661 1924 1660 1926 1659 1927 1657 1927 1655 1926 1653 1925 1652 1923 1651 1920 1652 1916 1653 1914 1655 1912 1657 1911 1659 1912 
15 _pl _cp 
0 g _f _s _s 
0 g 1679 1922 _m
_sp 1679 1922 1677 1921 1675 1920 1673 1920 1671 1919 1670 1918 1669 1916 1669 1914 1669 1912 1670 1910 1672 1909 1673 1909 1674 1909 1676 1910 1677 1911 
1679 1912 1680 1910 1682 1909 1684 1910 1686 1911 1686 1913 1685 1912 1684 1911 1683 1912 1683 1914 1683 1922 1683 1923 1683 1924 1683 1925 1682 1926 
1681 1927 1680 1928 1678 1929 1676 1929 1673 1929 1671 1928 1670 1926 1669 1924 1670 1923 1671 1922 1672 1923 1673 1924 1673 1924 1673 1924 1673 1926 
1673 1926 1673 1926 1674 1927 1676 1928 1677 1928 1678 1927 1679 1925 1679 1923 53 _pl _cp 1679 1921 _m
_sp 1679 1921 1677 1920 1675 1919 1673 1918 1672 1916 1672 1915 1673 1913 1675 1912 1677 1912 1679 1914 10 _pl _cp 
0 g _f _s _s 
0 g 1687 1928 _m
_sp 1687 1928 1687 1927 1689 1927 1689 1915 1689 1912 1690 1911 1691 1909 1693 1909 1694 1909 1696 1910 1697 1911 1698 1913 1697 1913 1696 1912 1695 1911 
1694 1912 1693 1915 1693 1927 1697 1927 1697 1928 1693 1928 1693 1934 1692 1934 1691 1932 1689 1930 1688 1929 26 _pl _cp 
0 g _f _s _s 
0 g 1702 1921 _m
_sp 1702 1921 1715 1921 1714 1924 1713 1927 1711 1928 1708 1929 1704 1928 1702 1926 1700 1923 1699 1919 1700 1915 1701 1912 1704 1910 1707 1909 1710 1910 
1712 1911 1714 1913 1716 1916 1715 1917 1714 1915 1713 1913 1711 1912 1709 1912 1706 1913 1704 1915 1703 1917 1702 1921 1702 1921 28 _pl _cp 1711 1922 _m
_sp 1711 1922 1711 1924 1710 1926 1708 1927 1707 1927 1705 1927 1704 1926 1703 1924 1702 1922 9 _pl _cp 
0 g _f _s _s 
0 g 1735 1939 _m
_sp 1735 1939 1734 1939 1728 1937 1728 1936 1729 1936 1731 1935 1731 1933 1731 1927 1729 1929 1727 1929 1723 1928 1721 1926 1719 1922 1718 1918 1719 1914 
1720 1912 1723 1910 1726 1909 1727 1909 1729 1910 1730 1911 1731 1912 1731 1909 1732 1909 1738 1911 1738 1912 1737 1912 1735 1913 1735 1915 29 _pl _cp 1731 1914 _m
_sp 1731 1914 1731 1922 1731 1924 1730 1926 1729 1927 1727 1927 1725 1926 1723 1925 1722 1923 1722 1920 1722 1916 1724 1914 1725 1912 1728 1911 1730 1912 
15 _pl _cp 
0 g _f _s _s 
0 g 1759 1939 _m
_sp 1759 1939 1758 1939 1752 1937 1752 1936 1753 1936 1755 1935 1755 1933 1755 1912 1756 1911 1758 1910 1760 1909 1762 1909 1766 1910 1769 1912 1771 1916 
1772 1920 1771 1924 1770 1926 1768 1928 1765 1929 1763 1929 1762 1928 1760 1927 1759 1926 24 _pl _cp 1759 1912 _m
_sp 1759 1912 1761 1911 1763 1911 1765 1912 1767 1913 1768 1915 1768 1918 1768 1922 1767 1924 1765 1926 1763 1927 1760 1926 1759 1923 13 _pl _cp 
0 g _f _s _s 
0 g 1785 1916 _m
_sp 1785 1916 1781 1924 1780 1925 1780 1925 1780 1926 1780 1927 1781 1928 1782 1928 1782 1928 1782 1928 1774 1928 1774 1928 1776 1927 1777 1924 1783 1912 
1781 1907 1781 1905 1780 1905 1779 1904 1779 1904 1778 1904 1777 1905 1777 1905 1776 1905 1775 1904 1774 1903 1775 1901 1777 1900 1778 1900 1780 1901 
1781 1903 1782 1904 1790 1924 1792 1927 1793 1928 1793 1928 1787 1928 1787 1928 1787 1928 1789 1927 1789 1926 1789 1926 1789 1926 1789 1926 1789 1925 
1789 1925 1788 1924 47 _pl _cp 
0 g _f _s _s 
0 g 1419 1885 _m
_sp 1419 1885 1418 1885 1412 1882 1412 1881 1413 1881 1415 1881 1415 1878 1415 1869 1415 1866 1413 1866 1412 1866 1412 1865 1423 1865 1423 1866 1421 1866 
1419 1866 1419 1869 1419 1878 1420 1880 1421 1881 1422 1881 1422 1881 1423 1880 1424 1880 1425 1881 1426 1882 1425 1883 1423 1884 1421 1883 1419 1881 
30 _pl _cp 
0 g _f _s _s 
0 g 1427 1874 _m
_sp 1427 1874 1428 1870 1430 1868 1433 1866 1437 1865 1441 1866 1443 1868 1445 1871 1446 1875 1445 1879 1443 1882 1441 1883 1437 1884 1433 1883 1430 1881 
1428 1878 16 _pl _cp 1431 1876 _m
_sp 1431 1876 1432 1872 1433 1869 1435 1867 1437 1866 1439 1867 1441 1868 1442 1870 1442 1873 1442 1877 1441 1880 1439 1882 1436 1883 1434 1882 1432 1881 
1431 1879 1431 1876 1431 1876 18 _pl _cp 
0 g _f _s _s 
0 g 1454 1894 _m
_sp 1454 1894 1453 1894 1447 1892 1447 1891 1448 1891 1450 1891 1450 1888 1450 1867 1451 1866 1453 1866 1455 1865 1457 1865 1461 1866 1464 1868 1466 1871 
1467 1875 1466 1879 1465 1882 1463 1883 1460 1884 1458 1884 1457 1884 1455 1883 1454 1881 24 _pl _cp 1454 1868 _m
_sp 1454 1868 1456 1866 1458 1866 1460 1867 1462 1868 1463 1871 1463 1874 1463 1877 1462 1880 1460 1881 1458 1882 1455 1881 1454 1879 13 _pl _cp 
0 g _f _s _s 
0 g 1469 1874 _m
_sp 1469 1874 1470 1870 1472 1868 1475 1866 1479 1865 1483 1866 1485 1868 1487 1871 1488 1875 1487 1879 1486 1882 1483 1883 1479 1884 1475 1883 1472 1881 
1470 1878 16 _pl _cp 1473 1876 _m
_sp 1473 1876 1474 1872 1475 1869 1477 1867 1479 1866 1481 1867 1483 1868 1484 1870 1484 1873 1484 1877 1483 1880 1481 1882 1478 1883 1476 1882 1474 1881 
1473 1879 1473 1876 1473 1876 18 _pl _cp 
0 g _f _s _s 
0 g 1490 1883 _m
_sp 1490 1883 1490 1882 1492 1882 1492 1870 1492 1868 1493 1866 1494 1865 1496 1865 1497 1865 1499 1865 1500 1866 1501 1868 1500 1868 1499 1867 1498 1867 
1497 1868 1496 1870 1496 1882 1500 1882 1500 1884 1496 1884 1496 1889 1495 1889 1494 1887 1492 1885 1491 1884 26 _pl _cp 
0 g _f _s _s 
0 g 1527 1878 _m
_sp 1527 1878 1524 1876 1522 1875 1520 1875 1519 1874 1518 1873 1517 1871 1516 1869 1516 1867 1517 1866 1519 1865 1521 1865 1522 1865 1524 1865 1525 1866 
1527 1868 1528 1865 1529 1865 1531 1865 1533 1866 1533 1868 1532 1867 1531 1867 1531 1867 1530 1869 1530 1878 1530 1879 1530 1879 1530 1880 1530 1881 
1529 1882 1528 1883 1526 1884 1524 1884 1521 1884 1519 1883 1518 1881 1517 1880 1518 1878 1519 1878 1520 1878 1521 1879 1521 1880 1521 1880 1521 1881 
1521 1881 1521 1881 1522 1882 1523 1883 1525 1883 1526 1882 1527 1880 1527 1878 53 _pl _cp 1527 1876 _m
_sp 1527 1876 1524 1875 1523 1874 1521 1873 1520 1871 1520 1870 1521 1868 1523 1867 1525 1868 1527 1869 10 _pl _cp 
0 g _f _s _s 
0 g 1541 1885 _m
_sp 1541 1885 1540 1885 1534 1882 1534 1881 1534 1881 1536 1881 1537 1878 1537 1869 1537 1866 1534 1866 1534 1866 1534 1865 1544 1865 1544 1866 1543 1866 
1541 1866 1541 1869 1541 1879 1543 1881 1545 1882 1546 1882 1547 1881 1548 1879 1548 1876 1548 1869 1548 1866 1546 1866 1545 1866 1545 1865 1555 1865 
1555 1866 1554 1866 1552 1866 1552 1869 1552 1879 1552 1881 1551 1883 1549 1884 1547 1884 1546 1884 1544 1883 1543 1882 1541 1881 43 _pl _cp 
0 g _f _s _s 
0 g 1573 1894 _m
_sp 1573 1894 1573 1894 1566 1892 1566 1891 1567 1891 1569 1891 1569 1888 1569 1883 1567 1884 1565 1884 1561 1883 1559 1881 1557 1878 1556 1874 1557 1870 
1558 1868 1561 1866 1564 1865 1567 1865 1569 1867 1569 1865 1570 1865 1576 1867 1576 1868 1575 1868 1573 1868 1573 1871 27 _pl _cp 1569 1869 _m
_sp 1569 1869 1569 1877 1569 1880 1568 1882 1567 1883 1565 1883 1563 1882 1561 1881 1560 1878 1560 1875 1560 1872 1562 1869 1563 1868 1566 1867 1568 1867 
15 _pl _cp 
0 g _f _s _s 
0 g 1597 1885 _m
_sp 1597 1885 1597 1885 1590 1882 1590 1881 1591 1881 1593 1881 1593 1878 1593 1869 1593 1866 1591 1866 1590 1866 1590 1865 1600 1865 1600 1866 1600 1866 
1598 1866 1597 1869 1597 1879 1598 1880 1600 1881 1601 1882 1602 1882 1603 1882 1604 1881 1605 1879 1605 1877 1605 1869 1604 1866 1602 1866 1602 1866 
1602 1865 1611 1865 1611 1866 1611 1866 1609 1866 1608 1869 1608 1879 1609 1880 1611 1881 1612 1882 1613 1882 1615 1881 1616 1878 1616 1869 1615 1866 
1614 1866 1613 1866 1613 1865 1623 1865 1623 1866 1622 1866 1620 1866 1620 1869 1620 1878 1620 1881 1619 1883 1617 1884 1614 1884 1613 1884 1611 1883 
1610 1882 1608 1881 1606 1883 1604 1884 1602 1884 1601 1884 1599 1883 1597 1881 68 _pl _cp 
0 g _f _s _s 
0 g 1624 1874 _m
_sp 1624 1874 1625 1870 1627 1868 1629 1866 1633 1865 1637 1866 1640 1868 1642 1871 1643 1875 1642 1879 1640 1882 1638 1883 1634 1884 1630 1883 1627 1881 
1625 1878 16 _pl _cp 1628 1876 _m
_sp 1628 1876 1628 1872 1630 1869 1631 1867 1634 1866 1636 1867 1638 1868 1639 1870 1639 1873 1638 1877 1637 1880 1635 1882 1633 1883 1631 1882 1629 1881 
1628 1879 1628 1876 1628 1876 18 _pl _cp 
0 g _f _s _s 
0 g 1662 1894 _m
_sp 1662 1894 1661 1894 1655 1892 1655 1891 1656 1891 1658 1891 1658 1888 1658 1883 1656 1884 1654 1884 1650 1883 1648 1881 1646 1878 1645 1874 1646 1870 
1647 1868 1650 1866 1653 1865 1656 1865 1658 1867 1658 1865 1659 1865 1665 1867 1665 1868 1664 1868 1662 1868 1662 1871 27 _pl _cp 1658 1869 _m
_sp 1658 1869 1658 1877 1658 1880 1657 1882 1656 1883 1654 1883 1652 1882 1650 1881 1649 1878 1649 1875 1649 1872 1651 1869 1652 1868 1655 1867 1657 1867 
15 _pl _cp 
0 g _f _s _s 
0 g 1669 1877 _m
_sp 1669 1877 1682 1877 1681 1880 1680 1882 1678 1883 1675 1884 1671 1883 1669 1881 1667 1878 1666 1874 1667 1870 1668 1867 1671 1866 1674 1865 1677 1865 
1679 1867 1681 1869 1683 1872 1682 1872 1681 1870 1680 1869 1678 1868 1676 1867 1673 1868 1671 1870 1670 1872 1669 1876 1669 1876 28 _pl _cp 1678 1878 _m
_sp 1678 1878 1678 1880 1677 1882 1675 1883 1674 1883 1672 1883 1671 1882 1670 1880 1669 1878 9 _pl _cp 
0 g _f _s _s 
0 g 1691 1894 _m
_sp 1691 1894 1691 1894 1685 1892 1685 1891 1685 1891 1687 1891 1688 1888 1688 1869 1687 1866 1685 1866 1685 1866 1685 1865 1695 1865 1695 1866 1694 1866 
1692 1866 1691 1869 17 _pl _cp 
0 g _f _s _s 
0 g 1419 2356 _m
_sp 1419 2356 1418 2354 1416 2353 1415 2352 1413 2352 1410 2353 1409 2355 1407 2357 1407 2360 1407 2363 1408 2365 1410 2366 1412 2367 1414 2367 1415 2365 
1416 2363 1417 2362 1418 2363 1419 2364 1418 2366 1417 2368 1415 2369 1413 2369 1409 2368 1406 2366 1404 2363 1403 2359 1404 2355 1406 2352 1408 2350 
1411 2349 1413 2349 1414 2350 1416 2350 1417 2351 1418 2352 1418 2353 1419 2354 1420 2356 39 _pl _cp 
0 g _f _s _s 
0 g 1422 2359 _m
_sp 1422 2359 1423 2355 1425 2352 1427 2350 1431 2349 1435 2350 1438 2352 1440 2356 1441 2360 1440 2364 1438 2366 1435 2368 1431 2369 1427 2368 1425 2366 
1423 2363 16 _pl _cp 1426 2360 _m
_sp 1426 2360 1426 2356 1428 2353 1429 2352 1432 2351 1434 2351 1436 2353 1437 2355 1437 2358 1436 2362 1435 2364 1433 2366 1431 2367 1429 2367 1427 2366 
1426 2364 1426 2361 1426 2360 18 _pl _cp 
0 g _f _s _s 
0 g 1449 2369 _m
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1449 2351 1449 2354 1449 2364 1451 2366 1453 2367 1454 2367 1455 2366 1456 2364 1456 2362 1456 2354 1456 2351 1454 2350 1454 2350 1454 2350 1463 2350 
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609 2457 610 2456 611 2454 611 2454 611 2454 608 2452 608 2450 609 2449 53 _pl _cp 611 2447 _m
_sp 611 2447 610 2446 609 2444 609 2443 611 2442 613 2441 616 2441 619 2441 621 2442 622 2444 623 2445 622 2446 620 2447 614 2447 613 2447 
612 2447 612 2447 17 _pl _cp 611 2461 _m
_sp 611 2461 612 2459 613 2457 614 2456 615 2455 618 2456 619 2459 619 2462 618 2464 616 2465 614 2466 612 2465 611 2462 611 2462 14 _pl _cp 
0 g _f _s _s 
0 g 633 2467 _m
_sp 633 2467 632 2467 626 2465 626 2464 627 2464 629 2463 629 2461 629 2452 629 2449 627 2449 626 2449 626 2448 637 2448 637 2449 635 2449 
633 2449 633 2452 633 2461 634 2463 635 2464 636 2464 636 2463 637 2463 638 2463 639 2463 640 2465 639 2466 637 2467 635 2466 633 2464 
30 _pl _cp 
0 g _f _s _s 
0 g 652 2460 _m
_sp 652 2460 649 2459 647 2458 645 2458 644 2457 643 2456 642 2454 641 2452 641 2450 642 2448 644 2447 646 2447 647 2447 649 2448 650 2449 
652 2450 653 2448 654 2447 656 2448 658 2449 658 2451 657 2450 656 2449 656 2450 655 2452 655 2460 655 2461 655 2462 655 2463 655 2464 
654 2465 653 2466 651 2467 649 2467 646 2467 644 2466 643 2464 642 2462 643 2461 644 2460 645 2461 646 2462 646 2462 646 2462 646 2464 
646 2464 646 2464 647 2465 648 2466 650 2466 651 2465 652 2463 652 2461 53 _pl _cp 652 2459 _m
_sp 652 2459 649 2458 648 2457 646 2456 645 2454 645 2453 646 2451 648 2450 650 2450 652 2452 10 _pl _cp 
0 g _f _s _s 
0 g 659 2466 _m
_sp 659 2466 659 2465 662 2465 662 2453 662 2450 663 2449 664 2447 665 2447 666 2447 668 2448 669 2449 670 2451 670 2451 669 2450 668 2449 
666 2450 665 2453 665 2465 669 2465 669 2466 665 2466 665 2472 665 2472 663 2470 661 2468 660 2467 26 _pl _cp 
0 g _f _s _s 
0 g 675 2459 _m
_sp 675 2459 688 2459 687 2462 686 2465 683 2466 680 2467 677 2466 674 2464 673 2461 672 2457 673 2453 674 2450 677 2448 680 2447 683 2448 
685 2449 687 2451 689 2454 688 2455 687 2453 685 2451 683 2450 681 2450 679 2451 677 2453 676 2455 675 2459 675 2459 28 _pl _cp 683 2460 _m
_sp 683 2460 683 2462 682 2464 681 2465 679 2465 678 2465 676 2464 675 2462 675 2460 9 _pl _cp 
0 g _f _s _s 
0 g 708 2459 _m
_sp 708 2459 721 2459 720 2462 719 2465 716 2466 713 2467 710 2466 707 2464 706 2461 705 2457 706 2453 707 2450 710 2448 713 2447 715 2448 
718 2449 720 2451 722 2454 721 2455 720 2453 718 2451 716 2450 714 2450 712 2451 710 2453 709 2455 708 2459 708 2459 28 _pl _cp 716 2460 _m
_sp 716 2460 716 2462 715 2464 713 2465 712 2465 711 2465 709 2464 708 2462 708 2460 9 _pl _cp 
0 g _f _s _s 
0 g 737 2465 _m
_sp 737 2465 735 2467 733 2467 729 2466 726 2464 724 2460 723 2456 724 2452 725 2450 727 2448 730 2447 732 2447 733 2448 735 2449 736 2450 
736 2443 736 2440 734 2440 733 2440 733 2439 743 2439 743 2440 743 2440 741 2440 740 2443 740 2467 740 2467 27 _pl _cp 736 2452 _m
_sp 736 2452 736 2461 735 2464 733 2465 730 2464 729 2463 727 2460 727 2457 727 2454 729 2452 730 2451 733 2450 735 2450 13 _pl _cp 
0 g _f _s _s 
0 g 750 2466 _m
_sp 750 2466 743 2466 743 2466 744 2466 746 2465 746 2462 746 2454 746 2451 748 2449 749 2447 752 2447 753 2447 755 2448 756 2449 757 2450 
757 2447 758 2447 764 2449 764 2450 761 2450 761 2453 761 2466 754 2466 754 2466 755 2466 757 2465 757 2462 757 2452 755 2450 753 2449 
752 2449 751 2450 750 2452 750 2454 34 _pl _cp 
0 g _f _s _s 
0 g 776 2460 _m
_sp 776 2460 773 2459 771 2458 770 2458 768 2457 767 2456 766 2454 766 2452 766 2450 767 2448 768 2447 770 2447 771 2447 773 2448 774 2449 
776 2450 777 2448 779 2447 781 2448 783 2449 783 2451 782 2450 781 2449 780 2450 780 2452 780 2460 780 2461 780 2462 779 2463 779 2464 
778 2465 777 2466 775 2467 773 2467 770 2467 768 2466 767 2464 766 2462 767 2461 768 2460 769 2461 770 2462 770 2462 770 2462 770 2464 
770 2464 770 2464 771 2465 773 2466 774 2466 775 2465 776 2463 776 2461 53 _pl _cp 776 2459 _m
_sp 776 2459 774 2458 772 2457 770 2456 769 2454 769 2453 770 2451 772 2450 774 2450 776 2452 10 _pl _cp 
0 g _f _s _s 
0 g 784 2466 _m
_sp 784 2466 784 2465 786 2465 786 2453 786 2450 787 2449 788 2447 790 2447 791 2447 793 2448 794 2449 795 2451 794 2451 793 2450 792 2449 
790 2450 790 2453 790 2465 794 2465 794 2466 790 2466 790 2472 789 2472 788 2470 786 2468 785 2467 26 _pl _cp 
0 g _f _s _s 
0 g 803 2467 _m
_sp 803 2467 802 2467 796 2465 796 2464 796 2464 798 2463 799 2461 799 2452 799 2449 796 2449 796 2449 796 2448 806 2448 806 2449 805 2449 
803 2449 803 2452 17 _pl _cp 798 2474 _m
_sp 798 2474 799 2473 801 2472 802 2473 803 2474 802 2476 801 2477 799 2476 8 _pl _cp 
0 g _f _s _s 
0 g 808 2457 _m
_sp 808 2457 809 2453 811 2450 813 2448 817 2447 821 2448 824 2450 826 2454 827 2458 826 2462 824 2464 821 2466 817 2467 813 2466 811 2464 
809 2461 16 _pl _cp 812 2458 _m
_sp 812 2458 812 2454 814 2451 815 2450 818 2449 820 2449 822 2451 823 2453 823 2456 822 2460 821 2463 819 2464 817 2465 815 2465 813 2464 
812 2462 812 2459 812 2459 18 _pl _cp 
0 g _f _s _s 
0 g 834 2467 _m
_sp 834 2467 834 2467 828 2465 828 2464 828 2464 830 2463 831 2461 831 2452 830 2449 828 2449 828 2449 828 2448 837 2448 837 2449 837 2449 
835 2449 834 2452 834 2462 835 2463 837 2464 838 2465 839 2465 840 2465 841 2464 842 2462 842 2459 842 2452 842 2449 840 2449 839 2449 
839 2448 849 2448 849 2449 848 2449 846 2449 846 2452 846 2461 846 2464 845 2466 843 2467 841 2467 839 2467 838 2466 836 2465 834 2464 
45 _pl _cp 
0 g _f _s _s 
0 g 850 2448 _m
_sp 850 2448 851 2448 851 2448 852 2448 853 2448 854 2448 856 2447 857 2447 860 2448 862 2449 863 2451 864 2453 864 2455 862 2456 861 2457 
861 2458 859 2458 857 2459 854 2461 853 2463 854 2465 857 2466 858 2466 860 2465 861 2463 862 2461 863 2461 863 2466 862 2466 862 2466 
861 2466 861 2466 860 2466 859 2467 858 2467 856 2467 854 2467 852 2466 851 2464 850 2462 850 2460 851 2459 853 2457 855 2456 858 2455 
860 2453 861 2451 860 2450 857 2449 855 2449 853 2450 852 2452 851 2454 850 2454 54 _pl _cp 
0 g _f _s _s 
0 g 880 2457 _m
_sp 880 2457 881 2453 883 2450 886 2448 890 2447 894 2448 896 2450 898 2454 899 2458 898 2462 897 2464 894 2466 890 2467 886 2466 883 2464 
881 2461 16 _pl _cp 884 2458 _m
_sp 884 2458 885 2454 886 2451 888 2450 890 2449 892 2449 894 2451 895 2453 895 2456 895 2460 894 2463 892 2464 889 2465 887 2465 885 2464 
884 2462 884 2459 884 2459 18 _pl _cp 
0 g _f _s _s 
0 g 904 2466 _m
_sp 904 2466 901 2466 901 2465 904 2465 904 2452 904 2449 902 2449 901 2449 901 2448 912 2448 912 2449 911 2449 909 2449 908 2452 908 2465 
913 2465 913 2466 908 2466 908 2468 908 2472 909 2474 910 2475 911 2475 912 2474 914 2473 915 2472 916 2473 916 2474 915 2476 912 2477 
909 2476 906 2474 905 2472 904 2468 34 _pl _cp 
0 g _f _s _s 
0 g 936 2467 _m
_sp 936 2467 935 2467 929 2465 929 2464 930 2464 932 2463 932 2461 932 2452 932 2449 930 2449 929 2449 929 2448 938 2448 938 2449 938 2449 
936 2449 936 2452 936 2462 938 2464 940 2465 941 2465 942 2464 943 2462 943 2460 943 2452 943 2449 941 2449 940 2449 940 2448 950 2448 
950 2449 949 2449 947 2449 947 2452 947 2462 949 2464 951 2465 952 2465 953 2464 954 2462 954 2460 954 2452 954 2449 952 2449 952 2449 
952 2448 961 2448 961 2449 960 2449 958 2449 958 2452 958 2461 958 2464 957 2466 955 2467 953 2467 951 2467 949 2466 948 2465 946 2463 
944 2466 942 2467 941 2467 939 2466 938 2465 936 2464 66 _pl _cp 
0 g _f _s _s 
0 g 962 2457 _m
_sp 962 2457 963 2453 965 2450 968 2448 972 2447 976 2448 978 2450 980 2454 981 2458 980 2462 979 2464 976 2466 972 2467 968 2466 965 2464 
963 2461 16 _pl _cp 966 2458 _m
_sp 966 2458 967 2454 968 2451 970 2450 972 2449 974 2449 976 2451 977 2453 977 2456 977 2460 976 2463 974 2464 971 2465 969 2465 967 2464 
966 2462 966 2459 966 2459 18 _pl _cp 
0 g _f _s _s 
0 g 983 2466 _m
_sp 983 2466 983 2465 985 2465 985 2453 985 2450 986 2449 987 2447 989 2447 990 2447 992 2448 993 2449 994 2451 993 2451 992 2450 991 2449 
990 2450 989 2453 989 2465 993 2465 993 2466 989 2466 989 2472 988 2472 987 2470 985 2468 984 2467 26 _pl _cp 
0 g _f _s _s 
0 g 1002 2467 _m
_sp 1002 2467 1001 2467 995 2465 995 2464 996 2464 998 2463 998 2461 998 2452 998 2449 996 2449 995 2449 995 2448 1005 2448 1005 2449 1004 2449 
1002 2449 1002 2452 17 _pl _cp 997 2474 _m
_sp 997 2474 998 2473 1000 2472 1001 2473 1002 2474 1001 2476 1000 2477 998 2476 8 _pl _cp 
0 g _f _s _s 
0 g 1007 2457 _m
_sp 1007 2457 1008 2453 1010 2450 1012 2448 1016 2447 1020 2448 1023 2450 1025 2454 1026 2458 1025 2462 1023 2464 1021 2466 1017 2467 1013 2466 1010 2464 
1008 2461 16 _pl _cp 1011 2458 _m
_sp 1011 2458 1011 2454 1013 2451 1014 2450 1017 2449 1019 2449 1021 2451 1022 2453 1022 2456 1021 2460 1020 2463 1018 2464 1016 2465 1014 2465 1012 2464 
1011 2462 1011 2459 1011 2459 18 _pl _cp 
0 g _f _s _s 
0 g 1034 2467 _m
_sp 1034 2467 1033 2467 1027 2465 1027 2464 1028 2464 1029 2463 1030 2461 1030 2452 1030 2449 1028 2449 1027 2449 1027 2448 1037 2448 1037 2449 1036 2449 
1034 2449 1034 2452 1034 2462 1036 2464 1038 2465 1039 2465 1040 2464 1041 2462 1041 2459 1041 2452 1041 2449 1039 2449 1038 2449 1038 2448 1048 2448 
1048 2449 1047 2449 1045 2449 1045 2452 1045 2461 1045 2464 1044 2466 1042 2467 1040 2467 1039 2467 1037 2466 1036 2465 1034 2464 43 _pl _cp 
0 g _f _s 517 2417 _m
1058 2417 _l _s 
0 g 553 2379 _m
_sp 553 2379 549 2388 549 2389 549 2389 549 2390 549 2390 549 2391 550 2391 550 2391 550 2392 542 2392 542 2391 544 2391 545 2388 552 2373 
553 2373 559 2388 560 2390 562 2391 562 2392 556 2392 556 2391 557 2391 558 2390 558 2390 558 2390 558 2390 558 2389 558 2389 557 2388 
30 _pl _cp 
0 g _f _s _s 
0 g 570 2393 _m
_sp 570 2393 570 2393 564 2391 564 2390 564 2390 566 2389 567 2387 567 2377 566 2375 564 2374 563 2374 563 2373 574 2373 574 2374 573 2374 
571 2375 570 2377 17 _pl _cp 566 2400 _m
_sp 566 2400 567 2398 568 2397 570 2398 571 2400 570 2402 568 2403 567 2402 8 _pl _cp 
0 g _f _s _s 
0 g 581 2393 _m
_sp 581 2393 581 2393 574 2391 574 2390 575 2390 577 2389 578 2387 578 2377 577 2375 575 2374 574 2374 574 2373 585 2373 585 2374 584 2374 
582 2375 581 2377 581 2386 583 2389 584 2390 584 2390 585 2389 586 2388 587 2388 588 2389 588 2390 587 2392 586 2393 585 2393 584 2392 
582 2391 581 2389 32 _pl _cp 
0 g _f _s _s 
0 g 589 2392 _m
_sp 589 2392 589 2390 591 2390 591 2379 591 2376 592 2375 594 2373 595 2373 596 2373 598 2374 599 2375 600 2376 600 2377 598 2375 597 2375 
596 2376 595 2378 595 2390 599 2390 599 2392 595 2392 595 2398 594 2398 593 2396 593 2395 592 2394 591 2393 590 2392 28 _pl _cp 
0 g _f _s _s 
0 g 607 2392 _m
_sp 607 2392 600 2392 600 2391 601 2391 603 2391 603 2388 603 2380 603 2377 605 2375 606 2373 609 2373 610 2373 612 2374 613 2375 614 2376 
614 2373 615 2373 621 2375 621 2375 618 2376 618 2379 618 2392 611 2392 611 2391 612 2391 614 2391 614 2388 614 2377 612 2376 610 2375 
609 2375 608 2376 607 2378 607 2380 34 _pl _cp 
0 g _f _s _s 
0 g 633 2386 _m
_sp 633 2386 630 2385 628 2384 627 2383 625 2382 624 2381 623 2379 622 2377 622 2376 623 2374 625 2373 627 2373 628 2373 630 2373 631 2374 
633 2376 634 2374 636 2373 638 2373 639 2375 639 2376 639 2375 638 2375 637 2376 637 2377 637 2386 637 2387 637 2388 636 2389 636 2389 
635 2391 634 2392 632 2393 630 2393 627 2393 625 2392 624 2390 623 2388 624 2387 625 2386 626 2387 627 2388 627 2388 627 2388 627 2389 
627 2389 627 2390 628 2391 630 2391 632 2390 633 2387 51 _pl _cp 633 2384 _m
_sp 633 2384 631 2383 629 2382 627 2381 626 2380 626 2379 627 2376 629 2375 631 2376 633 2377 10 _pl _cp 
0 g _f _s _s 
0 g 648 2403 _m
_sp 648 2403 647 2403 641 2400 641 2400 642 2400 644 2399 644 2396 644 2377 644 2375 642 2374 641 2374 641 2373 651 2373 651 2374 650 2374 
648 2375 648 2377 17 _pl _cp 
0 g _f _s _s 
0 g 677 2378 _m
_sp 677 2378 673 2388 673 2389 673 2389 673 2390 673 2390 673 2391 674 2391 674 2391 674 2392 666 2392 666 2391 668 2391 669 2388 676 2373 
676 2373 681 2384 686 2373 687 2373 693 2388 694 2391 696 2391 696 2392 690 2392 690 2391 690 2391 691 2391 692 2390 692 2390 692 2390 
692 2390 692 2389 692 2389 691 2388 687 2379 684 2388 683 2389 683 2389 683 2390 683 2390 684 2391 685 2391 685 2391 685 2392 677 2392 
677 2391 679 2391 680 2388 681 2386 49 _pl _cp 
0 g _f _s _s 
0 g 697 2382 _m
_sp 697 2382 698 2378 700 2376 703 2374 707 2373 711 2374 713 2376 715 2379 716 2383 715 2387 714 2390 711 2392 707 2393 703 2392 700 2390 
698 2386 16 _pl _cp 701 2384 _m
_sp 701 2384 702 2380 703 2377 705 2375 707 2374 709 2375 711 2376 712 2379 712 2382 712 2386 711 2388 709 2390 706 2391 704 2390 702 2389 
701 2387 701 2384 701 2384 18 _pl _cp 
0 g _f _s _s 
0 g 724 2393 _m
_sp 724 2393 724 2393 717 2391 717 2390 718 2390 720 2389 720 2387 720 2377 720 2375 718 2374 717 2374 717 2373 728 2373 728 2374 727 2374 
725 2375 724 2377 724 2386 726 2389 727 2390 727 2390 728 2389 729 2388 729 2388 731 2389 731 2390 730 2392 729 2393 728 2393 727 2392 
725 2391 724 2389 32 _pl _cp 
0 g _f _s _s 
0 g 739 2403 _m
_sp 739 2403 738 2403 732 2400 732 2400 733 2400 735 2399 735 2396 735 2377 735 2375 733 2374 732 2374 732 2373 742 2373 742 2374 742 2374 
740 2375 739 2377 17 _pl _cp 
0 g _f _s _s 
0 g 761 2403 _m
_sp 761 2403 761 2403 754 2400 754 2400 755 2400 757 2399 758 2396 758 2391 756 2392 753 2393 749 2392 747 2390 745 2386 744 2382 745 2378 
747 2376 749 2374 752 2373 753 2373 755 2373 756 2374 758 2375 758 2373 758 2373 764 2375 764 2376 764 2376 762 2376 761 2379 29 _pl _cp 758 2377 _m
_sp 758 2377 758 2385 758 2388 757 2390 755 2391 753 2391 751 2390 749 2389 748 2387 748 2384 749 2380 750 2378 752 2376 754 2375 756 2376 
15 _pl _cp 
0 g _f _s _s 
0 g 786 2393 _m
_sp 786 2393 785 2393 779 2391 779 2390 780 2390 782 2389 782 2387 782 2377 782 2375 780 2374 779 2374 779 2373 789 2373 789 2374 788 2374 
786 2375 786 2377 17 _pl _cp 782 2400 _m
_sp 782 2400 783 2398 784 2397 785 2398 786 2400 785 2402 784 2403 783 2402 8 _pl _cp 
0 g _f _s _s 
0 g 797 2393 _m
_sp 797 2393 796 2393 790 2391 790 2390 791 2390 793 2389 793 2387 793 2377 793 2375 791 2374 790 2374 790 2373 800 2373 800 2374 799 2374 
797 2375 797 2377 797 2387 799 2390 801 2391 803 2391 804 2389 804 2387 804 2384 804 2377 804 2375 802 2374 801 2374 801 2373 811 2373 
811 2374 810 2374 808 2375 808 2377 808 2387 808 2389 807 2391 805 2392 803 2393 802 2393 800 2392 799 2391 797 2389 43 _pl _cp 
0 g _f _s _s 
0 g 812 2392 _m
_sp 812 2392 812 2390 814 2390 814 2379 814 2376 815 2375 816 2373 818 2373 819 2373 821 2374 822 2375 823 2376 822 2377 821 2375 820 2375 
818 2376 818 2378 818 2390 822 2390 822 2392 818 2392 818 2398 817 2398 816 2396 816 2395 815 2394 814 2393 813 2392 28 _pl _cp 
0 g _f _s _s 
0 g 827 2385 _m
_sp 827 2385 840 2385 839 2388 838 2391 836 2392 833 2393 829 2392 827 2390 825 2386 824 2382 825 2378 826 2376 829 2374 832 2373 835 2373 
837 2375 839 2377 841 2380 840 2381 839 2379 838 2377 836 2376 834 2375 831 2376 829 2378 828 2380 827 2384 827 2385 28 _pl _cp 836 2386 _m
_sp 836 2386 835 2388 834 2390 833 2391 832 2391 830 2391 829 2390 828 2388 827 2386 9 _pl _cp 
0 g _f _s _s 
0 g 849 2393 _m
_sp 849 2393 848 2393 842 2391 842 2390 842 2390 844 2389 845 2387 845 2377 844 2375 842 2374 842 2374 842 2373 852 2373 852 2374 851 2374 
849 2375 849 2377 849 2386 850 2389 851 2390 852 2390 852 2389 853 2388 854 2388 855 2389 856 2390 855 2392 853 2393 851 2392 849 2389 
30 _pl _cp 
0 g _f _s _s 
0 g 860 2392 _m
_sp 860 2392 856 2392 856 2390 860 2390 860 2377 859 2375 857 2374 856 2374 856 2373 867 2373 867 2374 866 2374 864 2375 863 2377 863 2390 
869 2390 869 2392 863 2392 863 2393 864 2398 864 2400 866 2401 867 2401 868 2399 869 2398 870 2398 871 2399 872 2400 871 2401 867 2402 
864 2401 862 2400 860 2397 860 2393 34 _pl _cp 
0 g _f _s _s 
0 g 881 2386 _m
_sp 881 2386 879 2385 877 2384 875 2383 874 2382 873 2381 871 2379 871 2377 872 2374 875 2373 877 2373 878 2373 880 2374 881 2376 882 2374 
884 2373 886 2373 888 2375 888 2376 887 2375 886 2375 885 2376 885 2377 885 2386 885 2387 885 2388 885 2389 885 2389 884 2391 883 2392 
881 2393 878 2393 876 2393 874 2392 873 2390 872 2388 873 2387 874 2386 875 2387 875 2388 875 2388 875 2388 875 2389 875 2389 875 2390 
876 2391 878 2391 880 2390 881 2387 49 _pl _cp 881 2384 _m
_sp 881 2384 879 2383 876 2381 875 2379 876 2376 877 2375 879 2376 881 2377 8 _pl _cp 
0 g _f _s _s 
0 g 906 2380 _m
_sp 906 2380 905 2378 903 2377 902 2376 900 2376 897 2377 895 2378 894 2381 893 2384 893 2387 895 2389 896 2390 899 2391 900 2391 901 2389 
902 2387 903 2386 905 2387 905 2388 904 2390 903 2392 901 2393 899 2393 895 2392 893 2390 891 2386 890 2382 891 2378 892 2376 895 2374 
898 2373 901 2374 903 2375 904 2376 905 2377 905 2378 906 2380 37 _pl _cp 
0 g _f _s _s 
0 g 912 2385 _m
_sp 912 2385 924 2385 923 2388 922 2391 920 2392 917 2393 913 2392 911 2390 909 2386 908 2382 909 2378 911 2376 913 2374 916 2373 919 2373 
921 2375 923 2377 925 2380 924 2381 923 2379 922 2377 920 2376 918 2375 915 2376 914 2378 912 2380 912 2384 912 2385 28 _pl _cp 920 2386 _m
_sp 920 2386 920 2388 919 2390 917 2391 916 2391 915 2391 913 2390 912 2388 912 2386 9 _pl _cp 
0 g _f _s _s 
0 g 560 2358 _m
_sp 560 2358 559 2358 553 2356 553 2355 554 2355 556 2355 556 2352 556 2346 554 2348 552 2348 548 2347 546 2345 544 2342 543 2338 544 2334 
545 2331 547 2330 550 2329 552 2329 553 2329 555 2330 556 2331 556 2328 557 2328 563 2330 563 2331 562 2331 560 2332 560 2335 29 _pl _cp 556 2333 _m
_sp 556 2333 556 2341 556 2344 555 2346 554 2347 552 2347 550 2346 548 2345 547 2342 547 2339 547 2335 548 2333 550 2331 552 2330 554 2331 
15 _pl _cp 
0 g _f _s _s 
0 g 574 2335 _m
_sp 574 2335 571 2344 570 2345 570 2345 570 2346 570 2346 570 2347 571 2347 572 2347 572 2347 563 2347 563 2347 565 2346 566 2344 573 2331 
571 2326 570 2325 570 2324 569 2323 568 2323 568 2323 567 2324 566 2324 566 2324 565 2323 564 2322 565 2321 567 2320 570 2321 571 2323 
580 2344 581 2346 583 2347 583 2347 577 2347 577 2347 577 2347 578 2347 579 2346 579 2346 579 2346 579 2345 578 2345 578 2344 578 2344 
45 _pl _cp 
0 g _f _s _s 
0 g 591 2349 _m
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591 2330 591 2333 591 2343 593 2345 595 2346 596 2346 597 2345 598 2343 598 2340 598 2333 598 2330 596 2330 595 2330 595 2329 605 2329 
605 2330 604 2330 602 2330 602 2333 602 2342 602 2345 601 2347 599 2348 597 2348 596 2348 594 2347 593 2346 591 2345 43 _pl _cp 
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619 2329 621 2329 623 2330 623 2332 622 2331 621 2330 620 2331 620 2333 620 2341 620 2342 620 2343 620 2344 620 2345 619 2346 618 2347 
616 2348 614 2348 611 2348 609 2347 608 2345 607 2343 608 2342 609 2341 610 2342 611 2343 611 2343 611 2344 611 2345 611 2345 610 2345 
611 2346 613 2347 615 2347 616 2346 616 2344 616 2342 51 _pl _cp 616 2340 _m
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0 g _f _s _s 
0 g 631 2349 _m
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631 2330 631 2333 631 2343 633 2345 635 2346 636 2346 637 2345 638 2343 638 2341 638 2333 638 2330 636 2330 635 2330 635 2329 645 2329 
645 2330 644 2330 642 2330 642 2333 642 2343 644 2345 646 2346 648 2345 649 2342 649 2333 649 2330 647 2330 647 2330 647 2329 656 2329 
656 2330 655 2330 654 2330 653 2333 653 2342 653 2345 652 2347 650 2348 648 2348 646 2348 645 2347 643 2346 641 2345 640 2347 637 2348 
636 2348 634 2347 633 2346 631 2345 64 _pl _cp 
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665 2330 664 2333 17 _pl _cp 660 2355 _m
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682 2343 683 2342 684 2342 685 2344 684 2345 683 2347 681 2348 679 2348 675 2347 672 2345 670 2342 669 2338 670 2334 672 2332 674 2330 
678 2329 680 2329 683 2331 684 2333 686 2335 35 _pl _cp 
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699 2339 697 2339 695 2340 692 2342 691 2344 692 2346 695 2347 696 2347 698 2346 699 2344 700 2342 701 2342 701 2347 700 2347 700 2347 
699 2347 699 2347 698 2347 697 2348 696 2348 694 2348 692 2348 690 2347 689 2345 688 2343 688 2341 689 2340 691 2338 693 2337 696 2336 
698 2335 699 2333 698 2331 695 2330 693 2330 691 2331 690 2333 689 2335 688 2335 54 _pl _cp 
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725 2330 724 2333 724 2342 726 2344 727 2345 727 2345 728 2345 729 2344 729 2344 731 2345 731 2346 730 2347 729 2348 728 2348 727 2347 
725 2346 724 2345 32 _pl _cp 
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746 2331 748 2333 749 2336 749 2336 748 2334 746 2333 744 2331 742 2331 739 2332 738 2334 736 2336 736 2340 736 2340 28 _pl _cp 744 2342 _m
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762 2339 760 2339 758 2340 755 2342 754 2344 755 2346 758 2347 760 2347 761 2346 762 2344 763 2342 764 2342 764 2347 763 2347 763 2347 
762 2347 762 2347 762 2347 760 2348 759 2348 758 2348 755 2348 753 2347 752 2345 751 2343 751 2341 752 2340 754 2338 756 2337 759 2336 
762 2335 762 2333 761 2331 759 2330 757 2330 755 2331 753 2333 752 2335 751 2335 54 _pl _cp 
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776 2321 774 2322 773 2324 773 2330 775 2329 777 2329 781 2330 784 2332 785 2335 786 2339 786 2343 784 2345 782 2347 779 2348 778 2348 
776 2347 775 2346 32 _pl _cp 773 2343 _m
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15 _pl _cp 
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790 2342 16 _pl _cp 793 2340 _m
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793 2343 793 2340 793 2340 18 _pl _cp 
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816 2330 816 2333 816 2343 818 2345 820 2346 821 2346 822 2345 823 2343 823 2340 823 2333 823 2330 821 2330 820 2330 820 2329 830 2329 
830 2330 829 2330 827 2330 827 2333 827 2342 827 2345 826 2347 824 2348 822 2348 821 2348 819 2347 818 2346 816 2345 43 _pl _cp 
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842 2339 840 2339 838 2340 835 2342 834 2344 835 2346 838 2347 839 2347 841 2346 842 2344 843 2342 844 2342 844 2347 843 2347 843 2347 
842 2347 842 2347 841 2347 840 2348 839 2348 838 2348 835 2348 833 2347 832 2345 831 2343 831 2341 832 2340 834 2338 836 2337 839 2336 
841 2335 842 2333 841 2331 838 2330 836 2330 834 2331 833 2333 832 2335 831 2335 54 _pl _cp 
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860 2331 862 2333 864 2336 864 2336 863 2334 861 2333 859 2331 857 2331 854 2332 853 2334 851 2336 851 2340 851 2340 28 _pl _cp 859 2342 _m
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0 g _f _s _s 
0 g 560 2314 _m
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545 2287 547 2285 550 2284 552 2284 553 2284 555 2285 556 2286 556 2284 557 2284 563 2286 563 2287 562 2287 560 2287 560 2290 29 _pl _cp 556 2288 _m
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15 _pl _cp 
0 g _f _s _s 
0 g 567 2296 _m
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577 2286 579 2288 581 2291 580 2291 579 2290 578 2288 576 2287 574 2286 571 2287 569 2289 568 2291 567 2295 567 2296 28 _pl _cp 575 2297 _m
_sp 575 2297 575 2299 574 2301 573 2302 571 2302 570 2302 568 2301 567 2299 567 2297 9 _pl _cp 
0 g _f _s _s 
0 g 593 2297 _m
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596 2284 598 2284 600 2286 600 2287 599 2286 598 2286 597 2287 597 2288 597 2297 597 2298 597 2298 596 2299 596 2300 595 2301 594 2302 
592 2303 590 2303 587 2303 585 2302 584 2300 583 2299 584 2298 585 2297 586 2298 587 2299 587 2299 587 2299 587 2300 587 2300 587 2300 
588 2301 590 2302 592 2301 593 2298 49 _pl _cp 593 2295 _m
_sp 593 2295 591 2294 589 2293 587 2292 586 2290 586 2289 587 2287 589 2286 591 2287 593 2288 10 _pl _cp 
0 g _f _s _s 
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604 2287 606 2285 609 2284 610 2284 612 2284 613 2285 615 2286 615 2284 615 2284 621 2286 621 2287 621 2287 619 2287 618 2290 29 _pl _cp 615 2288 _m
_sp 615 2288 615 2296 615 2299 614 2301 612 2302 610 2302 608 2301 606 2300 605 2297 605 2294 606 2291 607 2289 609 2287 611 2286 613 2287 
15 _pl _cp 
0 g _f _s _s 
0 g 642 2304 _m
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643 2286 642 2288 642 2297 644 2300 645 2301 645 2301 646 2300 647 2299 648 2299 649 2300 649 2301 648 2303 647 2303 646 2303 645 2303 
643 2302 642 2300 32 _pl _cp 
0 g _f _s _s 
0 g 654 2296 _m
_sp 654 2296 667 2296 666 2299 665 2301 662 2302 659 2303 656 2302 653 2300 652 2297 651 2293 652 2289 653 2286 656 2285 659 2284 662 2284 
664 2286 666 2288 668 2291 667 2291 666 2290 664 2288 662 2287 660 2286 658 2287 656 2289 655 2291 654 2295 654 2296 28 _pl _cp 662 2297 _m
_sp 662 2297 662 2299 661 2301 660 2302 658 2302 657 2302 655 2301 654 2299 654 2297 9 _pl _cp 
0 g _f _s _s 
0 g 685 2291 _m
_sp 685 2291 684 2289 682 2288 681 2287 679 2287 677 2288 675 2289 674 2292 673 2295 673 2298 674 2300 676 2301 678 2302 680 2301 681 2300 
682 2298 683 2297 684 2298 685 2299 684 2300 683 2302 681 2303 679 2303 675 2302 672 2300 670 2297 669 2293 670 2289 672 2287 674 2285 
678 2284 681 2285 683 2286 685 2288 686 2290 35 _pl _cp 
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0 g 695 2295 _m
_sp 695 2295 695 2314 694 2314 688 2311 688 2311 689 2311 690 2310 691 2307 691 2288 691 2286 689 2285 688 2285 688 2284 698 2284 698 2285 
697 2285 695 2286 695 2288 695 2295 700 2288 701 2287 701 2286 701 2285 700 2285 700 2284 709 2284 709 2285 709 2285 708 2285 707 2286 
705 2287 704 2288 698 2296 701 2299 703 2300 705 2301 706 2302 707 2302 708 2302 708 2303 700 2303 700 2302 700 2302 700 2302 701 2302 
701 2301 701 2300 699 2299 48 _pl _cp 
0 g _f _s _s 
0 g 709 2293 _m
_sp 709 2293 710 2289 712 2287 715 2285 719 2284 723 2285 725 2287 727 2290 728 2294 727 2298 725 2301 723 2302 719 2303 715 2302 712 2300 
710 2297 16 _pl _cp 713 2295 _m
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713 2298 713 2295 713 2295 18 _pl _cp 
0 g _f _s _s 
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736 2286 736 2288 736 2298 738 2301 740 2301 742 2301 743 2300 744 2298 744 2295 744 2288 743 2286 741 2285 741 2285 741 2284 750 2284 
750 2285 750 2285 748 2286 747 2288 747 2298 747 2300 746 2302 744 2303 742 2303 741 2303 739 2303 738 2302 736 2300 43 _pl _cp 
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0 g 758 2304 _m
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759 2286 758 2288 17 _pl _cp 754 2311 _m
_sp 754 2311 755 2309 756 2308 757 2309 758 2311 757 2312 756 2313 755 2312 8 _pl _cp 
0 g _f _s _s 
0 g 769 2304 _m
_sp 769 2304 768 2304 762 2301 762 2301 763 2301 765 2300 765 2298 765 2288 765 2286 763 2285 762 2285 762 2284 772 2284 772 2285 771 2285 
769 2286 769 2288 769 2298 771 2301 773 2301 775 2301 776 2300 776 2298 776 2295 776 2288 776 2286 774 2285 773 2285 773 2284 783 2284 
783 2285 783 2285 780 2286 780 2288 780 2298 780 2300 779 2302 777 2303 775 2303 774 2303 772 2303 771 2302 769 2300 43 _pl _cp 
0 g _f _s _s 
0 g 788 2284 _m
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802 2286 800 2287 797 2287 793 2287 790 2287 789 2288 790 2289 791 2291 793 2290 794 2290 796 2291 799 2292 800 2294 801 2297 801 2298 
800 2300 803 2300 803 2302 800 2302 799 2302 798 2303 798 2303 797 2303 795 2303 793 2303 790 2303 788 2302 787 2300 786 2297 786 2295 
787 2294 788 2292 790 2291 789 2291 789 2290 787 2288 786 2286 787 2285 53 _pl _cp 790 2284 _m
_sp 790 2284 788 2282 788 2281 788 2280 790 2278 791 2277 794 2277 797 2277 799 2278 800 2280 801 2281 800 2283 799 2283 792 2284 792 2284 
791 2284 790 2284 17 _pl _cp 790 2298 _m
_sp 790 2298 790 2295 791 2294 792 2292 794 2292 796 2293 797 2295 797 2298 796 2300 794 2301 793 2302 791 2301 790 2298 790 2298 14 _pl _cp 
0 g _f _s _s 
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826 2286 825 2288 825 2297 827 2300 828 2301 828 2301 829 2300 830 2299 830 2299 832 2300 832 2301 831 2303 830 2303 829 2303 828 2303 
826 2302 825 2300 32 _pl _cp 
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847 2286 849 2288 851 2291 850 2291 849 2290 847 2288 845 2287 843 2286 841 2287 839 2289 838 2291 837 2295 837 2296 28 _pl _cp 845 2297 _m
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863 2294 861 2295 859 2296 856 2298 855 2299 856 2301 859 2302 861 2302 863 2301 864 2299 864 2297 865 2297 865 2303 864 2303 864 2303 
864 2303 863 2303 863 2303 861 2303 860 2303 859 2303 856 2303 854 2302 853 2300 852 2298 852 2297 853 2295 855 2294 857 2293 860 2291 
863 2290 864 2288 863 2286 860 2285 858 2286 856 2286 855 2287 854 2288 854 2289 853 2291 852 2291 56 _pl _cp 
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877 2276 875 2277 875 2280 875 2285 877 2284 878 2284 882 2285 885 2287 887 2290 888 2294 887 2298 886 2301 883 2302 880 2303 877 2303 
30 _pl _cp 875 2298 _m
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891 2297 16 _pl _cp 894 2295 _m
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894 2298 894 2295 894 2295 18 _pl _cp 
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917 2286 917 2288 917 2298 919 2301 921 2301 922 2301 923 2300 924 2298 924 2295 924 2288 924 2286 922 2285 921 2285 921 2284 931 2284 
931 2285 930 2285 928 2286 928 2288 928 2298 928 2300 927 2302 925 2303 923 2303 922 2303 920 2303 919 2302 917 2300 43 _pl _cp 
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943 2294 941 2295 939 2296 936 2298 935 2299 936 2301 939 2302 940 2302 942 2301 943 2299 944 2297 945 2297 945 2303 944 2303 944 2303 
943 2303 943 2303 942 2303 941 2303 940 2303 939 2303 936 2303 934 2302 933 2300 932 2298 932 2297 933 2295 935 2294 937 2293 940 2291 
942 2290 943 2288 942 2286 939 2285 937 2286 935 2286 934 2288 933 2291 932 2291 54 _pl _cp 
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961 2286 963 2288 965 2291 965 2291 964 2290 962 2288 960 2287 958 2286 955 2287 954 2289 952 2291 952 2295 952 2296 28 _pl _cp 960 2297 _m
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0 g _f _s _s 
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1407 2622 1407 2625 1407 2635 1409 2637 1411 2638 1413 2638 1414 2637 1415 2635 1415 2632 1415 2625 1414 2622 1412 2622 1412 2622 1412 2621 1421 2621 
1421 2622 1421 2622 1418 2622 1418 2625 1418 2633 1418 2636 1417 2638 1415 2640 1413 2640 1412 2640 1410 2639 1409 2638 1407 2637 43 _pl _cp 
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1429 2618 1429 2616 1428 2616 1427 2615 1427 2615 1426 2615 1425 2616 1425 2616 1424 2616 1423 2615 1422 2614 1423 2612 1425 2611 1426 2611 1428 2612 
1429 2614 1430 2615 1438 2635 1440 2638 1441 2639 1441 2639 1435 2639 1435 2639 1436 2639 1437 2638 1437 2637 1437 2637 1437 2637 1437 2637 1437 2637 
1437 2636 1437 2635 47 _pl _cp 
0 g _f _s _s 
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1446 2623 1448 2621 1451 2620 1453 2620 1454 2621 1456 2622 1457 2623 1457 2620 1457 2620 1463 2622 1463 2623 1463 2623 1461 2624 1461 2626 29 _pl _cp 1457 2625 _m
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15 _pl _cp 
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1471 2622 1470 2625 1470 2634 1472 2636 1473 2637 1473 2637 1474 2637 1475 2636 1476 2636 1477 2637 1477 2638 1476 2639 1475 2640 1474 2640 1473 2639 
1471 2638 1470 2637 32 _pl _cp 
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1480 2634 16 _pl _cp 1483 2631 _m
_sp 1483 2631 1483 2627 1485 2625 1486 2623 1489 2622 1491 2622 1493 2624 1494 2626 1494 2629 1493 2633 1492 2636 1490 2638 1488 2639 1486 2638 1484 2637 
1483 2635 1483 2632 1483 2632 18 _pl _cp 
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1691 1244 1692 1245 1694 1246 1695 1248 1693 1241 1692 1238 1690 1237 1689 1237 1689 1236 1700 1236 1700 1237 1699 1237 1698 1238 1697 1239 1697 1239 
1697 1239 1697 1240 1698 1240 1698 1240 1698 1241 1704 1263 1699 1263 37 _pl _cp 1696 1261 _m
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1698 1257 1698 1259 1697 1260 18 _pl _cp 
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1709 1258 1707 1256 1706 1253 18 _pl _cp 1708 1246 _m
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1710 1256 1710 1255 1710 1253 1709 1251 1709 1248 20 _pl _cp 
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1748 1244 1749 1245 1751 1246 1752 1248 1750 1241 1749 1238 1747 1237 1746 1237 1746 1236 1757 1236 1757 1237 1756 1237 1755 1238 1754 1239 1754 1239 
1754 1239 1754 1240 1755 1240 1755 1240 1755 1241 1761 1263 1756 1263 37 _pl _cp 1753 1261 _m
_sp 1753 1261 1752 1261 1751 1260 1749 1258 1748 1255 1747 1253 1747 1251 1746 1250 1746 1249 1747 1248 1748 1247 1750 1248 1752 1249 1753 1252 1754 1254 
1755 1257 1755 1259 1754 1260 18 _pl _cp 
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1768 1246 1768 1246 1768 1247 1772 1261 1771 1261 1770 1261 1768 1260 1765 1260 23 _pl _cp 
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1805 1244 1806 1245 1808 1246 1809 1248 1807 1241 1806 1238 1804 1237 1803 1237 1802 1236 1814 1236 1814 1237 1813 1237 1812 1238 1811 1239 1811 1239 
1811 1239 1811 1240 1811 1240 1811 1240 1812 1241 1817 1263 1813 1263 37 _pl _cp 1810 1261 _m
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1811 1257 1811 1259 1811 1260 18 _pl _cp 
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1826 1261 1825 1261 1823 1260 1822 1259 1820 1257 1821 1257 1823 1258 1824 1259 1826 1258 1827 1256 1827 1255 1826 1254 1825 1252 1823 1250 1823 1250 
1822 1249 1820 1247 32 _pl _cp 
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1861 1244 1862 1245 1864 1246 1865 1248 1863 1241 1862 1238 1860 1237 1859 1237 1859 1236 1870 1236 1870 1237 1869 1237 1868 1238 1868 1239 1868 1239 
1868 1239 1868 1240 1868 1240 1868 1240 1868 1241 1874 1263 1869 1263 37 _pl _cp 1866 1261 _m
_sp 1866 1261 1865 1261 1864 1260 1862 1258 1861 1255 1860 1253 1860 1251 1860 1250 1860 1249 1860 1248 1862 1247 1864 1248 1865 1249 1866 1252 1867 1254 
1868 1257 1868 1259 1867 1260 18 _pl _cp 
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_sp 1878 1253 1880 1253 1881 1252 1882 1251 1882 1249 1881 1246 1880 1245 1879 1245 1878 1246 1877 1247 1876 1247 1875 1247 1875 1246 1876 1245 1878 1244 
1881 1245 1884 1246 1885 1248 1886 1250 1885 1252 1883 1254 1885 1256 1886 1258 1885 1260 1883 1261 1881 1261 1879 1260 1878 1259 1877 1258 1878 1257 
1880 1259 1881 1259 1882 1258 1883 1257 1883 1256 1882 1255 1881 1254 1879 1254 38 _pl _cp 
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1722 1194 1724 1192 1725 1193 1723 1195 1721 1197 1720 1199 1719 1201 1718 1203 1718 1205 1718 1208 1718 1210 1718 1212 1718 1215 1718 1217 1719 1219 
1720 1221 1721 1223 1723 1225 1725 1227 34 _pl _cp 
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1740 1201 1742 1203 1744 1206 1743 1207 1742 1205 1741 1203 1739 1202 1737 1201 1734 1202 1732 1204 1731 1207 1730 1211 1730 1211 28 _pl _cp 1738 1212 _m
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1759 1199 1759 1199 1765 1201 1765 1202 1763 1202 1762 1205 1762 1218 1755 1218 1755 1218 1756 1218 1758 1217 1759 1214 1759 1204 1758 1203 1757 1202 
1755 1201 1754 1201 1753 1201 1752 1202 1751 1204 1751 1206 36 _pl _cp 
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1774 1201 1773 1204 17 _pl _cp 
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1791 1201 1793 1203 1795 1206 1794 1207 1793 1205 1792 1203 1790 1202 1788 1201 1785 1202 1783 1204 1782 1207 1781 1211 1781 1211 28 _pl _cp 1790 1212 _m
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1803 1201 1803 1204 1803 1213 1804 1215 1805 1216 1806 1216 1806 1215 1807 1215 1808 1214 1809 1215 1810 1216 1809 1218 1807 1219 1805 1218 1803 1216 
30 _pl _cp 
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_sp 1831 1216 1831 1219 1831 1219 1824 1217 1824 1216 1825 1216 1827 1215 1827 1213 1827 1195 1827 1192 1825 1192 1824 1192 1824 1191 1835 1191 1835 1192 
1834 1192 1831 1192 1831 1195 1831 1201 1833 1199 1835 1199 1839 1200 1841 1202 1843 1206 1844 1210 1843 1214 1842 1216 1840 1218 1837 1219 1836 1219 
1834 1218 1833 1217 32 _pl _cp 1831 1214 _m
_sp 1831 1214 1831 1203 1833 1201 1835 1201 1837 1202 1839 1203 1840 1205 1840 1208 1840 1211 1839 1214 1837 1215 1835 1216 1833 1216 13 _pl _cp 
0 g _f _s _s 
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_sp 1857 1212 1854 1211 1852 1210 1850 1209 1849 1208 1848 1207 1847 1205 1846 1203 1846 1202 1847 1200 1849 1199 1851 1199 1852 1199 1854 1200 1855 1201 
1857 1202 1858 1200 1860 1199 1862 1200 1863 1201 1863 1202 1862 1201 1862 1201 1861 1202 1860 1203 1860 1212 1860 1213 1860 1214 1860 1215 1860 1216 
1859 1217 1858 1218 1856 1219 1854 1219 1851 1219 1849 1218 1848 1216 1847 1214 1848 1213 1849 1212 1850 1213 1851 1214 1851 1214 1851 1214 1851 1216 
1851 1216 1851 1216 1852 1217 1854 1218 1855 1218 1856 1217 1857 1215 1857 1213 53 _pl _cp 1857 1211 _m
_sp 1857 1211 1855 1210 1853 1209 1851 1208 1850 1206 1850 1205 1851 1202 1853 1201 1855 1202 1857 1203 10 _pl _cp 
0 g _f _s _s 
0 g 1871 1219 _m
_sp 1871 1219 1870 1219 1864 1217 1864 1216 1865 1216 1867 1215 1867 1213 1867 1204 1867 1201 1865 1200 1864 1200 1864 1200 1875 1200 1875 1200 1873 1200 
1871 1201 1871 1204 1871 1213 1872 1215 1873 1216 1874 1216 1874 1215 1875 1215 1876 1214 1877 1215 1878 1216 1877 1218 1875 1219 1873 1218 1871 1216 
30 _pl _cp 
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1890 1202 1891 1200 1892 1199 1894 1200 1896 1201 1896 1202 1895 1201 1894 1201 1894 1202 1893 1203 1893 1212 1893 1213 1893 1214 1893 1215 1893 1216 
1892 1217 1891 1218 1889 1219 1887 1219 1884 1219 1882 1218 1881 1216 1880 1214 1881 1213 1882 1212 1883 1213 1884 1214 1884 1214 1884 1214 1884 1216 
1884 1216 1884 1216 1885 1217 1886 1218 1888 1218 1889 1217 1890 1215 1890 1213 53 _pl _cp 1890 1211 _m
_sp 1890 1211 1887 1210 1886 1209 1884 1208 1883 1206 1883 1205 1884 1202 1886 1201 1888 1202 1890 1203 10 _pl _cp 
0 g _f _s _s 
0 g 1904 1219 _m
_sp 1904 1219 1903 1219 1897 1217 1897 1216 1898 1216 1900 1215 1900 1213 1900 1204 1900 1201 1898 1200 1897 1200 1897 1200 1907 1200 1907 1200 1906 1200 
1904 1201 1904 1204 1904 1214 1906 1216 1908 1217 1909 1217 1910 1216 1911 1214 1911 1212 1911 1204 1911 1201 1909 1200 1909 1200 1909 1200 1918 1200 
1918 1200 1918 1200 1916 1201 1915 1204 1915 1214 1917 1216 1919 1217 1920 1217 1922 1216 1923 1214 1923 1212 1923 1204 1922 1201 1920 1200 1920 1200 
1920 1200 1929 1200 1929 1200 1929 1200 1927 1201 1926 1204 1926 1212 1926 1215 1925 1217 1923 1219 1921 1219 1920 1219 1918 1218 1917 1217 1915 1215 
1914 1217 1913 1218 1911 1219 1910 1219 1909 1219 1907 1218 1906 1217 1904 1216 68 _pl _cp 
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_sp 1934 1211 1947 1211 1946 1214 1945 1217 1942 1218 1939 1219 1936 1218 1933 1216 1932 1213 1931 1209 1932 1205 1933 1202 1936 1200 1939 1199 1942 1199 
1944 1201 1946 1203 1948 1206 1947 1207 1946 1205 1944 1203 1942 1202 1940 1201 1938 1202 1936 1204 1935 1207 1934 1211 1934 1211 28 _pl _cp 1942 1212 _m
_sp 1942 1212 1942 1214 1941 1216 1940 1217 1938 1217 1937 1217 1935 1216 1934 1214 1934 1212 9 _pl _cp 
0 g _f _s _s 
0 g 1949 1218 _m
_sp 1949 1218 1949 1217 1951 1217 1951 1205 1951 1202 1952 1201 1953 1199 1955 1199 1956 1199 1958 1200 1959 1201 1960 1202 1959 1203 1958 1202 1957 1201 
1956 1202 1955 1205 1955 1217 1959 1217 1959 1218 1955 1218 1955 1224 1954 1224 1953 1222 1951 1220 1950 1219 26 _pl _cp 
0 g _f _s _s 
0 g 1964 1211 _m
_sp 1964 1211 1977 1211 1976 1214 1975 1217 1973 1218 1970 1219 1966 1218 1964 1216 1962 1213 1961 1209 1962 1205 1963 1202 1966 1200 1969 1199 1972 1199 
1974 1201 1976 1203 1978 1206 1977 1207 1976 1205 1975 1203 1973 1202 1971 1201 1968 1202 1966 1204 1965 1207 1964 1211 1964 1211 28 _pl _cp 1973 1212 _m
_sp 1973 1212 1973 1214 1972 1216 1970 1217 1969 1217 1967 1217 1966 1216 1965 1214 1964 1212 9 _pl _cp 
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_sp 1986 1219 1985 1219 1979 1217 1979 1216 1980 1216 1982 1215 1982 1213 1982 1204 1982 1201 1980 1200 1979 1200 1979 1200 1989 1200 1989 1200 1988 1200 
1986 1201 1986 1204 1986 1213 1987 1215 1988 1216 1989 1216 1989 1215 1990 1215 1991 1214 1992 1215 1993 1216 1992 1218 1990 1219 1988 1218 1986 1216 
30 _pl _cp 
0 g _f _s _s 
0 g 1994 1200 _m
_sp 1994 1200 1995 1200 1995 1200 1996 1200 1997 1200 1998 1200 2000 1199 2001 1199 2004 1199 2006 1201 2007 1202 2008 1205 2008 1207 2006 1208 2005 1209 
2005 1209 2003 1210 2001 1211 1998 1213 1997 1215 1998 1217 2001 1218 2002 1218 2004 1217 2005 1215 2006 1212 2007 1212 2007 1218 2006 1218 2006 1218 
2005 1218 2005 1218 2004 1218 2003 1219 2002 1219 2000 1219 1998 1219 1996 1218 1995 1216 1994 1214 1994 1212 1995 1211 1997 1209 1999 1208 2002 1207 
2004 1205 2005 1203 2004 1201 2001 1200 1999 1201 1997 1202 1996 1204 1995 1206 1994 1206 54 _pl _cp 
0 g _f _s _s 
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_sp 2011 1192 2013 1194 2014 1195 2016 1197 2017 1198 2019 1200 2020 1203 2021 1206 2021 1210 2021 1213 2020 1216 2019 1219 2017 1222 2016 1224 2014 1225 
2013 1227 2011 1228 2010 1227 2012 1225 2014 1223 2015 1221 2016 1219 2017 1217 2017 1215 2017 1212 2017 1210 2017 1208 2017 1205 2017 1203 2016 1201 
2015 1199 2014 1197 2012 1195 2010 1193 34 _pl _cp 
0 g _f _s 1653 1172 _m
2086 1172 _l _s 
0 g 1692 1150 _m
_sp 1692 1150 1691 1150 1685 1147 1685 1146 1686 1146 1688 1146 1688 1143 1688 1134 1688 1131 1686 1131 1685 1131 1685 1130 1696 1130 1696 1131 1695 1131 
1692 1131 1692 1134 1692 1143 1693 1145 1694 1146 1695 1146 1695 1146 1696 1145 1697 1145 1698 1146 1699 1147 1698 1148 1696 1149 1694 1148 1692 1146 
30 _pl _cp 
0 g _f _s _s 
0 g 1700 1139 _m
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1701 1143 16 _pl _cp 1704 1141 _m
_sp 1704 1141 1705 1137 1706 1134 1708 1132 1710 1131 1712 1132 1714 1133 1715 1135 1715 1138 1715 1142 1714 1145 1712 1147 1709 1148 1707 1147 1705 1146 
1704 1144 1704 1141 1704 1141 18 _pl _cp 
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_sp 1721 1148 1721 1147 1723 1147 1723 1135 1723 1133 1724 1131 1725 1130 1727 1130 1728 1130 1730 1130 1731 1131 1732 1133 1731 1133 1730 1132 1729 1132 
1728 1133 1727 1135 1727 1147 1731 1147 1731 1149 1727 1149 1727 1154 1726 1154 1725 1152 1723 1150 1722 1149 26 _pl _cp 
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1746 1130 1748 1130 1750 1131 1750 1133 1749 1132 1748 1132 1748 1132 1747 1134 1747 1143 1747 1144 1747 1144 1747 1145 1747 1146 1746 1147 1745 1148 
1743 1149 1741 1149 1738 1149 1736 1148 1735 1146 1734 1145 1735 1143 1736 1143 1737 1143 1738 1144 1738 1145 1738 1145 1738 1146 1738 1146 1737 1146 
1738 1147 1740 1148 1742 1148 1743 1147 1743 1145 1743 1143 51 _pl _cp 1743 1141 _m
_sp 1743 1141 1741 1140 1740 1139 1738 1138 1737 1136 1737 1135 1738 1133 1740 1132 1742 1133 1743 1134 10 _pl _cp 
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1758 1133 1757 1135 1757 1147 1761 1147 1761 1149 1757 1149 1757 1154 1757 1154 1755 1152 1753 1150 1752 1149 26 _pl _cp 
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1777 1132 1779 1134 1781 1137 1780 1137 1779 1135 1777 1134 1775 1133 1773 1132 1771 1133 1769 1135 1768 1137 1767 1141 1767 1141 28 _pl _cp 1775 1143 _m
_sp 1775 1143 1775 1145 1774 1147 1773 1148 1771 1148 1770 1148 1768 1147 1767 1145 1767 1143 9 _pl _cp 
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0 g 1726 1114 _m
_sp 1726 1114 1724 1113 1722 1111 1720 1110 1719 1108 1718 1105 1717 1102 1716 1099 1716 1096 1716 1092 1717 1089 1718 1086 1719 1084 1720 1083 1722 1081 
1724 1080 1726 1078 1726 1079 1725 1081 1723 1083 1722 1085 1720 1087 1720 1089 1720 1091 1719 1094 1719 1096 1719 1098 1720 1101 1720 1103 1720 1105 
1722 1107 1723 1109 1725 1111 1726 1113 34 _pl _cp 
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_sp 1728 1086 1729 1086 1730 1086 1730 1086 1731 1086 1732 1086 1734 1085 1736 1085 1739 1085 1741 1087 1742 1088 1743 1091 1742 1093 1741 1094 1740 1095 
1739 1095 1737 1096 1735 1097 1732 1099 1731 1101 1732 1103 1735 1104 1737 1104 1739 1103 1740 1101 1741 1098 1741 1098 1741 1104 1741 1104 1740 1104 
1740 1104 1739 1104 1739 1104 1737 1105 1736 1105 1735 1105 1732 1105 1730 1104 1729 1102 1728 1100 1728 1098 1729 1097 1731 1095 1733 1094 1736 1093 
1739 1091 1740 1089 1739 1087 1736 1086 1734 1087 1732 1088 1730 1090 1729 1092 1728 1092 54 _pl _cp 
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1751 1088 1750 1091 1750 1103 1754 1103 1754 1104 1750 1104 1750 1110 1750 1110 1748 1107 1746 1106 1745 1105 26 _pl _cp 
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1770 1087 1772 1089 1774 1092 1773 1093 1772 1091 1770 1089 1768 1088 1766 1087 1764 1088 1762 1090 1761 1093 1760 1097 1760 1097 28 _pl _cp 1768 1098 _m
_sp 1768 1098 1768 1100 1767 1102 1765 1103 1764 1103 1763 1103 1761 1102 1760 1100 1760 1098 9 _pl _cp 
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1784 1078 1781 1078 1781 1081 1781 1087 1783 1085 1785 1085 1789 1086 1791 1088 1793 1092 1794 1096 1793 1100 1792 1102 1790 1104 1787 1105 1786 1105 
1784 1104 1783 1103 32 _pl _cp 1781 1100 _m
_sp 1781 1100 1781 1089 1783 1087 1785 1087 1787 1088 1789 1089 1790 1091 1790 1094 1790 1097 1789 1100 1787 1101 1785 1102 1783 1102 13 _pl _cp 
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1812 1099 16 _pl _cp 1814 1096 _m
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1814 1100 1814 1097 1814 1096 18 _pl _cp 
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1838 1087 1837 1090 1837 1099 1839 1101 1840 1102 1840 1102 1841 1101 1842 1101 1843 1100 1844 1101 1844 1102 1843 1104 1842 1105 1841 1105 1840 1104 
1838 1103 1837 1102 32 _pl _cp 
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1867 1087 1866 1090 17 _pl _cp 1862 1112 _m
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1878 1087 1877 1090 1877 1100 1878 1101 1880 1102 1881 1103 1882 1103 1883 1103 1884 1102 1885 1100 1885 1097 1885 1090 1884 1087 1882 1086 1882 1086 
1882 1086 1892 1086 1892 1086 1891 1086 1889 1087 1888 1090 1888 1099 1888 1101 1887 1103 1885 1104 1883 1105 1882 1105 1880 1104 1879 1103 1877 1102 
45 _pl _cp 
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1905 1099 1906 1098 1908 1099 1908 1100 1907 1102 1906 1104 1904 1105 1902 1105 1898 1104 1896 1102 1894 1099 1893 1095 1894 1091 1895 1088 1898 1086 
1901 1085 1904 1086 1906 1087 1907 1088 1908 1089 1908 1090 1909 1092 37 _pl _cp 
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1918 1087 1917 1090 1917 1099 1918 1101 1919 1102 1920 1102 1921 1101 1922 1101 1922 1100 1923 1101 1924 1102 1923 1104 1922 1105 1921 1105 1920 1104 
1918 1103 1917 1102 32 _pl _cp 
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_sp 1929 1097 1942 1097 1941 1100 1939 1103 1937 1104 1934 1105 1930 1104 1928 1102 1926 1099 1925 1095 1926 1091 1928 1088 1930 1086 1933 1085 1936 1085 
1938 1087 1940 1089 1942 1092 1942 1093 1941 1091 1939 1089 1937 1088 1935 1087 1932 1088 1931 1090 1929 1093 1929 1097 1929 1097 28 _pl _cp 1937 1098 _m
_sp 1937 1098 1937 1100 1936 1102 1934 1103 1933 1103 1932 1103 1930 1102 1929 1100 1929 1098 9 _pl _cp 
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_sp 1950 1105 1949 1105 1943 1103 1943 1102 1944 1102 1946 1101 1946 1099 1946 1090 1946 1087 1944 1086 1943 1086 1943 1086 1953 1086 1953 1086 1953 1086 
1951 1087 1950 1090 1950 1100 1951 1101 1953 1102 1954 1103 1955 1103 1956 1103 1957 1102 1958 1100 1958 1098 1958 1090 1957 1087 1955 1086 1955 1086 
1955 1086 1964 1086 1964 1086 1964 1086 1962 1087 1961 1090 1961 1100 1962 1101 1964 1102 1965 1103 1966 1103 1967 1103 1968 1102 1969 1100 1969 1098 
1969 1090 1968 1087 1966 1086 1966 1086 1966 1086 1976 1086 1976 1086 1975 1086 1973 1087 1973 1090 1973 1098 1973 1101 1972 1103 1970 1105 1967 1105 
1966 1105 1964 1104 1963 1103 1961 1101 1959 1104 1957 1105 1955 1105 1954 1104 1952 1103 1950 1102 70 _pl _cp 
0 g _f _s _s 
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_sp 1980 1097 1993 1097 1992 1100 1991 1103 1989 1104 1986 1105 1982 1104 1979 1102 1978 1099 1977 1095 1978 1091 1979 1088 1982 1086 1985 1085 1988 1085 
1990 1087 1992 1089 1994 1092 1993 1093 1992 1091 1991 1089 1989 1088 1987 1087 1984 1088 1982 1090 1981 1093 1980 1097 1980 1097 28 _pl _cp 1988 1098 _m
_sp 1988 1098 1988 1100 1987 1102 1986 1103 1984 1103 1983 1103 1981 1102 1980 1100 1980 1098 9 _pl _cp 
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1793 1054 16 _pl _cp 1796 1052 _m
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30 _pl _cp 
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1704 998 1704 1000 1704 1010 1706 1013 1708 1014 1709 1014 1710 1013 1711 1011 1711 1008 1711 1000 1711 998 1709 997 1708 997 1708 997 1718 997 
1718 997 1717 997 1715 998 1715 1000 1715 1010 1715 1012 1714 1014 1712 1015 1710 1016 1709 1016 1707 1015 1706 1014 1704 1012 43 _pl _cp 
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1730 1006 1728 1007 1726 1008 1723 1010 1722 1012 1723 1013 1726 1014 1727 1014 1729 1013 1730 1011 1731 1009 1732 1009 1732 1015 1731 1015 1731 1015 
1730 1015 1730 1015 1729 1015 1728 1015 1727 1016 1726 1016 1723 1016 1721 1014 1720 1013 1719 1011 1719 1009 1720 1007 1722 1006 1724 1005 1727 1003 
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1744 989 1742 989 1741 992 1741 997 1743 996 1745 996 1749 997 1751 999 1753 1003 1754 1007 1753 1011 1752 1013 1750 1015 1747 1016 1746 1016 
1744 1015 1743 1014 32 _pl _cp 1741 1011 _m
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1788 1010 1789 1009 1790 1010 1791 1011 1790 1013 1789 1015 1787 1016 1785 1016 1781 1015 1778 1013 1776 1010 1775 1006 1776 1002 1778 999 1780 997 
1784 996 1787 997 1789 998 1790 999 1790 1000 1791 1001 1792 1003 37 _pl _cp 
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1813 998 1812 1000 17 _pl _cp 1808 1023 _m
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1819 1010 16 _pl _cp 1821 1007 _m
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1821 1011 1821 1008 1821 1007 18 _pl _cp 
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1849 997 1859 997 1859 997 1858 997 1856 998 1855 1000 1855 1010 1855 1012 1854 1014 1852 1015 1850 1016 1849 1016 1847 1015 1846 1014 1844 1012 
45 _pl _cp 
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1880 998 1880 1000 1880 1011 1882 1013 1884 1014 1885 1014 1886 1013 1887 1011 1887 1009 1887 1000 1887 998 1885 997 1884 997 1884 997 1894 997 
1894 997 1893 997 1891 998 1891 1000 1891 1011 1893 1013 1895 1014 1896 1014 1897 1013 1898 1011 1898 1009 1898 1000 1898 998 1896 997 1896 997 
1896 997 1905 997 1905 997 1905 997 1903 998 1902 1000 1902 1009 1902 1012 1901 1014 1899 1016 1897 1016 1895 1016 1894 1015 1892 1014 1890 1012 
1889 1015 1886 1016 1885 1016 1883 1015 1882 1014 1880 1012 66 _pl _cp 
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1919 998 1921 1000 1923 1003 1923 1004 1922 1002 1920 1000 1918 999 1916 998 1913 999 1912 1001 1910 1004 1910 1008 1910 1008 28 _pl _cp 1918 1009 _m
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1943 998 1943 1000 1943 1011 1945 1013 1947 1014 1948 1014 1949 1013 1950 1011 1950 1008 1950 1000 1950 998 1948 997 1947 997 1947 997 1957 997 
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1959 1010 16 _pl _cp 1962 1007 _m
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1962 1011 1962 1008 1962 1007 18 _pl _cp 
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15 _pl _cp 
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2011 1002 2012 1000 2011 998 2008 997 2006 998 2004 999 2002 1000 2001 1003 2000 1003 54 _pl _cp 
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500 2892 501 2891 501 2890 501 2889 501 2887 501 2884 501 2849 501 2845 501 2844 501 2843 500 2841 498 2839 495 2839 493 2839 493 2836 
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532 2895 533 2894 534 2892 535 2891 536 2890 536 2889 536 2887 536 2884 536 2870 84 _pl _cp 
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563 2828 562 2826 562 2824 563 2821 564 2819 567 2817 571 2817 574 2817 577 2818 579 2820 582 2823 584 2828 598 2866 599 2870 600 2870 
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624 2870 625 2871 627 2872 628 2873 630 2873 631 2873 633 2873 635 2871 23 _pl _cp 
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680 2873 676 2869 47 _pl _cp 
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786 2841 785 2843 785 2845 785 2897 765 2897 765 2895 768 2895 770 2894 772 2892 772 2891 772 2887 41 _pl _cp 772 2869 _m
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926 2849 926 2865 926 2868 925 2870 924 2872 922 2874 919 2876 916 2877 912 2878 908 2878 902 2877 897 2876 893 2873 891 2870 890 2867 
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909 2856 911 2857 17 _pl _cp 
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935 2838 934 2838 934 2836 956 2836 956 2838 955 2838 953 2839 952 2841 951 2842 951 2846 951 2867 953 2869 955 2871 957 2872 959 2872 
961 2872 962 2871 963 2869 963 2866 963 2846 963 2843 963 2842 963 2841 962 2839 961 2839 959 2838 958 2838 958 2836 980 2836 980 2838 
980 2838 977 2839 976 2841 976 2842 976 2846 976 2867 978 2869 979 2871 981 2872 983 2872 986 2871 987 2869 988 2868 988 2865 988 2846 
988 2843 987 2842 987 2841 987 2839 985 2839 983 2838 983 2838 983 2836 1005 2836 1005 2838 1004 2838 1002 2839 1000 2841 1000 2842 1000 2846 
1000 2865 1000 2868 999 2870 999 2872 998 2874 996 2876 994 2877 991 2878 988 2878 985 2878 982 2876 979 2874 976 2870 974 2873 972 2876 
969 2877 965 2878 962 2878 960 2877 958 2876 956 2875 955 2874 954 2873 952 2872 951 2870 100 _pl _cp 
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1012 2839 1010 2838 1009 2838 1009 2836 1031 2836 1031 2838 1031 2838 1028 2839 1027 2841 1026 2842 1026 2846 26 _pl _cp 1027 2892 _m
_sp 1027 2892 1026 2894 1025 2896 1023 2897 1020 2898 1018 2897 1015 2896 1014 2894 1013 2892 1014 2889 1015 2887 1018 2886 1020 2885 1023 2886 1025 2887 
1026 2889 16 _pl _cp 
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1054 2875 1057 2874 1058 2872 1058 2870 1058 2867 1059 2865 1061 2863 1063 2863 1065 2863 1067 2864 1068 2866 1069 2868 1068 2871 1066 2874 1063 2876 
1059 2877 1055 2878 1050 2877 1046 2876 1042 2873 1039 2870 1037 2866 1035 2861 1035 2856 1036 2850 1037 2845 1040 2841 1043 2838 1048 2836 1053 2835 
1057 2835 1061 2836 1064 2838 1068 2841 1071 2845 50 _pl _cp 
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1104 2843 1105 2845 1105 2848 1105 2850 1104 2852 1104 2854 1103 2856 1102 2857 1100 2859 1098 2860 1095 2861 1094 2862 1092 2863 1091 2864 1090 2864 
1088 2865 1086 2866 1085 2868 1084 2871 1085 2873 1086 2874 1088 2876 1090 2876 1092 2876 1094 2875 1095 2874 1097 2873 1098 2871 1099 2870 1100 2868 
1101 2865 1103 2865 1103 2878 1101 2878 1100 2877 1099 2876 1097 2877 1094 2877 1092 2878 1089 2878 1084 2877 1081 2876 1078 2873 1076 2869 1075 2865 
1076 2861 1078 2858 1080 2855 1084 2853 1092 2849 1094 2848 1096 2847 1097 2845 1097 2843 1096 2841 1095 2839 1093 2838 1090 2838 1088 2838 1086 2839 
1083 2840 1081 2841 1080 2843 1079 2844 1078 2846 1078 2849 1075 2849 82 _pl _cp 
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1152 2843 1151 2841 1149 2839 1146 2839 1144 2839 1144 2836 1164 2836 1164 2839 1162 2839 1160 2839 1158 2840 1157 2841 1156 2843 1156 2844 1156 2845 
1156 2846 1156 2849 1156 2889 1178 2836 1180 2836 1203 2888 1203 2849 1203 2846 1203 2844 1202 2842 1201 2841 1199 2839 1196 2839 1195 2839 1195 2836 
1226 2836 1226 2839 1224 2839 1222 2839 1220 2840 1219 2841 1218 2843 1217 2844 1217 2845 1217 2846 1217 2849 1217 2884 1217 2888 1218 2889 1218 2891 
1219 2893 1221 2894 1224 2895 1226 2895 1226 2897 1203 2897 1184 2854 67 _pl _cp 
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1269 2862 1268 2866 1266 2870 1263 2873 1259 2876 1255 2877 1250 2878 1245 2877 1241 2876 1237 2873 1234 2870 1232 2866 1230 2862 28 _pl _cp 1243 2860 _m
_sp 1243 2860 1243 2866 1244 2870 1245 2873 1247 2874 1250 2875 1253 2874 1255 2872 1256 2869 1257 2863 1257 2856 1257 2851 1257 2847 1256 2844 1256 2842 
1255 2840 1253 2839 1250 2838 1248 2838 1246 2839 1245 2841 1244 2843 1244 2846 1243 2850 1243 2852 1243 2855 1243 2857 27 _pl _cp 
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1283 2837 1287 2836 1292 2835 1295 2835 1298 2837 1301 2838 1303 2841 1303 2835 1306 2835 1309 2836 1313 2837 1316 2837 1321 2838 1321 2840 1319 2840 
1317 2841 1316 2843 1316 2845 1316 2897 1296 2897 1296 2895 1299 2895 1301 2894 1303 2892 1303 2891 1303 2887 41 _pl _cp 1303 2869 _m
_sp 1303 2869 1303 2846 1301 2843 1300 2842 1298 2840 1296 2840 1295 2840 1293 2841 1292 2842 1291 2843 1290 2845 1289 2848 1288 2852 1288 2857 1288 2861 
1289 2865 1290 2868 1291 2870 1292 2871 1293 2872 1295 2873 1297 2873 1298 2873 1300 2873 1301 2871 25 _pl _cp 
0 g _f _s _s 
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1325 2857 1325 2851 1327 2846 1329 2842 1332 2839 1335 2837 1339 2835 1344 2835 1348 2835 1352 2836 1355 2838 1358 2842 1361 2846 1359 2847 1357 2844 
1354 2843 1352 2841 1349 2841 1347 2841 1345 2842 1344 2843 1342 2844 1340 2846 1339 2849 1338 2853 40 _pl _cp 1337 2861 _m
_sp 1337 2861 1338 2867 1338 2871 1340 2874 1341 2875 1344 2876 1347 2875 1349 2873 1350 2869 1350 2864 1349 2861 11 _pl _cp 
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1365 2838 1365 2836 1387 2836 1387 2838 1386 2838 1385 2839 1383 2839 1382 2840 1382 2842 1382 2844 1382 2846 26 _pl _cp 
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1430 2883 1428 2878 1426 2873 1426 2867 1426 2861 1428 2855 1430 2850 1433 2846 1437 2842 1441 2839 1446 2837 1451 2835 1457 2835 1461 2835 1465 2836 
1469 2837 1473 2839 1476 2841 1480 2844 1483 2848 1480 2850 1478 2848 1476 2847 1474 2845 1473 2844 1470 2842 1467 2841 1463 2840 1460 2840 1455 2840 
1451 2842 1448 2845 1445 2849 1443 2854 1442 2860 1442 2867 1442 2873 1443 2878 1444 2882 1445 2886 1447 2889 1449 2892 1451 2894 1454 2895 1458 2895 
1461 2895 1464 2894 1467 2892 1471 2889 1473 2887 1475 2884 1476 2881 1478 2877 1481 2877 1481 2898 70 _pl _cp 
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1490 2838 1490 2836 1512 2836 1512 2838 1511 2838 1510 2839 1508 2839 1507 2840 1507 2842 1507 2844 1507 2846 26 _pl _cp 
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1536 2838 1539 2841 1541 2838 1542 2836 1544 2835 1547 2835 1550 2835 1552 2836 1555 2838 1557 2840 1556 2842 1555 2841 1554 2841 1553 2842 1552 2844 
1552 2849 1552 2865 1552 2868 1551 2870 1550 2872 1549 2874 1546 2876 1543 2877 1539 2878 1534 2878 1529 2877 1524 2876 1520 2873 1518 2870 1517 2867 
1517 2865 1519 2863 1520 2862 1523 2861 1525 2861 1527 2862 1528 2864 1529 2866 1528 2868 1527 2870 1527 2871 1526 2872 1527 2873 1528 2874 1530 2875 
1532 2875 1536 2875 1538 2873 1540 2870 1540 2866 1540 2864 66 _pl _cp 1539 2858 _m
_sp 1539 2858 1539 2845 1538 2843 1536 2842 1535 2841 1533 2841 1531 2841 1529 2843 1528 2844 1528 2847 1528 2849 1529 2851 1530 2852 1532 2854 1534 2855 
1535 2856 1537 2857 17 _pl _cp 
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1590 2843 1591 2845 1591 2848 1591 2850 1590 2852 1589 2854 1588 2856 1587 2857 1586 2859 1584 2860 1581 2861 1580 2862 1578 2863 1577 2864 1576 2864 
1574 2865 1572 2866 1571 2868 1570 2871 1571 2873 1572 2874 1574 2876 1576 2876 1578 2876 1580 2875 1581 2874 1583 2873 1584 2871 1585 2870 1586 2868 
1587 2865 1589 2865 1589 2878 1587 2878 1586 2877 1585 2876 1583 2877 1580 2877 1578 2878 1575 2878 1570 2877 1567 2876 1564 2873 1562 2869 1561 2865 
1562 2861 1563 2858 1566 2855 1570 2853 1578 2849 1580 2848 1581 2847 1582 2845 1582 2843 1582 2841 1581 2839 1579 2838 1576 2838 1574 2838 1571 2839 
1569 2840 1567 2841 1566 2843 1565 2844 1564 2846 1564 2849 1561 2849 82 _pl _cp 
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1625 2843 1626 2845 1626 2848 1626 2850 1625 2852 1624 2854 1623 2856 1622 2857 1621 2859 1619 2860 1616 2861 1615 2862 1613 2863 1612 2864 1611 2864 
1609 2865 1607 2866 1606 2868 1605 2871 1606 2873 1607 2874 1609 2876 1611 2876 1613 2876 1615 2875 1616 2874 1618 2873 1619 2871 1620 2870 1621 2868 
1622 2865 1624 2865 1624 2878 1622 2878 1621 2877 1620 2876 1618 2877 1615 2877 1613 2878 1610 2878 1605 2877 1602 2876 1599 2873 1597 2869 1596 2865 
1597 2861 1598 2858 1601 2855 1605 2853 1613 2849 1615 2848 1616 2847 1617 2845 1617 2843 1617 2841 1616 2839 1614 2838 1611 2838 1609 2838 1606 2839 
1604 2840 1602 2841 1601 2843 1600 2844 1599 2846 1599 2849 1596 2849 82 _pl _cp 
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1672 2892 1673 2891 1674 2890 1674 2889 1674 2887 1674 2884 1674 2849 1674 2845 1674 2844 1673 2843 1672 2841 1670 2839 1667 2839 1665 2839 1665 2836 
1697 2836 1697 2839 1695 2839 1693 2839 1691 2840 1690 2841 1689 2843 1688 2844 1688 2845 1688 2846 1688 2849 1688 2865 1708 2865 1708 2849 1708 2845 
1708 2844 1708 2843 1707 2841 1705 2839 1702 2839 1700 2839 1700 2836 1731 2836 1731 2839 1729 2839 1727 2839 1725 2840 1724 2841 1723 2843 1723 2844 
1723 2845 1723 2846 1723 2849 1723 2884 1723 2888 1723 2889 1723 2891 1724 2893 1726 2894 1729 2895 1731 2895 1731 2897 1700 2897 1700 2895 1702 2895 
1704 2895 1706 2894 1707 2892 1708 2891 1708 2890 1708 2889 1708 2887 1708 2884 1708 2870 84 _pl _cp 
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1738 2839 1736 2838 1736 2838 1736 2836 1757 2836 1757 2838 1757 2838 1755 2839 1753 2841 1753 2842 1753 2846 26 _pl _cp 1753 2892 _m
_sp 1753 2892 1752 2894 1751 2896 1749 2897 1746 2898 1744 2897 1742 2896 1741 2894 1740 2892 1741 2889 1742 2887 1744 2886 1746 2885 1749 2886 1751 2887 
1752 2889 16 _pl _cp 
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1761 2857 1761 2851 1763 2846 1765 2842 1767 2839 1771 2837 1775 2835 1780 2835 1784 2835 1787 2836 1791 2838 1794 2842 1797 2846 1795 2847 1793 2844 
1790 2843 1788 2841 1785 2841 1783 2841 1781 2842 1780 2843 1778 2844 1776 2846 1775 2849 1774 2853 40 _pl _cp 1773 2861 _m
_sp 1773 2861 1773 2867 1774 2871 1775 2874 1777 2875 1779 2876 1782 2875 1784 2873 1785 2869 1785 2864 1785 2861 11 _pl _cp 
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1803 2839 1801 2838 1801 2838 1801 2836 1824 2836 1824 2838 1822 2838 1820 2839 1818 2841 1818 2842 1818 2846 1818 2859 1819 2863 1820 2867 1822 2869 
1825 2870 1827 2870 1828 2868 1829 2867 1831 2866 1832 2865 1833 2865 1835 2866 1837 2867 1838 2869 1838 2871 1837 2874 1836 2876 1834 2877 1831 2878 
1828 2878 1825 2876 1822 2873 1818 2869 49 _pl _cp 
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1862 2838 1865 2841 1866 2838 1867 2836 1869 2835 1872 2835 1875 2835 1878 2836 1881 2838 1883 2840 1881 2842 1880 2841 1879 2841 1878 2842 1877 2844 
1877 2849 1877 2865 1877 2868 1876 2870 1875 2872 1874 2874 1871 2876 1868 2877 1864 2878 1860 2878 1854 2877 1849 2876 1845 2873 1843 2870 1842 2867 
1843 2865 1844 2863 1846 2862 1848 2861 1851 2861 1853 2862 1854 2864 1854 2866 1854 2868 1853 2870 1852 2871 1851 2872 1852 2873 1853 2874 1855 2875 
1857 2875 1861 2875 1863 2873 1865 2870 1865 2866 1865 2864 66 _pl _cp 1865 2858 _m
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1861 2856 1862 2857 17 _pl _cp 
0 g _f _s _s 
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1888 2839 1886 2838 1886 2838 1886 2836 1909 2836 1909 2838 1907 2838 1905 2839 1903 2841 1903 2842 1903 2846 1903 2859 1904 2863 1905 2867 1907 2869 
1910 2870 1912 2870 1913 2868 1914 2867 1916 2866 1917 2865 1918 2865 1920 2866 1922 2867 1923 2869 1924 2871 1923 2874 1922 2876 1919 2877 1916 2878 
1913 2878 1910 2876 1907 2873 1903 2869 49 _pl _cp 
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1946 2875 1949 2874 1950 2872 1950 2870 1950 2867 1951 2865 1953 2863 1955 2863 1957 2863 1959 2864 1960 2866 1960 2868 1959 2871 1958 2874 1955 2876 
1951 2877 1946 2878 1941 2877 1937 2876 1933 2873 1930 2870 1928 2866 1926 2861 1926 2856 1926 2851 1928 2846 1930 2843 1933 2839 1936 2837 1940 2835 
1945 2835 1949 2835 1953 2836 1956 2838 1959 2841 1962 2845 51 _pl _cp 
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1966 2838 1966 2836 1988 2836 1988 2838 1986 2838 1985 2839 1984 2840 1983 2841 1983 2842 1983 2846 1983 2867 1985 2869 1987 2871 1988 2872 1990 2872 
1992 2872 1994 2871 1995 2869 1995 2866 1995 2846 1995 2843 1995 2842 1995 2841 1994 2839 1993 2839 1991 2838 1991 2836 2012 2836 2012 2838 2012 2838 
2010 2839 2008 2841 2008 2842 2008 2846 2008 2862 2008 2865 2007 2867 2007 2869 2006 2871 2005 2874 2003 2876 2000 2877 1996 2878 1994 2878 1991 2877 
1989 2876 1987 2875 1985 2873 1983 2871 64 _pl _cp 
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2021 2870 2022 2866 2036 2837 2034 2831 2032 2826 2030 2823 2029 2821 2027 2821 2026 2822 2025 2824 2025 2826 2024 2828 2022 2829 2020 2829 2018 2829 
2016 2828 2015 2826 2015 2824 2016 2821 2017 2819 2020 2817 2024 2817 2027 2817 2030 2818 2032 2820 2035 2823 2037 2828 2051 2866 2052 2870 2052 2870 
2054 2872 2055 2873 2057 2874 2058 2875 2058 2877 2044 2877 2044 2875 2046 2875 2048 2874 2049 2872 2049 2871 2048 2870 2048 2868 2047 2866 59 _pl _cp 
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1192 1241 1191 1243 1191 1254 1193 1256 1195 1257 1197 1257 1198 1255 1199 1253 1199 1250 1199 1243 1198 1241 1196 1240 1196 1240 1196 1239 1205 1239 
1205 1240 1205 1240 1203 1241 1202 1243 1202 1252 1202 1255 1201 1257 1199 1258 1197 1258 1196 1258 1194 1258 1193 1257 1191 1256 43 _pl _cp 
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1207 1252 16 _pl _cp 1210 1250 _m
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1210 1253 1210 1250 1210 1250 18 _pl _cp 
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1234 1241 1233 1243 1233 1252 1235 1255 1236 1256 1236 1256 1237 1255 1238 1254 1239 1254 1240 1255 1240 1256 1239 1258 1238 1258 1237 1258 1236 1258 
1234 1257 1233 1255 32 _pl _cp 
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1249 1241 1248 1243 17 _pl _cp 1244 1266 _m
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1264 1256 16 _pl _cp 
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1273 1252 16 _pl _cp 1276 1250 _m
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1276 1253 1276 1250 1276 1250 18 _pl _cp 
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1299 1241 1299 1243 1299 1253 1301 1256 1303 1257 1305 1257 1306 1255 1306 1253 1306 1250 1306 1243 1306 1241 1304 1240 1304 1240 1304 1239 1313 1239 
1313 1240 1313 1240 1310 1241 1310 1243 1310 1253 1310 1255 1309 1257 1307 1258 1305 1258 1304 1258 1302 1258 1301 1257 1299 1255 43 _pl _cp 
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1321 1242 1320 1244 1320 1256 1324 1256 1324 1258 1320 1258 1320 1264 1319 1264 1318 1262 1318 1261 1317 1260 1316 1259 1315 1258 28 _pl _cp 
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1339 1239 1341 1239 1343 1241 1343 1242 1342 1241 1341 1241 1341 1242 1340 1243 1340 1252 1340 1253 1340 1253 1340 1254 1340 1255 1339 1256 1338 1257 
1336 1258 1334 1258 1331 1258 1329 1257 1328 1256 1327 1254 1328 1253 1329 1252 1330 1253 1331 1254 1331 1254 1331 1254 1331 1255 1331 1255 1330 1255 
1331 1256 1333 1257 1336 1256 1336 1253 49 _pl _cp 1336 1250 _m
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1352 1241 1351 1243 17 _pl _cp 
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573 1104 572 1103 32 _pl _cp 570 1100 _m
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611 1087 610 1090 610 1099 612 1101 613 1102 613 1102 614 1102 615 1101 615 1101 617 1102 617 1103 616 1104 615 1105 614 1105 613 1104 
611 1103 610 1102 32 _pl _cp 
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650 1099 16 _pl _cp 653 1097 _m
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653 1100 653 1097 653 1097 18 _pl _cp 
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676 1087 676 1090 676 1099 677 1101 678 1102 679 1102 679 1102 680 1101 681 1101 682 1102 683 1103 682 1104 680 1105 678 1104 676 1102 
30 _pl _cp 
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550 1043 550 1045 17 _pl _cp 546 1068 _m
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601 1034 599 1034 598 1037 598 1042 600 1041 602 1041 606 1042 608 1044 610 1048 611 1052 611 1056 609 1058 607 1060 604 1061 603 1061 
601 1060 600 1059 32 _pl _cp 598 1056 _m
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15 _pl _cp 
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670 1043 670 1045 17 _pl _cp 665 1068 _m
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676 1054 16 _pl _cp 679 1052 _m
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679 1055 679 1052 679 1052 18 _pl _cp 
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45 _pl _cp 
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816 1054 16 _pl _cp 819 1052 _m
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819 1055 819 1052 819 1052 18 _pl _cp 
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15 _pl _cp 
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614 997 621 1012 622 1014 624 1015 624 1015 618 1015 618 1015 619 1014 619 1013 619 1013 619 1013 619 1013 619 1013 619 1013 619 1012 
30 _pl _cp 
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651 998 651 1001 17 _pl _cp 
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657 1010 16 _pl _cp 660 1008 _m
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660 1011 660 1008 660 1008 18 _pl _cp 
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631 2063 630 2062 32 _pl _cp 628 2059 _m
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15 _pl _cp 
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648 2059 648 2056 648 2055 18 _pl _cp 
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671 2046 671 2049 671 2058 672 2060 673 2061 674 2061 674 2060 675 2060 676 2059 677 2060 678 2061 677 2063 675 2064 673 2063 671 2060 
30 _pl _cp 
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717 2058 718 2057 720 2058 720 2059 720 2061 719 2063 717 2064 714 2064 710 2063 708 2061 706 2058 705 2054 706 2050 707 2047 710 2045 
713 2044 716 2045 718 2046 719 2047 720 2048 720 2049 721 2051 37 _pl _cp 
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725 2058 16 _pl _cp 727 2055 _m
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727 2059 727 2056 727 2055 18 _pl _cp 
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751 2046 750 2049 750 2058 751 2060 753 2061 754 2062 755 2062 756 2062 757 2061 758 2059 758 2056 758 2049 757 2046 755 2045 755 2045 
755 2045 765 2045 765 2045 764 2045 762 2046 761 2049 761 2058 761 2060 760 2062 758 2063 756 2064 755 2064 753 2063 752 2062 750 2060 
45 _pl _cp 
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772 2046 771 2049 771 2058 772 2060 774 2061 775 2062 776 2062 777 2062 778 2061 779 2059 779 2056 779 2049 778 2046 776 2045 776 2045 
776 2045 786 2045 786 2045 785 2045 783 2046 783 2049 783 2058 783 2060 782 2062 780 2063 777 2064 776 2064 774 2063 773 2062 771 2060 
45 _pl _cp 
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800 2046 802 2048 804 2051 803 2052 802 2050 801 2048 799 2047 797 2046 794 2047 792 2049 791 2052 790 2056 790 2056 28 _pl _cp 798 2057 _m
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818 2058 819 2057 821 2058 821 2059 820 2061 819 2063 817 2064 815 2064 811 2063 809 2061 807 2058 806 2054 807 2050 808 2047 811 2045 
814 2044 817 2045 819 2046 820 2047 821 2048 821 2049 822 2051 37 _pl _cp 
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830 2047 830 2049 830 2062 834 2062 834 2063 830 2063 830 2069 829 2069 828 2067 828 2066 827 2065 826 2064 825 2064 28 _pl _cp 
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843 2046 843 2049 17 _pl _cp 838 2071 _m
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849 2058 16 _pl _cp 852 2055 _m
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852 2059 852 2056 852 2055 18 _pl _cp 
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875 2046 875 2049 875 2058 877 2061 879 2062 880 2062 881 2061 882 2059 882 2056 882 2049 882 2046 880 2045 879 2045 879 2045 889 2045 
889 2045 888 2045 886 2046 886 2049 886 2058 886 2060 885 2062 883 2063 881 2064 880 2064 878 2063 877 2062 875 2060 43 _pl _cp 
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906 2047 909 2045 912 2044 915 2045 917 2046 917 2044 918 2044 924 2046 924 2047 923 2047 921 2047 921 2050 27 _pl _cp 917 2048 _m
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15 _pl _cp 
0 g _f _s _s 
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935 2047 937 2045 938 2044 940 2045 942 2046 942 2047 941 2046 940 2046 940 2047 939 2048 939 2057 939 2058 939 2059 939 2060 939 2060 
938 2062 937 2063 935 2064 933 2064 930 2064 928 2063 927 2061 926 2059 927 2058 928 2057 929 2058 930 2059 930 2059 930 2059 930 2060 
930 2060 930 2061 931 2062 932 2062 935 2061 935 2058 51 _pl _cp 935 2055 _m
_sp 935 2055 933 2054 930 2052 929 2050 930 2047 932 2046 934 2047 935 2048 8 _pl _cp 
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950 2047 949 2049 949 2062 953 2062 953 2063 949 2063 949 2069 949 2069 948 2067 947 2066 946 2065 945 2064 944 2064 28 _pl _cp 
0 g _f _s _s 
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969 2044 971 2045 973 2046 973 2047 972 2046 971 2046 970 2047 970 2048 970 2057 970 2058 970 2059 970 2060 969 2060 968 2062 967 2063 
965 2064 963 2064 960 2064 958 2063 957 2061 956 2059 957 2058 958 2057 959 2058 960 2059 960 2059 960 2059 960 2060 960 2060 960 2061 
961 2062 963 2062 965 2061 966 2058 49 _pl _cp 966 2055 _m
_sp 966 2055 964 2054 962 2053 960 2052 959 2051 959 2050 960 2047 962 2046 964 2047 966 2048 10 _pl _cp 
0 g _f _s _s 
0 g 549 2012 _m
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560 2025 559 2026 558 2027 556 2027 554 2028 552 2028 549 2028 541 2028 541 2027 541 2027 543 2027 544 2026 544 2024 544 2022 544 2005 
544 2002 541 2001 541 2001 541 2000 553 2000 553 2001 552 2001 549 2002 549 2005 39 _pl _cp 549 2014 _m
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0 g _f _s _s 
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570 2001 570 2004 570 2013 571 2015 572 2016 573 2016 573 2016 574 2015 575 2015 576 2016 577 2017 576 2018 574 2019 572 2018 570 2016 
30 _pl _cp 
0 g _f _s _s 
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579 2013 16 _pl _cp 582 2011 _m
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582 2014 582 2011 582 2011 18 _pl _cp 
0 g _f _s _s 
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606 2003 605 2005 605 2017 609 2017 609 2019 605 2019 605 2024 604 2024 603 2022 601 2020 600 2019 26 _pl _cp 
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612 2013 16 _pl _cp 615 2011 _m
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615 2014 615 2011 615 2011 18 _pl _cp 
0 g _f _s _s 
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645 2014 646 2013 647 2014 648 2015 647 2016 646 2018 644 2019 642 2019 638 2018 635 2016 633 2013 632 2009 633 2005 635 2003 637 2001 
641 2000 644 2000 646 2002 647 2004 649 2006 35 _pl _cp 
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652 2013 16 _pl _cp 655 2011 _m
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655 2014 655 2011 655 2011 18 _pl _cp 
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679 2001 679 2004 17 _pl _cp 
0 g _f _s _s 
0 g 698 2028 _m
_sp 698 2028 698 2027 698 2027 700 2027 701 2026 701 2024 701 2022 701 2005 701 2002 698 2001 698 2001 698 2000 709 2000 713 2000 717 2001 
720 2002 722 2004 723 2006 724 2009 725 2011 725 2014 725 2017 724 2019 723 2022 722 2024 719 2026 716 2027 712 2028 707 2028 29 _pl _cp 706 2005 _m
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717 2022 715 2024 713 2025 711 2026 708 2026 708 2026 707 2026 706 2025 706 2025 706 2022 25 _pl _cp 
0 g _f _s _s 
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741 2000 743 2000 745 2001 745 2003 744 2002 743 2001 743 2002 742 2004 742 2012 742 2013 742 2014 742 2015 742 2016 741 2017 740 2018 
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734 2017 735 2018 737 2018 738 2017 738 2015 738 2013 51 _pl _cp 738 2011 _m
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753 2003 752 2005 752 2017 756 2017 756 2019 752 2019 752 2024 752 2024 750 2022 748 2020 747 2019 26 _pl _cp 
0 g _f _s _s 
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772 2000 774 2000 776 2001 776 2003 775 2002 774 2001 773 2002 773 2004 773 2012 773 2013 773 2014 773 2015 772 2016 771 2017 770 2018 
768 2019 766 2019 763 2019 761 2018 760 2016 759 2014 760 2013 761 2012 762 2013 763 2014 763 2014 763 2015 763 2016 763 2016 763 2016 
764 2017 766 2018 767 2018 768 2017 769 2015 769 2013 51 _pl _cp 769 2011 _m
_sp 769 2011 767 2010 765 2009 763 2008 762 2006 762 2005 763 2003 765 2002 767 2002 769 2004 10 _pl _cp 
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805 2000 807 2000 809 2000 811 2001 813 2002 814 2003 815 2005 816 2007 816 2010 816 2022 816 2024 817 2026 818 2027 820 2027 820 2027 
820 2028 810 2028 810 2027 811 2027 813 2027 814 2026 814 2024 814 2022 814 2010 814 2008 814 2006 814 2005 813 2004 812 2003 810 2002 
808 2001 806 2001 805 2001 803 2002 802 2003 801 2004 800 2005 800 2007 799 2009 799 2012 799 2022 799 2024 800 2026 801 2027 803 2027 
803 2027 803 2028 62 _pl _cp 
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828 2001 827 2004 827 2014 828 2015 830 2016 831 2017 832 2017 833 2017 834 2016 835 2014 835 2011 835 2004 834 2001 832 2001 832 2001 
832 2000 842 2000 842 2001 841 2001 839 2001 839 2004 839 2013 839 2016 838 2018 836 2019 834 2019 832 2019 831 2018 829 2017 827 2016 
45 _pl _cp 
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850 2001 849 2004 17 _pl _cp 845 2027 _m
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861 2003 860 2005 860 2017 864 2017 864 2019 860 2019 860 2024 859 2024 858 2022 856 2020 855 2019 26 _pl _cp 
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890 1994 892 1992 893 1993 891 1995 889 1997 888 1999 887 2001 886 2003 886 2006 885 2008 885 2010 885 2013 886 2015 886 2017 887 2019 
888 2022 889 2024 891 2026 893 2027 34 _pl _cp 
0 g _f _s _s 
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908 2028 906 2028 903 2028 894 2028 894 2027 895 2027 896 2027 897 2026 898 2024 898 2022 898 2005 897 2002 895 2001 894 2001 894 2000 
906 2000 906 2001 906 2001 903 2002 902 2005 35 _pl _cp 902 2014 _m
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939 2002 941 2004 943 2006 944 2009 945 2011 945 2014 945 2017 944 2019 943 2022 941 2024 939 2026 935 2027 931 2028 926 2028 29 _pl _cp 926 2005 _m
_sp 926 2005 926 2003 926 2002 928 2002 930 2002 931 2002 933 2002 934 2003 937 2004 939 2007 940 2010 940 2014 940 2016 939 2018 938 2020 
937 2022 935 2024 933 2025 931 2026 928 2026 928 2026 927 2026 926 2025 926 2025 926 2022 25 _pl _cp 
0 g _f _s _s 
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962 2000 964 2000 966 2000 967 2001 969 2002 971 2003 972 2005 973 2007 973 2010 973 2022 973 2024 973 2026 974 2027 976 2027 977 2027 
977 2028 967 2028 967 2027 967 2027 969 2027 970 2026 971 2024 971 2022 971 2010 971 2008 970 2006 970 2005 969 2004 968 2003 967 2002 
965 2001 963 2001 961 2001 959 2002 958 2003 957 2004 956 2005 956 2007 956 2009 956 2012 956 2022 956 2024 956 2026 957 2027 959 2027 
959 2027 959 2028 62 _pl _cp 
0 g _f _s _s 
0 g 979 1992 _m
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981 2027 979 2028 978 2027 980 2026 982 2024 983 2022 984 2019 985 2017 985 2015 985 2013 985 2010 985 2008 985 2006 985 2003 984 2001 
983 1999 982 1997 980 1995 978 1993 34 _pl _cp 
0 g _f _s _s 
0 g 540 1973 _m
_sp 540 1973 540 1972 543 1972 543 1960 543 1958 544 1956 545 1955 546 1955 547 1955 549 1956 550 1957 551 1958 551 1959 550 1957 549 1957 
547 1958 546 1960 546 1972 550 1972 550 1974 546 1974 546 1980 546 1980 545 1978 544 1977 543 1976 542 1975 541 1974 28 _pl _cp 
0 g _f _s _s 
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560 1957 559 1959 17 _pl _cp 555 1982 _m
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571 1957 570 1959 570 1970 571 1971 573 1972 574 1973 575 1973 576 1973 577 1972 578 1970 578 1968 578 1959 577 1957 575 1956 575 1956 
575 1955 584 1955 584 1956 584 1956 582 1957 582 1959 582 1970 584 1972 586 1973 587 1973 588 1972 589 1970 589 1968 589 1959 589 1957 
587 1956 586 1956 586 1955 596 1955 596 1956 595 1956 593 1957 593 1959 593 1968 593 1971 592 1973 590 1975 587 1975 586 1975 584 1974 
583 1973 581 1971 579 1974 577 1975 575 1975 574 1974 572 1973 570 1971 68 _pl _cp 
0 g _f _s _s 
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610 1957 612 1959 614 1962 613 1962 612 1961 611 1959 609 1958 607 1957 604 1958 602 1960 601 1962 600 1966 600 1967 28 _pl _cp 609 1968 _m
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0 g 615 1952 _m
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638 1968 16 _pl _cp 641 1966 _m
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641 1969 641 1966 641 1966 18 _pl _cp 
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670 1972 670 1974 665 1974 665 1975 665 1980 665 1982 667 1983 668 1983 669 1981 670 1980 671 1980 672 1981 673 1982 672 1983 668 1984 
665 1983 663 1982 662 1979 661 1975 34 _pl _cp 
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700 1957 700 1959 17 _pl _cp 
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718 1955 720 1955 722 1957 722 1958 721 1957 720 1957 719 1958 719 1959 719 1968 719 1969 719 1970 719 1971 719 1971 718 1972 717 1974 
715 1975 713 1975 710 1975 708 1974 707 1972 706 1970 707 1969 708 1968 709 1969 709 1970 709 1970 709 1970 709 1971 709 1971 709 1972 
710 1973 712 1973 714 1972 715 1969 49 _pl _cp 715 1966 _m
_sp 715 1966 713 1965 711 1964 710 1963 709 1961 709 1960 710 1958 711 1957 713 1958 715 1959 10 _pl _cp 
0 g _f _s _s 
0 g 724 1955 _m
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734 1965 733 1966 731 1967 729 1968 727 1969 726 1970 726 1971 727 1972 730 1973 732 1973 734 1972 735 1970 736 1968 736 1968 736 1974 
736 1974 735 1974 735 1974 735 1974 734 1974 733 1974 732 1975 730 1975 727 1975 726 1973 724 1972 724 1970 724 1968 725 1966 727 1965 
729 1964 732 1962 734 1961 735 1959 734 1957 731 1956 729 1957 727 1957 726 1958 726 1959 725 1960 724 1962 724 1962 58 _pl _cp 
0 g _f _s _s 
0 g 739 1973 _m
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746 1958 745 1960 745 1972 749 1972 749 1974 745 1974 745 1980 745 1980 744 1978 743 1977 743 1976 742 1975 741 1974 28 _pl _cp 
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792 1981 791 1982 790 1982 788 1983 786 1983 784 1983 781 1983 773 1983 773 1982 773 1982 776 1981 776 1978 776 1961 776 1958 773 1957 
773 1957 773 1955 785 1955 785 1957 784 1957 781 1958 781 1961 37 _pl _cp 781 1969 _m
_sp 781 1969 783 1969 786 1969 788 1971 789 1972 790 1975 789 1978 788 1980 785 1981 782 1981 781 1981 781 1979 12 _pl _cp 
0 g _f _s _s 
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_sp 796 1983 796 1982 796 1982 799 1981 799 1978 799 1961 799 1958 796 1957 796 1957 796 1955 808 1955 812 1955 815 1956 818 1958 820 1960 
821 1962 823 1964 824 1966 824 1969 824 1972 823 1975 821 1977 820 1979 818 1981 814 1982 810 1983 805 1983 27 _pl _cp 804 1961 _m
_sp 804 1961 804 1958 804 1957 806 1957 808 1957 809 1958 811 1958 812 1958 815 1960 817 1962 818 1965 819 1969 819 1972 818 1974 817 1976 
816 1978 814 1979 812 1980 809 1981 806 1981 806 1981 805 1981 804 1981 804 1980 804 1978 25 _pl _cp 
0 g _f _s _s 
0 g 826 1983 _m
_sp 826 1983 826 1982 827 1982 829 1981 830 1978 830 1967 830 1964 830 1962 831 1960 832 1959 833 1957 835 1956 837 1955 840 1955 842 1955 
844 1956 846 1956 848 1957 849 1959 850 1960 851 1962 851 1965 851 1978 852 1981 855 1982 855 1982 855 1983 845 1983 845 1982 846 1982 
849 1981 849 1978 849 1965 849 1962 848 1960 847 1959 845 1958 843 1957 841 1957 838 1958 836 1959 835 1961 835 1962 834 1964 834 1967 
834 1978 835 1981 838 1982 838 1982 838 1983 50 _pl _cp 
0 g _f _s _s 
0 g 551 1897 _m
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1214 1920 1211 1921 1211 1923 1211 1929 1213 1928 1215 1928 1219 1929 1221 1931 1223 1934 1224 1938 1223 1942 1222 1944 1220 1946 1217 1947 1216 1947 
1214 1946 1213 1945 32 _pl _cp 1211 1942 _m
_sp 1211 1942 1211 1931 1213 1930 1215 1929 1217 1930 1219 1931 1220 1934 1220 1937 1220 1940 1219 1943 1217 1944 1215 1945 1213 1944 13 _pl _cp 
0 g _f _s _s 
0 g 1226 1937 _m
_sp 1226 1937 1227 1933 1229 1931 1232 1929 1236 1928 1240 1929 1242 1931 1244 1934 1245 1938 1244 1942 1242 1945 1240 1946 1236 1947 1232 1946 1229 1944 
1227 1941 16 _pl _cp 1230 1939 _m
_sp 1230 1939 1231 1935 1232 1932 1234 1930 1236 1929 1238 1930 1240 1931 1241 1933 1241 1936 1241 1940 1240 1943 1238 1945 1235 1946 1233 1945 1231 1944 
1230 1942 1230 1939 1230 1939 18 _pl _cp 
0 g _f _s _s 
0 g 1253 1948 _m
_sp 1253 1948 1253 1948 1246 1945 1246 1944 1247 1944 1249 1944 1249 1941 1249 1932 1249 1929 1247 1929 1246 1929 1246 1928 1257 1928 1257 1929 1256 1929 
1254 1929 1253 1932 1253 1941 1255 1943 1256 1944 1256 1944 1257 1944 1258 1943 1258 1943 1260 1944 1260 1945 1259 1946 1258 1947 1257 1947 1256 1946 
1254 1945 1253 1944 32 _pl _cp 
0 g _f _s _s 
0 g 1272 1940 _m
_sp 1272 1940 1269 1939 1267 1938 1266 1938 1264 1937 1263 1936 1262 1934 1262 1932 1263 1929 1266 1928 1267 1928 1269 1928 1270 1929 1272 1930 1273 1928 
1275 1928 1277 1928 1278 1929 1278 1931 1278 1930 1277 1929 1276 1930 1276 1932 1276 1940 1276 1941 1276 1942 1275 1943 1275 1944 1274 1945 1273 1946 
1271 1947 1269 1947 1266 1947 1264 1946 1263 1944 1262 1942 1263 1941 1264 1940 1265 1941 1266 1942 1266 1942 1266 1943 1266 1944 1266 1944 1266 1944 
1267 1945 1269 1946 1270 1946 1271 1945 1272 1943 1272 1941 51 _pl _cp 1272 1939 _m
_sp 1272 1939 1270 1938 1268 1937 1266 1936 1265 1934 1265 1933 1266 1931 1268 1930 1270 1930 1272 1932 10 _pl _cp 
0 g _f _s _s 
0 g 1286 1948 _m
_sp 1286 1948 1286 1948 1279 1945 1279 1944 1280 1944 1282 1944 1282 1941 1282 1932 1282 1929 1280 1929 1279 1929 1279 1928 1290 1928 1290 1929 1289 1929 
1286 1929 1286 1932 1286 1941 1287 1943 1288 1944 1289 1944 1289 1944 1291 1943 1291 1943 1292 1944 1293 1945 1292 1946 1291 1947 1290 1947 1288 1946 
1287 1945 1286 1944 32 _pl _cp 
0 g _f _s _s 
0 g 1305 1934 _m
_sp 1305 1934 1301 1943 1300 1944 1300 1944 1300 1945 1300 1945 1301 1946 1302 1946 1302 1946 1302 1947 1294 1947 1294 1946 1296 1945 1297 1943 1303 1930 
1301 1925 1301 1924 1300 1923 1299 1922 1299 1922 1298 1923 1297 1923 1297 1923 1296 1923 1295 1922 1294 1921 1295 1920 1297 1919 1298 1919 1300 1920 
1301 1921 1302 1922 1310 1943 1312 1945 1313 1946 1313 1947 1307 1947 1307 1946 1308 1946 1309 1946 1309 1945 1309 1945 1309 1945 1309 1944 1309 1944 
1309 1944 1308 1943 47 _pl _cp 
0 g _f _s _s 
0 g 1142 1892 _m
_sp 1142 1892 1143 1888 1145 1886 1147 1884 1151 1883 1155 1884 1158 1886 1160 1889 1161 1893 1160 1897 1158 1900 1156 1902 1152 1903 1148 1902 1145 1900 
1143 1896 16 _pl _cp 1146 1894 _m
_sp 1146 1894 1147 1890 1148 1887 1150 1885 1152 1884 1154 1885 1156 1886 1157 1889 1157 1892 1157 1896 1156 1898 1154 1900 1151 1901 1149 1900 1147 1899 
1146 1897 1146 1894 1146 1894 18 _pl _cp 
0 g _f _s _s 
0 g 1173 1888 _m
_sp 1173 1888 1169 1898 1169 1899 1169 1899 1169 1900 1169 1900 1169 1901 1170 1901 1171 1901 1171 1902 1163 1902 1163 1901 1164 1901 1166 1898 1172 1883 
1172 1883 1178 1894 1182 1883 1183 1883 1189 1898 1190 1901 1192 1901 1192 1902 1186 1902 1186 1901 1186 1901 1187 1901 1188 1900 1188 1900 1188 1900 
1188 1900 1188 1899 1188 1899 1187 1898 1184 1889 1180 1898 1180 1899 1179 1899 1179 1900 1179 1900 1180 1901 1181 1901 1181 1901 1181 1902 1173 1902 
1173 1901 1175 1901 1176 1898 1177 1896 49 _pl _cp 
0 g _f _s _s 
0 g 1199 1903 _m
_sp 1199 1903 1199 1903 1192 1901 1192 1900 1193 1900 1195 1899 1195 1897 1195 1887 1195 1885 1193 1884 1192 1884 1192 1883 1202 1883 1202 1884 1202 1884 
1200 1885 1199 1887 1199 1897 1200 1899 1202 1900 1203 1901 1204 1901 1205 1901 1206 1899 1207 1897 1207 1894 1207 1887 1206 1885 1204 1884 1204 1884 
1204 1883 1214 1883 1214 1884 1213 1884 1211 1885 1210 1887 1210 1897 1210 1899 1209 1901 1207 1902 1205 1903 1204 1903 1202 1902 1201 1901 1199 1899 
45 _pl _cp 
0 g _f _s _s 
0 g 1218 1895 _m
_sp 1218 1895 1231 1895 1230 1898 1229 1901 1226 1902 1223 1903 1220 1902 1217 1900 1216 1896 1215 1892 1216 1888 1217 1886 1220 1884 1223 1883 1226 1883 
1228 1885 1230 1887 1232 1890 1231 1890 1230 1889 1228 1887 1226 1886 1224 1885 1222 1886 1220 1888 1219 1890 1218 1894 1218 1895 28 _pl _cp 1226 1896 _m
_sp 1226 1896 1226 1898 1225 1900 1224 1901 1222 1901 1221 1901 1219 1900 1218 1898 1218 1896 9 _pl _cp 
0 g _f _s _s 
0 g 1239 1903 _m
_sp 1239 1903 1239 1903 1232 1901 1232 1900 1233 1900 1235 1899 1235 1897 1235 1887 1235 1885 1233 1884 1232 1884 1232 1883 1243 1883 1243 1884 1242 1884 
1239 1885 1239 1887 1239 1896 1240 1899 1241 1900 1242 1900 1243 1899 1244 1898 1244 1898 1245 1899 1246 1900 1245 1902 1244 1903 1243 1903 1242 1902 
1240 1901 1239 1899 32 _pl _cp 
0 g _f _s _s 
0 g 1247 1883 _m
_sp 1247 1883 1248 1883 1249 1884 1249 1884 1250 1884 1251 1883 1253 1883 1255 1883 1258 1883 1260 1884 1261 1886 1262 1888 1261 1890 1260 1892 1259 1893 
1258 1893 1256 1894 1254 1895 1251 1897 1250 1899 1251 1900 1254 1901 1256 1901 1258 1900 1259 1898 1260 1896 1260 1896 1260 1902 1260 1902 1259 1902 
1259 1902 1258 1902 1258 1902 1256 1902 1255 1903 1254 1903 1251 1903 1249 1901 1248 1900 1247 1898 1247 1896 1248 1894 1250 1893 1252 1892 1255 1890 
1258 1889 1259 1887 1258 1885 1255 1884 1253 1885 1251 1885 1250 1886 1249 1887 1249 1888 1248 1890 1247 1890 56 _pl _cp 
0 g _f _s _s 
0 g 1269 1913 _m
_sp 1269 1913 1269 1913 1263 1910 1263 1910 1263 1910 1265 1909 1266 1906 1266 1887 1265 1885 1263 1884 1263 1884 1263 1883 1272 1883 1272 1884 1272 1884 
1270 1885 1269 1887 1269 1898 1271 1899 1272 1900 1273 1901 1274 1901 1275 1901 1276 1899 1277 1897 1277 1894 1277 1887 1276 1885 1275 1884 1274 1884 
1274 1883 1284 1883 1284 1884 1283 1884 1281 1885 1281 1887 1281 1896 1281 1899 1280 1901 1278 1902 1275 1903 1274 1903 1272 1902 1271 1901 1269 1900 
45 _pl _cp 
0 g _f _s _s 
0 g 1291 1903 _m
_sp 1291 1903 1291 1903 1285 1901 1285 1900 1285 1900 1287 1899 1288 1897 1288 1887 1287 1885 1285 1884 1285 1884 1285 1883 1295 1883 1295 1884 1294 1884 
1292 1885 1291 1887 17 _pl _cp 1287 1910 _m
_sp 1287 1910 1288 1908 1289 1907 1291 1908 1292 1910 1291 1912 1289 1913 1288 1912 8 _pl _cp 
0 g _f _s _s 
0 g 1302 1900 _m
_sp 1302 1900 1302 1903 1302 1903 1296 1901 1296 1900 1296 1900 1298 1899 1299 1896 1299 1879 1298 1876 1296 1876 1296 1876 1296 1875 1306 1875 1306 1876 
1305 1876 1303 1876 1302 1879 1302 1884 1304 1883 1306 1883 1310 1884 1312 1886 1314 1890 1315 1894 1315 1898 1313 1900 1311 1902 1308 1903 1307 1903 
1305 1902 1304 1901 32 _pl _cp 1302 1898 _m
_sp 1302 1898 1302 1887 1303 1886 1305 1885 1306 1884 1307 1884 1309 1885 1311 1886 1312 1889 1312 1892 1312 1895 1311 1898 1309 1899 1307 1900 1305 1899 
15 _pl _cp 
0 g _f _s 
_s 0 g 0 0 0 0 _cw 
_s grestore 1608 2187 _m
/Times-BoldR 600 _ff
(Figure)_S 67 _t
(6.7)_S /Times-RomanR 600 _ff
(.)_S 134 _t
(General)_S 67 _t
(real-time)_S 67 _t
(DIS-networked)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(class)_S 67 _t
(hierarchy.)_S 4950 1288 _m
(164)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
gsave 4 4 scale 16 _sr _s 
_s [] 0 _d 2 _lc 0 g _s 375 1619 _m
_sp 2174 1619 2174 1622 375 1622 3 _pl _pf _np _s _s 2171 1619 _m
_sp 2174 1619 2174 2999 2171 2999 3 _pl _pf _np _s _s 375 2996 _m
_sp 2174 2996 2174 2999 375 2999 3 _pl _pf _np _s _s 375 1619 _m
_sp 378 1619 378 2999 375 2999 3 _pl _pf _np 
_s 0 g 1312 1731 409 1653 _cw 

_s 12 _w 0 g 450 2801 _m
450 1687 _l 450 1687 _m
2099 1687 _l 2099 1687 _m
2099 2801 _l 2099 2801 _m
450 2801 _l 450 2594 _m
2099 2594 _l 450 1935 _m
2099 1935 _l 450 2931 _m
450 2866 _l 450 2866 _m
2097 2864 _l 2097 2864 _m
2097 2931 _l 2097 2931 _m
450 2931 _l 
_s 5 _w 0 g 450 2677 _m
2099 2677 _l 450 2471 _m
2099 2471 _l 450 1811 _m
2099 1811 _l _s 
1 _w 0 g 492 2916 _m
_sp 492 2916 491 2915 490 2914 490 2914 489 2914 487 2915 485 2916 482 2916 477 2915 474 2913 471 2910 469 2906 468 2902 469 2897 471 2893 
474 2890 477 2888 482 2887 485 2887 488 2889 491 2890 494 2893 493 2894 491 2893 490 2891 489 2890 487 2890 486 2889 484 2889 480 2890 
477 2892 476 2896 475 2902 475 2905 476 2908 477 2910 478 2912 479 2913 480 2914 482 2915 483 2915 485 2915 486 2914 488 2913 489 2912 
490 2911 491 2909 491 2908 492 2906 493 2906 493 2916 51 _pl _cp 
0 g _f _s _s 
0 g 505 2916 _m
_sp 505 2916 497 2916 497 2915 498 2915 499 2914 499 2913 500 2913 500 2911 500 2892 500 2891 500 2890 499 2890 499 2889 499 2889 498 2889 
497 2889 497 2888 507 2888 507 2889 507 2889 507 2889 506 2889 505 2890 505 2892 24 _pl _cp 
0 g _f _s _s 
0 g 520 2899 _m
_sp 520 2899 518 2898 516 2898 514 2897 513 2897 511 2896 510 2894 509 2893 509 2891 509 2890 510 2888 512 2887 514 2887 516 2887 517 2888 
519 2889 520 2890 521 2888 523 2887 526 2888 528 2889 527 2890 527 2890 526 2890 526 2890 526 2891 526 2893 526 2901 525 2903 524 2905 
523 2906 522 2906 520 2907 518 2907 515 2907 512 2906 511 2904 510 2902 511 2900 512 2899 514 2900 515 2901 515 2902 514 2903 514 2904 
514 2904 515 2905 517 2906 518 2906 519 2905 520 2903 520 2901 520 2900 53 _pl _cp 520 2897 _m
_sp 520 2897 520 2892 519 2890 517 2890 516 2891 515 2893 515 2895 517 2896 518 2897 9 _pl _cp 
0 g _f _s _s 
0 g 530 2887 _m
_sp 530 2887 531 2887 532 2888 532 2888 533 2888 533 2888 535 2887 537 2887 540 2888 542 2889 543 2891 543 2893 543 2895 542 2897 541 2898 
539 2899 539 2899 538 2900 537 2900 537 2900 536 2901 535 2901 534 2903 534 2904 535 2905 537 2906 539 2905 540 2904 541 2903 542 2901 
543 2901 543 2907 542 2907 541 2906 541 2906 540 2906 538 2906 537 2907 536 2907 534 2906 532 2905 531 2903 530 2901 530 2899 531 2898 
532 2896 534 2895 538 2894 539 2893 540 2891 539 2889 536 2888 535 2889 533 2890 532 2892 531 2894 530 2894 57 _pl _cp 
0 g _f _s _s 
0 g 546 2887 _m
_sp 546 2887 547 2887 548 2888 548 2888 549 2888 550 2888 552 2887 553 2887 556 2888 558 2889 559 2891 560 2893 559 2895 558 2897 557 2898 
555 2899 555 2899 554 2900 553 2900 553 2900 552 2901 551 2901 550 2903 550 2904 551 2905 553 2906 555 2905 556 2904 557 2903 558 2901 
559 2901 559 2907 558 2907 558 2906 557 2906 556 2906 554 2906 553 2907 552 2907 550 2906 548 2905 547 2903 546 2901 546 2899 547 2898 
548 2896 550 2895 554 2894 555 2893 556 2891 555 2889 553 2888 551 2889 549 2890 548 2892 547 2894 546 2894 57 _pl _cp 
0 g _f _s _s 
0 g 586 2916 _m
_sp 586 2916 577 2916 577 2914 578 2914 580 2914 581 2912 581 2912 581 2909 581 2894 581 2892 581 2891 581 2891 581 2890 580 2889 578 2889 
577 2889 577 2888 587 2888 587 2889 586 2889 584 2889 583 2891 583 2891 583 2894 583 2909 601 2887 602 2887 602 2909 602 2911 602 2912 
602 2913 603 2913 604 2914 605 2914 606 2914 606 2916 596 2916 596 2914 598 2914 599 2914 600 2912 600 2912 600 2909 600 2898 44 _pl _cp 
0 g _f _s _s 
0 g 619 2899 _m
_sp 619 2899 616 2898 614 2898 613 2897 612 2897 610 2896 609 2894 608 2893 608 2891 609 2888 612 2887 614 2887 616 2888 617 2889 619 2890 
620 2888 622 2887 625 2888 627 2889 626 2890 626 2890 625 2890 625 2890 624 2891 624 2893 624 2901 624 2903 623 2905 621 2906 620 2906 
618 2907 616 2907 613 2907 611 2906 609 2904 608 2902 609 2900 611 2899 613 2900 614 2901 614 2902 613 2903 613 2904 612 2904 613 2905 
615 2906 617 2906 618 2905 619 2903 619 2901 619 2900 51 _pl _cp 619 2897 _m
_sp 619 2897 619 2892 618 2890 616 2890 614 2891 613 2893 614 2895 615 2896 617 2897 9 _pl _cp 
0 g _f _s _s 
0 g 636 2906 _m
_sp 636 2906 628 2906 628 2905 629 2905 630 2904 630 2904 630 2901 630 2892 630 2891 630 2890 630 2890 630 2889 629 2889 628 2889 628 2889 
628 2888 638 2888 638 2889 638 2889 637 2889 636 2890 636 2890 636 2892 636 2902 638 2904 639 2904 641 2903 641 2901 641 2892 641 2891 
641 2890 641 2890 641 2889 641 2889 640 2889 639 2889 639 2888 649 2888 649 2889 649 2889 648 2889 647 2890 647 2890 647 2892 647 2902 
649 2903 651 2904 652 2904 652 2903 653 2902 653 2901 653 2892 653 2891 653 2890 652 2890 652 2889 652 2889 651 2889 650 2889 650 2888 
660 2888 660 2889 660 2889 659 2889 658 2890 658 2890 658 2892 658 2901 658 2903 657 2905 655 2906 653 2907 652 2907 650 2906 649 2905 
647 2903 646 2905 645 2906 644 2907 642 2907 640 2906 638 2905 637 2904 636 2903 84 _pl _cp 
0 g _f _s _s 
0 g 669 2897 _m
_sp 669 2897 679 2897 679 2900 678 2901 678 2903 677 2904 676 2905 675 2906 673 2907 671 2907 668 2906 665 2904 664 2901 663 2897 664 2893 
665 2890 668 2888 671 2887 673 2887 675 2888 677 2890 679 2892 678 2893 676 2891 674 2890 672 2890 670 2891 669 2892 669 2894 669 2895 
30 _pl _cp 668 2899 _m
_sp 668 2899 668 2902 669 2904 670 2906 671 2906 672 2906 673 2905 674 2903 674 2900 674 2899 10 _pl _cp 
0 g _f _s _s 
0 g 683 2890 _m
_sp 683 2890 684 2888 687 2887 689 2888 690 2890 689 2893 687 2894 684 2893 8 _pl _cp 683 2903 _m
_sp 683 2903 684 2901 687 2900 689 2901 690 2903 689 2906 687 2907 684 2906 8 _pl _cp 
0 g _f _s _s 
0 g 481 2773 _m
_sp 481 2773 474 2773 474 2773 475 2772 476 2771 476 2771 476 2769 476 2760 476 2758 476 2758 476 2757 475 2756 475 2756 474 2756 474 2756 
474 2755 484 2755 484 2756 483 2756 483 2756 482 2757 481 2758 481 2760 481 2769 483 2771 485 2771 486 2770 487 2768 487 2760 487 2758 
487 2758 487 2757 487 2756 486 2756 485 2756 485 2756 485 2755 495 2755 495 2756 495 2756 494 2756 493 2757 493 2758 493 2760 493 2769 
495 2771 496 2771 497 2771 498 2770 498 2769 498 2768 498 2760 498 2758 498 2758 498 2757 498 2756 497 2756 496 2756 496 2756 496 2755 
506 2755 506 2756 506 2756 505 2756 504 2757 504 2758 504 2760 504 2768 504 2770 503 2772 501 2773 498 2774 497 2774 496 2773 494 2772 
493 2770 492 2772 491 2773 489 2774 488 2774 486 2774 484 2773 483 2772 481 2770 84 _pl _cp 
0 g _f _s _s 
0 g 514 2765 _m
_sp 514 2765 524 2765 524 2767 524 2768 524 2770 523 2771 522 2772 520 2773 519 2774 517 2774 513 2773 511 2771 509 2768 508 2764 509 2760 
511 2757 513 2755 517 2754 519 2754 521 2755 523 2757 525 2759 524 2760 523 2759 522 2758 520 2757 519 2757 518 2758 516 2758 515 2759 
515 2761 514 2763 32 _pl _cp 514 2766 _m
_sp 514 2766 514 2769 515 2771 516 2773 517 2773 518 2772 519 2768 519 2766 8 _pl _cp 
0 g _f _s _s 
0 g 534 2773 _m
_sp 534 2773 526 2773 526 2773 527 2772 528 2771 529 2771 529 2769 529 2760 529 2758 529 2758 528 2757 528 2756 528 2756 527 2756 526 2756 
526 2755 536 2755 536 2756 536 2756 535 2756 534 2757 534 2758 534 2760 534 2769 536 2771 538 2771 539 2770 540 2768 540 2760 540 2758 
540 2758 539 2757 539 2756 539 2756 538 2756 537 2756 537 2755 547 2755 547 2756 547 2756 546 2756 545 2757 545 2758 545 2760 545 2769 
547 2771 549 2771 550 2771 550 2770 551 2769 551 2768 551 2760 551 2758 551 2758 551 2757 550 2756 550 2756 549 2756 549 2756 549 2755 
559 2755 559 2756 558 2756 558 2756 557 2757 556 2758 556 2760 556 2768 556 2770 555 2772 553 2773 551 2774 550 2774 548 2773 547 2772 
545 2770 545 2772 544 2773 542 2774 540 2774 538 2774 536 2773 535 2772 534 2770 84 _pl _cp 
0 g _f _s _s 
0 g 569 2783 _m
_sp 569 2783 561 2783 561 2782 562 2781 563 2780 563 2780 563 2778 563 2755 564 2754 567 2756 570 2755 572 2754 576 2755 578 2757 580 2760 
581 2764 580 2768 579 2771 577 2773 574 2774 571 2773 569 2772 22 _pl _cp 569 2770 _m
_sp 569 2770 571 2771 572 2772 573 2771 574 2770 575 2767 575 2764 575 2760 574 2758 573 2756 571 2756 569 2757 569 2760 13 _pl _cp 
0 g _f _s _s 
0 g 590 2765 _m
_sp 590 2765 600 2765 600 2767 599 2768 599 2770 598 2771 597 2772 596 2773 594 2774 592 2774 589 2773 586 2771 585 2768 584 2764 585 2760 
586 2757 589 2755 592 2754 595 2754 597 2755 598 2757 600 2759 599 2760 597 2758 595 2757 593 2758 592 2758 591 2759 590 2761 590 2763 
30 _pl _cp 589 2766 _m
_sp 589 2766 590 2769 590 2771 591 2773 592 2773 593 2773 594 2772 595 2770 595 2768 595 2766 10 _pl _cp 
0 g _f _s _s 
0 g 610 2773 _m
_sp 610 2773 602 2773 602 2773 602 2773 603 2772 604 2771 604 2771 604 2769 604 2760 604 2758 604 2758 604 2757 604 2756 603 2756 602 2756 
602 2756 602 2755 613 2755 613 2756 612 2756 611 2756 610 2757 610 2758 610 2760 610 2765 610 2767 611 2769 612 2770 613 2770 614 2770 
615 2769 616 2768 616 2768 618 2769 619 2771 618 2773 616 2774 615 2774 613 2773 612 2772 610 2770 41 _pl _cp 
0 g _f _s _s 
0 g 649 2772 _m
_sp 649 2772 647 2773 645 2774 642 2773 639 2771 638 2768 637 2764 638 2760 639 2757 641 2755 644 2754 645 2754 647 2755 648 2756 649 2757 
649 2754 651 2755 653 2755 655 2755 657 2755 657 2756 656 2757 655 2759 655 2783 646 2783 646 2782 647 2782 648 2781 649 2780 649 2780 
649 2778 31 _pl _cp 649 2770 _m
_sp 649 2770 649 2760 648 2758 646 2757 645 2757 644 2758 643 2759 643 2760 643 2762 643 2764 643 2766 643 2768 643 2769 644 2770 645 2771 
646 2772 648 2771 17 _pl _cp 
0 g _f _s _s 
0 g 670 2766 _m
_sp 670 2766 668 2765 666 2765 665 2765 664 2764 662 2763 660 2762 659 2760 659 2758 659 2757 660 2755 662 2754 664 2754 666 2754 667 2755 
669 2756 670 2757 672 2755 674 2754 676 2755 678 2757 678 2758 677 2757 677 2757 676 2758 676 2758 676 2761 676 2768 676 2770 674 2772 
673 2773 672 2773 670 2774 668 2774 665 2774 662 2773 661 2771 660 2769 661 2767 663 2766 665 2767 666 2769 666 2770 665 2770 664 2771 
664 2771 665 2772 667 2773 669 2773 670 2772 670 2770 670 2768 670 2767 53 _pl _cp 670 2765 _m
_sp 670 2765 670 2759 669 2758 667 2757 666 2758 665 2760 666 2762 667 2763 669 2764 9 _pl _cp 
0 g _f _s _s 
0 g 680 2773 _m
_sp 680 2773 680 2772 682 2772 682 2759 682 2757 683 2756 685 2755 686 2754 688 2754 690 2755 691 2757 692 2759 691 2759 690 2757 689 2757 
688 2758 687 2759 687 2772 691 2772 691 2773 687 2773 687 2781 686 2781 684 2778 683 2776 681 2775 26 _pl _cp 
0 g _f _s _s 
0 g 705 2766 _m
_sp 705 2766 702 2765 700 2765 699 2765 698 2764 696 2763 695 2762 694 2760 694 2758 695 2755 698 2754 700 2754 702 2755 703 2756 705 2757 
706 2755 708 2754 709 2754 711 2755 712 2756 713 2757 712 2758 712 2757 711 2757 711 2758 710 2758 710 2761 710 2768 710 2770 709 2772 
707 2773 706 2773 704 2774 702 2774 699 2774 697 2773 695 2771 694 2769 695 2767 697 2766 699 2767 700 2769 700 2770 699 2770 699 2771 
699 2771 700 2772 701 2773 703 2773 704 2772 705 2770 705 2768 705 2767 53 _pl _cp 705 2765 _m
_sp 705 2765 705 2759 704 2758 702 2757 700 2758 700 2760 700 2762 701 2763 703 2764 9 _pl _cp 
0 g _f _s _s 
0 g 742 2755 _m
_sp 742 2755 742 2756 740 2756 739 2756 738 2757 738 2758 738 2760 738 2772 742 2772 742 2773 738 2773 738 2775 738 2779 739 2781 740 2782 
741 2782 741 2781 741 2781 741 2780 741 2780 741 2779 742 2777 743 2776 745 2777 746 2779 746 2781 745 2782 743 2783 740 2783 739 2783 
737 2783 736 2782 734 2781 733 2780 733 2779 732 2777 732 2775 732 2773 730 2773 730 2772 732 2772 732 2760 732 2758 732 2758 732 2757 
732 2756 731 2756 730 2756 730 2756 730 2755 50 _pl _cp 
0 g _f _s _s 
0 g 752 2773 _m
_sp 752 2773 744 2773 744 2773 744 2773 745 2772 746 2771 746 2771 746 2769 746 2760 746 2758 746 2758 746 2757 746 2756 745 2756 744 2756 
744 2756 744 2755 754 2755 754 2756 754 2756 753 2756 752 2757 752 2758 752 2760 24 _pl _cp 752 2780 _m
_sp 752 2780 751 2782 749 2783 747 2782 746 2780 747 2778 749 2777 751 2778 8 _pl _cp 
0 g _f _s _s 
0 g 761 2765 _m
_sp 761 2765 772 2765 772 2767 771 2768 771 2770 770 2771 769 2772 767 2773 766 2774 764 2774 760 2773 758 2771 756 2768 755 2764 756 2760 
758 2757 760 2755 764 2754 766 2754 768 2755 770 2757 772 2759 771 2760 770 2759 769 2758 767 2757 766 2757 765 2758 763 2758 762 2759 
762 2761 762 2763 32 _pl _cp 761 2766 _m
_sp 761 2766 761 2769 762 2771 763 2773 764 2773 765 2773 766 2772 767 2770 767 2768 767 2766 10 _pl _cp 
0 g _f _s _s 
0 g 782 2783 _m
_sp 782 2783 774 2783 774 2782 774 2782 775 2781 776 2780 776 2780 776 2778 776 2760 776 2758 776 2758 776 2757 776 2756 775 2756 774 2756 
774 2756 774 2755 784 2755 784 2756 783 2756 783 2756 782 2756 782 2757 782 2760 24 _pl _cp 
0 g _f _s _s 
0 g 798 2772 _m
_sp 798 2772 796 2773 793 2774 790 2773 788 2771 786 2768 785 2764 786 2760 788 2757 790 2755 793 2754 794 2754 796 2755 797 2756 798 2757 
798 2754 800 2755 802 2755 804 2755 806 2755 806 2756 804 2757 804 2759 804 2783 795 2783 795 2782 796 2782 797 2781 798 2780 798 2780 
798 2778 31 _pl _cp 798 2770 _m
_sp 798 2770 798 2760 797 2758 795 2757 794 2757 793 2758 792 2759 792 2760 791 2762 791 2764 791 2766 792 2768 792 2769 792 2770 794 2771 
795 2772 797 2771 17 _pl _cp 
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546 2572 549 2571 550 2568 550 2567 49 _pl _cp 550 2564 _m
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601 2570 602 2571 604 2572 606 2571 607 2568 607 2567 51 _pl _cp 607 2564 _m
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636 2557 636 2559 636 2567 636 2569 635 2571 633 2573 630 2573 629 2573 627 2572 626 2571 624 2569 56 _pl _cp 
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642 2556 644 2555 648 2554 650 2554 652 2555 654 2556 656 2558 655 2559 653 2557 650 2557 649 2557 647 2558 646 2559 646 2560 646 2562 
30 _pl _cp 645 2566 _m
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659 2568 16 _pl _cp 664 2565 _m
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666 2555 665 2555 664 2557 664 2560 664 2563 20 _pl _cp 
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733 2554 743 2554 743 2555 743 2555 742 2555 741 2556 741 2557 741 2559 741 2568 743 2570 745 2570 746 2570 747 2568 747 2559 747 2557 
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766 2554 766 2555 765 2555 765 2555 764 2556 764 2557 764 2559 764 2567 763 2569 762 2571 761 2573 758 2573 757 2573 755 2572 754 2571 
752 2569 752 2571 751 2572 749 2573 747 2573 745 2573 743 2572 742 2571 741 2569 84 _pl _cp 
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770 2556 773 2555 776 2554 779 2554 781 2555 782 2556 784 2558 783 2559 781 2557 779 2557 778 2557 776 2558 775 2559 775 2560 774 2562 
30 _pl _cp 774 2566 _m
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794 2557 794 2558 794 2571 798 2571 798 2573 794 2573 794 2580 793 2580 791 2577 790 2576 788 2574 26 _pl _cp 
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800 2555 800 2554 810 2554 810 2555 809 2555 808 2556 808 2557 808 2559 808 2568 810 2570 811 2570 812 2569 813 2568 813 2559 813 2557 
813 2557 813 2556 813 2556 812 2555 811 2555 811 2554 821 2554 821 2555 821 2555 820 2555 819 2556 819 2557 819 2559 819 2566 819 2568 
818 2570 817 2572 814 2573 812 2573 809 2572 809 2571 808 2570 52 _pl _cp 
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824 2568 16 _pl _cp 829 2565 _m
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831 2555 830 2555 830 2557 829 2560 829 2563 20 _pl _cp 
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860 2554 862 2554 864 2555 864 2556 863 2556 862 2558 862 2582 853 2582 853 2581 854 2581 856 2581 856 2580 856 2579 856 2577 29 _pl _cp 856 2569 _m
_sp 856 2569 856 2559 855 2557 853 2556 852 2556 851 2557 850 2558 850 2559 850 2561 850 2564 850 2567 851 2569 852 2570 853 2571 855 2571 
15 _pl _cp 
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876 2566 876 2566 875 2566 874 2567 874 2567 873 2568 872 2568 871 2569 871 2570 872 2571 874 2572 876 2572 877 2571 878 2569 879 2567 
880 2567 880 2573 879 2573 878 2573 878 2572 877 2573 875 2573 874 2573 873 2573 871 2573 869 2572 868 2570 867 2567 867 2566 868 2564 
869 2563 871 2562 875 2560 876 2559 877 2557 876 2556 873 2555 872 2555 870 2556 869 2558 868 2560 867 2560 57 _pl _cp 
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483 1896 483 1895 493 1895 493 1896 493 1896 492 1896 491 1897 491 1898 491 1900 24 _pl _cp 491 1920 _m
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494 1895 504 1895 504 1896 504 1896 503 1896 502 1897 502 1898 502 1900 502 1909 504 1911 506 1911 507 1910 508 1908 508 1900 508 1898 
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527 1895 527 1896 526 1896 525 1896 525 1897 524 1898 524 1900 524 1908 524 1910 523 1912 521 1913 519 1914 518 1914 516 1913 515 1912 
513 1910 513 1912 512 1913 510 1914 508 1914 506 1914 504 1913 503 1912 502 1910 84 _pl _cp 
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531 1897 534 1895 537 1894 540 1894 542 1895 543 1897 545 1899 544 1900 542 1898 540 1897 538 1898 537 1898 536 1899 535 1901 535 1903 
30 _pl _cp 534 1906 _m
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574 1907 575 1908 576 1909 576 1911 575 1913 573 1914 570 1914 566 1913 564 1911 562 1908 561 1904 562 1900 563 1897 566 1895 569 1894 
571 1894 573 1895 575 1897 577 1899 34 _pl _cp 
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580 1908 16 _pl _cp 585 1906 _m
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588 1896 587 1896 586 1898 585 1901 585 1903 20 _pl _cp 
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619 1898 619 1900 619 1908 619 1910 618 1912 616 1913 613 1914 612 1914 610 1913 609 1912 607 1910 56 _pl _cp 
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632 1906 632 1907 631 1907 630 1907 630 1907 629 1908 628 1909 627 1910 627 1911 628 1912 630 1913 632 1912 633 1911 634 1910 635 1908 
636 1908 636 1914 635 1914 634 1913 634 1913 633 1913 631 1914 630 1914 629 1914 627 1913 625 1912 624 1910 623 1908 623 1907 624 1905 
625 1904 627 1903 631 1901 632 1900 633 1898 632 1896 630 1896 628 1896 626 1897 625 1899 624 1901 623 1901 57 _pl _cp 
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651 1896 652 1897 652 1894 654 1895 655 1895 657 1895 658 1895 660 1895 660 1896 658 1897 657 1899 657 1901 657 1913 649 1913 649 1912 
650 1912 651 1912 652 1911 652 1910 652 1909 652 1899 650 1897 648 1897 647 1898 646 1900 40 _pl _cp 
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662 1895 672 1895 672 1896 671 1896 670 1896 670 1897 669 1898 669 1900 669 1909 671 1911 673 1911 674 1910 675 1908 675 1900 675 1898 
675 1898 675 1897 674 1896 674 1896 673 1896 673 1896 673 1895 683 1895 683 1896 682 1896 682 1896 681 1897 681 1898 681 1900 681 1909 
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694 1895 694 1896 694 1896 693 1896 692 1897 692 1898 692 1900 692 1908 692 1910 691 1912 689 1913 686 1914 685 1914 684 1913 682 1912 
681 1910 680 1912 679 1913 677 1914 676 1914 674 1914 671 1913 670 1912 669 1910 84 _pl _cp 
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696 1896 696 1895 706 1895 706 1896 706 1896 705 1896 704 1897 704 1898 704 1900 24 _pl _cp 704 1920 _m
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721 1908 721 1900 721 1898 721 1898 721 1897 720 1896 720 1896 719 1896 719 1896 719 1895 729 1895 729 1896 728 1896 728 1896 727 1897 
726 1898 726 1900 726 1908 726 1910 725 1912 724 1913 721 1914 720 1914 718 1913 717 1912 715 1910 56 _pl _cp 
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746 1897 743 1897 738 1897 737 1898 736 1899 736 1900 738 1901 740 1901 742 1901 743 1901 745 1902 746 1903 747 1905 748 1907 747 1909 
746 1911 749 1911 749 1913 744 1913 742 1914 740 1914 736 1914 734 1913 732 1911 731 1908 731 1906 732 1904 734 1903 736 1901 734 1900 
732 1899 731 1897 731 1896 732 1895 49 _pl _cp 736 1892 _m
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767 1895 777 1895 777 1896 777 1896 776 1896 775 1897 775 1898 775 1900 775 1909 777 1911 778 1911 780 1910 780 1908 780 1900 780 1898 
780 1898 780 1897 780 1896 779 1896 778 1896 778 1896 778 1895 788 1895 788 1896 788 1896 787 1896 786 1897 786 1898 786 1900 786 1909 
788 1911 789 1911 790 1911 791 1910 791 1909 791 1908 791 1900 791 1898 791 1898 791 1897 791 1896 791 1896 790 1896 789 1896 789 1895 
799 1895 799 1896 799 1896 798 1896 797 1897 797 1898 797 1900 797 1908 797 1910 796 1912 794 1913 792 1914 790 1914 789 1913 787 1912 
786 1910 785 1912 784 1913 783 1914 781 1914 779 1914 777 1913 776 1912 775 1910 84 _pl _cp 
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804 1897 806 1895 810 1894 812 1894 814 1895 816 1897 818 1899 817 1900 816 1899 815 1898 813 1897 812 1897 811 1898 809 1898 808 1899 
808 1901 808 1903 32 _pl _cp 807 1906 _m
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828 1898 827 1899 827 1911 831 1911 831 1913 827 1913 827 1921 826 1921 824 1918 823 1916 821 1915 26 _pl _cp 
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833 1896 833 1895 843 1895 843 1896 842 1896 841 1897 841 1898 841 1900 841 1909 843 1911 845 1911 846 1910 847 1909 847 1900 847 1898 
847 1898 847 1897 846 1896 846 1896 845 1896 845 1895 855 1895 855 1896 854 1896 854 1896 853 1897 852 1898 852 1900 852 1907 852 1909 
852 1911 851 1912 850 1913 848 1914 847 1914 845 1914 843 1913 842 1912 841 1911 54 _pl _cp 
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857 1908 16 _pl _cp 862 1906 _m
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865 1896 864 1896 863 1898 863 1901 862 1903 20 _pl _cp 
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890 1894 892 1895 894 1895 896 1895 898 1895 898 1896 896 1897 896 1899 896 1923 887 1923 887 1922 888 1922 889 1921 890 1920 890 1920 
890 1918 31 _pl _cp 890 1910 _m
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887 1912 889 1911 17 _pl _cp 
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913 1908 913 1914 912 1914 912 1913 911 1913 910 1913 909 1914 908 1914 907 1914 904 1913 902 1912 901 1910 900 1908 900 1907 901 1905 
903 1904 904 1903 908 1901 909 1900 910 1898 909 1896 907 1896 905 1896 903 1897 902 1899 901 1901 900 1901 57 _pl _cp 
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480 2826 484 2837 485 2839 487 2839 487 2840 482 2840 482 2839 483 2839 483 2838 483 2838 483 2838 483 2838 483 2838 483 2838 483 2837 
30 _pl _cp 
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493 2827 493 2829 17 _pl _cp 490 2846 _m
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663 2399 663 2402 663 2408 664 2410 664 2411 665 2411 665 2410 666 2410 667 2410 668 2410 668 2411 667 2412 666 2413 665 2412 663 2411 
30 _pl _cp 
0 g _f _s _s 
0 g 673 2413 _m
_sp 673 2413 668 2413 668 2412 668 2412 670 2412 670 2410 670 2403 670 2401 671 2399 673 2398 674 2398 677 2399 679 2400 679 2398 679 2398 
684 2399 684 2400 682 2400 682 2402 682 2413 676 2413 676 2412 677 2412 678 2412 679 2410 679 2402 677 2400 675 2400 674 2401 673 2404 
30 _pl _cp 
0 g _f _s _s 
0 g 697 2403 _m
_sp 697 2403 695 2401 692 2401 691 2401 689 2402 688 2404 688 2406 688 2409 689 2411 690 2412 692 2412 693 2412 694 2410 694 2409 695 2408 
696 2409 697 2410 697 2411 696 2412 694 2413 692 2413 689 2412 687 2411 686 2408 685 2405 686 2402 687 2400 689 2399 691 2398 693 2399 
695 2400 696 2401 697 2403 33 _pl _cp 
0 g _f _s _s 
0 g 699 2412 _m
_sp 699 2412 699 2411 700 2411 700 2402 701 2399 703 2398 705 2399 707 2401 707 2401 706 2400 705 2400 704 2401 703 2402 703 2411 706 2411 
706 2413 703 2413 703 2417 703 2417 702 2415 700 2414 700 2413 22 _pl _cp 
0 g _f _s _s 
0 g 708 2405 _m
_sp 708 2405 709 2402 710 2400 712 2399 715 2398 718 2399 721 2401 722 2403 723 2406 722 2409 721 2411 718 2412 715 2413 712 2412 710 2411 
709 2408 16 _pl _cp 711 2407 _m
_sp 711 2407 711 2404 712 2401 714 2400 716 2399 717 2399 719 2401 720 2402 720 2405 720 2408 719 2410 717 2411 715 2412 714 2412 712 2411 
711 2409 711 2407 711 2407 18 _pl _cp 
0 g _f _s _s 
0 g 729 2413 _m
_sp 729 2413 728 2413 723 2412 723 2411 724 2411 725 2410 726 2409 726 2402 725 2399 724 2399 723 2399 723 2398 732 2398 732 2399 731 2399 
729 2399 729 2402 729 2408 730 2410 730 2411 731 2411 731 2410 732 2410 733 2410 734 2410 734 2411 733 2412 732 2413 731 2412 729 2411 
30 _pl _cp 
0 g _f _s _s 
0 g 735 2398 _m
_sp 735 2398 736 2398 736 2399 736 2399 737 2399 738 2398 740 2398 741 2398 743 2398 744 2399 746 2401 746 2402 745 2404 744 2405 743 2406 
740 2407 738 2409 737 2410 738 2411 740 2412 742 2411 744 2408 745 2408 745 2413 744 2413 744 2413 743 2413 743 2413 743 2413 742 2413 
741 2413 740 2413 738 2413 736 2412 735 2410 735 2409 736 2407 739 2405 741 2404 743 2403 743 2401 742 2400 741 2399 739 2399 737 2400 
736 2402 736 2403 735 2403 48 _pl _cp 
0 g _f _s _s 
0 g 627 2337 _m
_sp 627 2337 628 2334 629 2332 631 2331 634 2330 637 2331 640 2333 641 2335 642 2338 641 2341 640 2343 638 2344 635 2345 632 2344 629 2343 
628 2340 16 _pl _cp 630 2339 _m
_sp 630 2339 630 2336 631 2333 633 2332 635 2331 636 2331 638 2333 639 2334 639 2337 639 2340 638 2342 636 2343 634 2344 633 2344 631 2343 
630 2341 630 2339 630 2339 18 _pl _cp 
0 g _f _s _s 
0 g 648 2343 _m
_sp 648 2343 648 2346 647 2346 643 2344 643 2343 643 2343 645 2343 645 2340 645 2327 645 2325 643 2325 643 2325 643 2324 651 2324 651 2325 
650 2325 648 2325 648 2327 648 2331 650 2330 651 2330 654 2331 656 2333 657 2335 658 2338 658 2341 657 2343 655 2344 652 2345 650 2344 
30 _pl _cp 648 2341 _m
_sp 648 2341 648 2333 650 2332 651 2331 652 2332 654 2333 655 2335 655 2337 655 2340 654 2342 652 2343 651 2343 650 2343 13 _pl _cp 
0 g _f _s _s 
0 g 662 2339 _m
_sp 662 2339 672 2339 671 2342 670 2344 668 2345 666 2345 663 2344 662 2343 660 2340 660 2337 660 2334 662 2332 663 2331 666 2330 668 2330 
670 2332 671 2333 672 2336 672 2336 671 2335 670 2333 669 2333 667 2332 665 2333 663 2334 662 2336 662 2339 662 2339 28 _pl _cp 668 2340 _m
_sp 668 2340 667 2343 665 2344 663 2343 662 2340 5 _pl _cp 
0 g _f _s _s 
0 g 678 2346 _m
_sp 678 2346 678 2346 673 2344 673 2343 674 2343 675 2343 675 2341 675 2334 675 2332 674 2331 673 2331 673 2331 681 2331 681 2331 680 2331 
678 2332 678 2334 678 2340 679 2342 680 2343 681 2343 681 2343 682 2342 682 2342 683 2343 684 2343 683 2344 682 2345 680 2344 678 2343 
30 _pl _cp 
0 g _f _s _s 
0 g 692 2340 _m
_sp 692 2340 691 2339 689 2338 688 2338 687 2337 686 2336 685 2335 685 2333 686 2331 688 2330 690 2331 692 2332 693 2331 695 2330 696 2331 
697 2332 697 2333 697 2332 696 2332 696 2332 695 2333 695 2340 695 2341 695 2341 695 2342 695 2343 693 2344 690 2345 688 2345 686 2344 
685 2343 685 2342 686 2341 687 2340 688 2341 688 2341 688 2342 688 2342 688 2343 688 2343 688 2343 689 2344 690 2344 692 2343 692 2341 
45 _pl _cp 692 2339 _m
_sp 692 2339 691 2338 688 2336 687 2334 688 2333 689 2332 691 2332 692 2333 8 _pl _cp 
0 g _f _s _s 
0 g 698 2344 _m
_sp 698 2344 698 2344 700 2344 700 2334 701 2331 703 2330 705 2331 707 2333 706 2333 706 2332 705 2332 703 2333 703 2334 703 2344 706 2344 
706 2345 703 2345 703 2349 702 2349 701 2347 700 2346 699 2345 22 _pl _cp 
0 g _f _s _s 
0 g 708 2337 _m
_sp 708 2337 709 2334 710 2332 712 2331 715 2330 718 2331 720 2333 721 2335 722 2338 721 2341 720 2343 718 2344 715 2345 712 2344 710 2343 
709 2340 16 _pl _cp 711 2339 _m
_sp 711 2339 711 2336 712 2333 714 2332 715 2331 717 2331 718 2333 719 2334 719 2337 719 2340 718 2342 716 2343 714 2344 713 2344 712 2343 
711 2341 711 2339 711 2339 18 _pl _cp 
0 g _f _s _s 
0 g 728 2346 _m
_sp 728 2346 728 2346 723 2344 723 2343 724 2343 725 2343 725 2341 725 2334 725 2332 724 2331 723 2331 723 2331 731 2331 731 2331 730 2331 
729 2332 728 2334 728 2340 729 2342 730 2343 731 2343 731 2343 732 2342 732 2342 733 2343 734 2343 733 2344 732 2345 730 2344 728 2343 
30 _pl _cp 
0 g _f _s _s 
0 g 735 2331 _m
_sp 735 2331 735 2331 736 2331 736 2331 736 2331 737 2331 739 2330 740 2330 742 2330 744 2331 745 2333 745 2334 745 2336 744 2337 743 2338 
740 2339 738 2341 737 2342 738 2343 740 2344 742 2343 744 2340 744 2340 744 2345 744 2345 743 2345 743 2345 743 2345 742 2345 741 2345 
741 2345 740 2345 738 2345 736 2344 735 2343 735 2341 736 2339 738 2337 741 2336 742 2335 743 2333 742 2332 740 2331 739 2332 737 2332 
736 2334 735 2335 735 2335 48 _pl _cp 
0 g _f _s _s 
0 g 517 2244 _m
_sp 517 2244 516 2244 511 2242 511 2241 512 2241 514 2241 514 2239 514 2232 514 2230 512 2229 511 2229 511 2229 519 2229 519 2229 518 2229 
517 2230 517 2232 517 2239 519 2241 520 2242 522 2241 522 2238 522 2232 522 2230 521 2229 520 2229 520 2229 527 2229 527 2229 527 2229 
525 2230 525 2232 525 2240 527 2241 529 2242 530 2241 531 2238 531 2232 531 2230 529 2229 529 2229 529 2229 536 2229 536 2229 536 2229 
534 2230 534 2232 534 2238 534 2240 533 2242 531 2243 530 2243 527 2243 525 2241 524 2242 522 2243 520 2243 517 2241 58 _pl _cp 
0 g _f _s _s 
0 g 539 2237 _m
_sp 539 2237 549 2237 549 2240 548 2242 546 2243 544 2243 541 2242 539 2241 538 2239 537 2236 537 2233 539 2230 540 2229 543 2228 545 2228 
547 2230 548 2231 550 2234 549 2234 548 2233 547 2231 546 2231 544 2230 542 2231 541 2232 540 2234 539 2237 539 2237 28 _pl _cp 546 2238 _m
_sp 546 2238 545 2241 543 2242 541 2241 539 2238 5 _pl _cp 
0 g _f _s _s 
0 g 556 2244 _m
_sp 556 2244 555 2244 551 2242 551 2241 551 2241 553 2241 553 2239 553 2232 553 2230 551 2229 551 2229 551 2229 558 2229 558 2229 558 2229 
556 2230 556 2232 556 2239 558 2241 559 2242 561 2241 561 2238 561 2232 561 2230 560 2229 559 2229 559 2229 566 2229 566 2229 566 2229 
565 2230 564 2232 564 2240 566 2241 568 2242 569 2241 570 2238 570 2232 570 2230 568 2229 568 2229 568 2229 575 2229 575 2229 575 2229 
573 2230 573 2232 573 2238 573 2240 572 2242 571 2243 569 2243 567 2243 564 2241 563 2242 561 2243 559 2243 556 2241 58 _pl _cp 
0 g _f _s _s 
0 g 580 2251 _m
_sp 580 2251 580 2251 575 2249 575 2249 576 2249 577 2248 578 2246 578 2230 580 2229 583 2228 586 2229 588 2231 589 2233 590 2236 590 2239 
589 2241 587 2242 585 2243 583 2243 580 2241 20 _pl _cp 580 2231 _m
_sp 580 2231 582 2230 584 2229 585 2230 587 2231 588 2233 588 2235 588 2238 587 2240 585 2241 584 2242 581 2241 580 2239 13 _pl _cp 
0 g _f _s _s 
0 g 595 2237 _m
_sp 595 2237 605 2237 604 2240 603 2242 601 2243 599 2243 596 2242 594 2241 593 2239 592 2236 593 2233 594 2230 596 2229 598 2228 600 2228 
602 2230 604 2231 605 2234 605 2234 604 2233 603 2231 602 2231 600 2230 598 2231 596 2232 595 2234 595 2237 595 2237 28 _pl _cp 601 2238 _m
_sp 601 2238 600 2241 598 2242 596 2241 595 2238 5 _pl _cp 
0 g _f _s _s 
0 g 611 2244 _m
_sp 611 2244 611 2244 606 2242 606 2241 606 2241 608 2241 608 2239 608 2232 608 2230 606 2229 606 2229 606 2229 614 2229 614 2229 613 2229 
611 2230 611 2232 611 2239 612 2240 613 2241 613 2241 614 2241 615 2240 615 2240 616 2241 616 2242 616 2243 614 2243 613 2243 611 2241 
30 _pl _cp 
0 g _f _s _s 
0 g 630 2243 _m
_sp 630 2243 628 2243 628 2242 630 2242 630 2232 630 2230 628 2229 628 2229 628 2229 636 2229 636 2229 635 2229 633 2230 633 2232 633 2242 
637 2242 637 2243 633 2243 633 2244 633 2247 634 2249 635 2250 636 2250 636 2249 637 2248 638 2247 639 2248 639 2249 638 2250 636 2251 
633 2250 632 2249 630 2247 630 2244 34 _pl _cp 
0 g _f _s _s 
0 g 643 2243 _m
_sp 643 2243 638 2243 638 2242 638 2242 640 2242 640 2240 640 2233 640 2231 641 2229 643 2228 644 2228 645 2228 647 2229 648 2230 649 2231 
649 2228 649 2228 654 2230 654 2230 652 2230 652 2233 652 2243 646 2243 646 2242 647 2242 648 2242 649 2240 649 2232 647 2231 645 2230 
644 2231 643 2234 32 _pl _cp 
0 g _f _s _s 
0 g 659 2244 _m
_sp 659 2244 659 2244 654 2242 654 2241 654 2241 656 2241 656 2239 656 2232 656 2230 654 2229 654 2229 654 2229 661 2229 661 2229 661 2229 
660 2230 659 2232 659 2239 661 2241 663 2242 664 2241 665 2237 665 2232 664 2230 663 2229 663 2229 663 2229 670 2229 670 2229 670 2229 
668 2230 668 2232 668 2239 667 2242 664 2243 662 2243 659 2241 37 _pl _cp 
0 g _f _s _s 
0 g 683 2234 _m
_sp 683 2234 682 2232 681 2231 679 2231 678 2231 677 2231 675 2233 674 2234 674 2237 674 2239 675 2241 676 2242 678 2242 679 2242 680 2240 
680 2239 681 2238 682 2239 683 2240 683 2241 682 2242 680 2243 678 2243 675 2242 673 2241 672 2239 671 2236 672 2233 673 2230 675 2229 
677 2228 679 2229 681 2230 682 2231 683 2233 35 _pl _cp 
0 g _f _s _s 
0 g 685 2242 _m
_sp 685 2242 685 2242 686 2242 686 2233 686 2231 687 2229 688 2228 689 2228 691 2229 693 2231 693 2231 692 2230 691 2230 690 2231 689 2232 
689 2242 692 2242 692 2243 689 2243 689 2247 689 2247 688 2245 686 2244 686 2243 24 _pl _cp 
0 g _f _s _s 
0 g 699 2244 _m
_sp 699 2244 699 2244 694 2242 694 2241 694 2241 696 2241 696 2239 696 2232 696 2230 694 2229 694 2229 694 2229 702 2229 702 2229 701 2229 
700 2230 699 2232 17 _pl _cp 696 2249 _m
_sp 696 2249 697 2248 698 2247 699 2248 699 2249 699 2250 698 2251 697 2250 8 _pl _cp 
0 g _f _s _s 
0 g 703 2236 _m
_sp 703 2236 704 2233 705 2230 707 2229 710 2228 713 2229 716 2231 717 2233 718 2236 717 2239 716 2241 713 2243 710 2243 707 2242 705 2241 
704 2239 16 _pl _cp 706 2237 _m
_sp 706 2237 706 2234 707 2231 709 2230 711 2229 712 2229 713 2231 714 2232 714 2235 714 2238 713 2240 712 2241 710 2242 708 2242 707 2241 
706 2239 706 2237 706 2237 18 _pl _cp 
0 g _f _s _s 
0 g 723 2244 _m
_sp 723 2244 723 2244 718 2242 718 2241 719 2241 720 2241 721 2239 721 2232 720 2230 719 2229 718 2229 718 2229 726 2229 726 2229 725 2229 
724 2230 723 2232 723 2239 725 2241 727 2242 729 2241 729 2237 729 2232 729 2230 727 2229 727 2229 727 2229 734 2229 734 2229 734 2229 
732 2230 732 2232 732 2239 731 2242 728 2243 726 2243 723 2241 37 _pl _cp 
0 g _f _s _s 
0 g 735 2229 _m
_sp 735 2229 736 2229 736 2229 736 2229 737 2229 738 2229 740 2228 741 2228 743 2228 745 2229 746 2231 746 2232 746 2234 745 2235 743 2236 
741 2237 738 2239 737 2240 738 2242 740 2242 743 2241 744 2238 745 2238 745 2243 744 2243 744 2243 744 2243 744 2243 743 2243 742 2243 
741 2243 740 2243 738 2243 736 2242 735 2241 735 2239 736 2237 739 2235 741 2234 743 2233 744 2231 743 2230 741 2229 740 2230 738 2230 
737 2232 736 2234 735 2234 48 _pl _cp 
0 g _f _s _s 
0 g 631 2013 _m
_sp 631 2013 631 2013 626 2012 626 2011 627 2011 628 2011 629 2009 629 2004 627 2005 625 2006 623 2005 621 2004 620 2001 619 1998 619 1995 
620 1993 622 1992 624 1991 627 1991 629 1992 629 1991 629 1991 634 1992 634 1993 633 1993 632 1993 631 1995 27 _pl _cp 629 1994 _m
_sp 629 1994 629 2000 629 2002 628 2004 627 2005 625 2005 624 2004 622 2003 621 2001 621 1999 621 1996 622 1994 624 1993 626 1992 628 1993 
15 _pl _cp 
0 g _f _s _s 
0 g 637 2000 _m
_sp 637 2000 647 2000 647 2002 646 2004 644 2005 641 2006 638 2005 637 2004 635 2001 635 1998 635 1995 637 1993 638 1991 641 1991 643 1991 
645 1992 646 1994 648 1996 647 1996 646 1995 645 1994 644 1993 642 1992 640 1993 638 1994 637 1996 637 1999 637 2000 28 _pl _cp 643 2001 _m
_sp 643 2001 642 2004 640 2005 638 2004 637 2001 5 _pl _cp 
0 g _f _s _s 
0 g 649 1991 _m
_sp 649 1991 649 1991 650 1991 650 1991 651 1991 652 1991 654 1991 655 1991 657 1991 658 1992 660 1993 660 1995 659 1997 658 1998 657 1998 
654 2000 652 2002 651 2003 652 2004 654 2005 656 2004 658 2001 659 2001 659 2005 658 2005 658 2005 657 2005 657 2005 657 2005 656 2005 
655 2006 654 2006 652 2006 650 2005 649 2003 649 2002 649 2001 650 2000 651 1998 653 1997 655 1996 657 1995 657 1994 656 1992 655 1992 
653 1992 651 1993 650 1994 649 1996 649 1996 50 _pl _cp 
0 g _f _s _s 
0 g 661 2005 _m
_sp 661 2005 661 2004 663 2004 663 1995 664 1992 666 1991 668 1991 669 1993 669 1994 668 1993 667 1992 666 1993 665 1995 665 2004 669 2004 
669 2005 665 2005 665 2009 665 2009 664 2008 663 2006 662 2005 22 _pl _cp 
0 g _f _s _s 
0 g 675 2006 _m
_sp 675 2006 674 2006 670 2004 670 2003 670 2003 672 2003 672 2001 672 1994 672 1992 670 1992 670 1992 670 1991 678 1991 678 1992 677 1992 
675 1992 675 1994 675 2001 676 2003 677 2003 677 2003 677 2003 678 2002 679 2002 680 2003 680 2004 679 2005 678 2006 677 2005 675 2003 
30 _pl _cp 
0 g _f _s _s 
0 g 685 2005 _m
_sp 685 2005 680 2005 680 2005 681 2005 682 2004 683 2002 683 1996 683 1994 684 1992 685 1991 687 1991 689 1991 691 1993 691 1991 692 1991 
696 1992 696 1993 694 1993 694 1995 694 2005 689 2005 689 2005 689 2005 691 2004 691 2002 691 1994 690 1993 688 1992 686 1993 685 1996 
30 _pl _cp 
0 g _f _s _s 
0 g 709 1996 _m
_sp 709 1996 707 1994 705 1993 703 1994 701 1995 700 1997 700 1999 700 2001 701 2003 703 2004 704 2005 705 2004 706 2003 707 2002 708 2001 
709 2001 709 2002 709 2003 708 2005 706 2006 704 2006 701 2005 699 2004 698 2001 697 1998 698 1995 699 1993 701 1992 703 1991 705 1991 
707 1992 709 1994 710 1996 33 _pl _cp 
0 g _f _s _s 
0 g 711 2005 _m
_sp 711 2005 711 2004 713 2004 713 1995 714 1992 716 1991 718 1991 719 1993 719 1994 718 1993 717 1992 716 1993 715 1995 715 2004 719 2004 
719 2005 715 2005 715 2009 715 2009 714 2008 713 2006 712 2005 22 _pl _cp 
0 g _f _s _s 
0 g 720 1998 _m
_sp 720 1998 721 1995 722 1993 725 1992 728 1991 731 1992 733 1993 734 1996 735 1999 734 2002 733 2004 731 2005 728 2006 725 2005 722 2004 
721 2001 16 _pl _cp 723 1999 _m
_sp 723 1999 723 1996 724 1994 726 1993 728 1992 729 1992 731 1993 732 1995 732 1997 732 2000 731 2003 729 2004 727 2005 726 2004 724 2003 
723 2001 723 1999 723 1999 18 _pl _cp 
0 g _f _s _s 
0 g 741 2006 _m
_sp 741 2006 740 2006 736 2004 736 2003 736 2003 738 2003 738 2001 738 1994 738 1992 736 1992 736 1992 736 1991 744 1991 744 1992 743 1992 
741 1992 741 1994 741 2001 742 2003 743 2003 743 2003 743 2003 744 2002 745 2002 746 2003 746 2004 745 2005 744 2006 743 2005 741 2003 
30 _pl _cp 
0 g _f _s _s 
0 g 1329 2902 _m
_sp 1329 2902 1323 2902 1323 2902 1323 2902 1324 2901 1324 2900 1325 2900 1325 2899 1325 2891 1325 2890 1325 2890 1325 2889 1324 2889 1324 2888 1323 2888 
1323 2888 1323 2887 1331 2887 1331 2888 1331 2888 1330 2889 1329 2889 1329 2890 1329 2891 24 _pl _cp 1329 2908 _m
_sp 1329 2908 1328 2909 1327 2910 1325 2909 1324 2908 1325 2906 1327 2905 1328 2906 8 _pl _cp 
0 g _f _s _s 
0 g 1338 2902 _m
_sp 1338 2902 1332 2902 1332 2902 1332 2902 1333 2901 1334 2900 1334 2900 1334 2899 1334 2891 1334 2890 1334 2890 1334 2889 1333 2889 1333 2888 1332 2888 
1332 2888 1332 2887 1340 2887 1340 2888 1340 2888 1339 2889 1338 2889 1338 2890 1338 2891 1338 2899 1340 2900 1341 2901 1342 2901 1342 2900 1343 2899 
1343 2898 1343 2891 1343 2890 1343 2890 1343 2889 1342 2889 1342 2888 1341 2888 1341 2888 1341 2887 1349 2887 1349 2888 1349 2888 1348 2889 1347 2889 
1347 2890 1347 2891 1347 2898 1347 2900 1347 2901 1345 2902 1343 2903 1342 2903 1341 2902 1339 2901 1338 2900 56 _pl _cp 
0 g _f _s _s 
0 g 1357 2910 _m
_sp 1357 2910 1350 2910 1350 2909 1351 2909 1352 2909 1352 2908 1352 2907 1352 2906 1352 2891 1352 2890 1352 2890 1352 2889 1352 2889 1351 2888 1351 2888 
1350 2888 1350 2887 1358 2887 1358 2888 1357 2889 1357 2889 1357 2890 1357 2891 1357 2899 1358 2900 1359 2901 1360 2900 1361 2898 1361 2891 1361 2890 
1361 2890 1361 2889 1361 2889 1360 2888 1359 2888 1359 2887 1367 2887 1367 2888 1367 2888 1366 2889 1366 2889 1366 2890 1366 2891 1366 2897 1366 2899 
1365 2900 1364 2902 1361 2903 1360 2903 1358 2902 1358 2901 1357 2900 52 _pl _cp 
0 g _f _s _s 
0 g 1373 2895 _m
_sp 1373 2895 1382 2895 1381 2898 1380 2900 1379 2901 1378 2902 1376 2903 1375 2903 1372 2902 1371 2901 1369 2898 1369 2895 1369 2892 1371 2889 1373 2888 
1376 2887 1378 2887 1379 2888 1381 2889 1382 2891 1381 2892 1379 2890 1377 2889 1376 2890 1375 2890 1374 2892 26 _pl _cp 1373 2897 _m
_sp 1373 2897 1373 2899 1374 2901 1375 2902 1376 2902 1377 2901 1378 2898 1378 2897 8 _pl _cp 
0 g _f _s _s 
0 g 1390 2902 _m
_sp 1390 2902 1383 2902 1383 2902 1384 2902 1385 2901 1385 2900 1385 2900 1385 2899 1385 2891 1385 2890 1385 2890 1385 2889 1385 2889 1384 2888 1384 2888 
1383 2888 1383 2887 1392 2887 1392 2888 1391 2888 1390 2889 1390 2889 1390 2890 1390 2891 1390 2896 1391 2899 1392 2900 1393 2900 1393 2899 1394 2898 
1395 2898 1396 2899 1397 2900 1396 2902 1394 2903 1392 2902 1390 2900 37 _pl _cp 
0 g _f _s _s 
0 g 1404 2902 _m
_sp 1404 2902 1398 2902 1398 2902 1398 2902 1399 2901 1400 2900 1400 2900 1400 2899 1400 2891 1400 2890 1400 2890 1400 2889 1399 2889 1399 2888 1398 2888 
1398 2888 1398 2887 1406 2887 1406 2888 1406 2888 1405 2889 1404 2889 1404 2890 1404 2891 24 _pl _cp 1405 2908 _m
_sp 1405 2908 1404 2909 1402 2910 1400 2909 1399 2908 1400 2906 1402 2905 1404 2906 8 _pl _cp 
0 g _f _s _s 
0 g 1407 2902 _m
_sp 1407 2902 1407 2901 1409 2901 1409 2891 1409 2889 1410 2888 1411 2887 1412 2887 1414 2887 1415 2888 1416 2889 1417 2891 1416 2891 1416 2889 1415 2889 
1414 2890 1413 2891 1413 2901 1416 2901 1416 2902 1413 2902 1413 2908 1412 2908 1411 2906 1410 2905 1408 2903 26 _pl _cp 
0 g _f _s _s 
0 g 1419 2887 _m
_sp 1419 2887 1419 2887 1420 2888 1420 2888 1421 2888 1421 2888 1423 2887 1424 2887 1426 2888 1428 2888 1429 2890 1429 2892 1429 2894 1428 2895 1427 2896 
1426 2897 1426 2897 1425 2897 1424 2898 1424 2898 1423 2898 1423 2899 1422 2900 1422 2900 1423 2901 1424 2902 1426 2902 1427 2901 1427 2900 1428 2898 
1429 2898 1429 2903 1428 2903 1428 2902 1427 2902 1426 2902 1425 2903 1425 2903 1424 2903 1422 2903 1420 2902 1419 2900 1419 2898 1420 2896 1422 2894 
1425 2892 1426 2891 1426 2890 1425 2889 1424 2888 1423 2889 1421 2889 1420 2891 1419 2892 1419 2892 55 _pl _cp 
0 g _f _s _s 
0 g 1433 2890 _m
_sp 1433 2890 1434 2888 1436 2887 1437 2888 1438 2890 1437 2892 1436 2893 1434 2892 8 _pl _cp 1433 2900 _m
_sp 1433 2900 1434 2898 1436 2897 1437 2898 1438 2900 1437 2902 1436 2903 1434 2902 8 _pl _cp 
0 g _f _s _s 
0 g 1542 1915 _m
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(\(OOSPICs\))_S 67 _t
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(vehicle)_S 67 _t
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(SIMULATING)_S 67 _t
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1980 6121 _m
(There)_S 67 _t
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(environment)_S 67 _t
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(water)_S 67 _t
(flow,)_S 67 _t
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(battery)_S 67 _t
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/Times-BoldItalicR 600 _ff
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(,)_S 67 _t
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(z)_S /Times-RomanR 600 _ff
67 _t
(and)_S 67 _t
(vehicle)_S 67 _t
(state)_S 67 _t
(vector)_S 67 _t
(values)_S 67 _t
(respectively.)_S 134 _t
(Normally)_S 67 _t
(these)_S 67 _t
(sensors)_S 1500 3676 _m
(are)_S 67 _t
(reasonably)_S 67 _t
(accurate)_S 67 _t
(with)_S 67 _t
(zero)_S 67 _t
(bias)_S 67 _t
(and)_S 67 _t
(less)_S 67 _t
(than)_S 67 _t
(5-10%)_S 67 _t
(error)_S 67 _t
(over)_S 67 _t
(their)_S 67 _t
(operating)_S 1500 3327 _m
(range.)_S 134 _t
(Inertial)_S 67 _t
(and)_S 67 _t
(gyroscopic)_S 67 _t
(detectors)_S 67 _t
(can)_S 67 _t
(also)_S 67 _t
(be)_S 67 _t
(modeled)_S 67 _t
(but)_S 67 _t
(additional)_S 1500 2978 _m
(considerations)_S 67 _t
(pertain.)_S 1980 2629 _m
(Inertial)_S 67 _t
(navigation)_S 67 _t
(sensors)_S 67 _t
(are)_S 67 _t
(often)_S 67 _t
(called)_S 67 _t
("strap-down")_S 67 _t
(systems)_S 67 _t
(since)_S 67 _t
(they)_S 67 _t
(are)_S 1500 2280 _m
(aligned)_S 67 _t
(with)_S 67 _t
(vehicle)_S 67 _t
(body)_S 67 _t
(coordinates)_S 67 _t
(and)_S 67 _t
(physically)_S 67 _t
(fixed)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(frame.)_S 67 _t
4950 1288 _m
(166)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11855 _m
(If)_S 67 _t
(possible)_S 67 _t
(they)_S 67 _t
(are)_S 67 _t
(kept)_S 67 _t
(near)_S 67 _t
(the)_S 67 _t
(center)_S 67 _t
(of)_S 67 _t
(gravity)_S 67 _t
(to)_S 67 _t
(minimize)_S 67 _t
(offset)_S 67 _t
(moment)_S 67 _t
(effects.)_S 67 _t
1500 11506 _m
(Complete)_S 67 _t
(packages)_S 67 _t
(using)_S 67 _t
(solid)_S 67 _t
(state)_S 67 _t
(sensors)_S 67 _t
(and)_S 67 _t
(integrated)_S 67 _t
(circuit)_S 67 _t
(processing)_S 67 _t
(are)_S 67 _t
(now)_S 1500 11157 _m
(available)_S 67 _t
(at)_S 67 _t
(relatively)_S 67 _t
(low)_S 67 _t
(cost,)_S 67 _t
(providing)_S 67 _t
(angular)_S 67 _t
(rate)_S 67 _t
(and)_S 67 _t
(acceleration)_S 67 _t
(values)_S 67 _t
(about)_S 1500 10808 _m
(all)_S 67 _t
(three)_S 67 _t
(body)_S 67 _t
(axes.)_S 134 _t
(Many)_S 67 _t
(other)_S 67 _t
(small)_S 67 _t
(inertial)_S 67 _t
(units)_S 67 _t
(are)_S 67 _t
(also)_S 67 _t
(available)_S 67 _t
(which)_S 67 _t
(can)_S 1500 10459 _m
(provide)_S 67 _t
(similar)_S 67 _t
(functionality)_S 67 _t
(for)_S 67 _t
(one)_S 67 _t
(or)_S 67 _t
(two)_S 67 _t
(body)_S 67 _t
(axes.)_S 134 _t
(Velocity)_S 67 _t
(outputs)_S 67 _t
(are)_S 67 _t
(integrated)_S 1500 10110 _m
(internally)_S 67 _t
(from)_S 67 _t
(accelerations,)_S 67 _t
(and)_S 67 _t
(posture)_S 67 _t
(values)_S 67 _t
(are)_S 67 _t
(then)_S 67 _t
(found)_S 67 _t
(by)_S 67 _t
(integration)_S 67 _t
(of)_S 1500 9761 _m
(velocity.)_S 1980 9412 _m
(Accuracy)_S 67 _t
(of)_S 67 _t
(inertial)_S 67 _t
(devices)_S 67 _t
(depends)_S 67 _t
(on)_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(roll)_S 67 _t
(angle)_S 67 _t
(estimation)_S 67 _t
(and)_S 1500 9063 _m
(sensitivity)_S 67 _t
(to)_S 67 _t
(acceleration.)_S 134 _t
(Inertial)_S 67 _t
(accelerometers)_S 67 _t
(are)_S 67 _t
(affected)_S 67 _t
(both)_S 67 _t
(by)_S 67 _t
(accelerations)_S 1500 8714 _m
(on)_S 67 _t
(the)_S 67 _t
(vehicle)_S 67 _t
(and)_S 67 _t
(accelerations)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(gravity.)_S 134 _t
(Since)_S 67 _t
(the)_S 67 _t
(acceleration)_S 67 _t
(due)_S 67 _t
(to)_S 67 _t
(gravity)_S 1500 8365 _m
(is)_S 67 _t
(about)_S 67 _t
(ten)_S 67 _t
(times)_S 67 _t
(the)_S 67 _t
(acceleration)_S 67 _t
(of)_S 67 _t
(propulsors)_S 67 _t
(used)_S 67 _t
(by)_S 67 _t
(slow)_S 67 _t
(speed)_S 67 _t
(vehicles,)_S 67 _t
(an)_S 1500 8016 _m
(accurate)_S 67 _t
(estimate)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(pitch)_S 67 _t
(and)_S 67 _t
(roll)_S 67 _t
(is)_S 67 _t
(essential)_S 67 _t
(for)_S 67 _t
(isolating)_S 67 _t
(acceleration)_S 1500 7667 _m
(components)_S 67 _t
(unique)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(vehicle.)_S 134 _t
(Because)_S 67 _t
(both)_S 67 _t
(position)_S 67 _t
(and)_S 67 _t
(rotation)_S 67 _t
(estimates)_S 67 _t
(are)_S 1500 7318 _m
(double)_S 67 _t
(integrations)_S 67 _t
(of)_S 67 _t
(accelerations,)_S 67 _t
(any)_S 67 _t
(noise)_S 67 _t
(or)_S 67 _t
(error)_S 67 _t
(in)_S 67 _t
(acceleration)_S 67 _t
(estimation)_S 67 _t
(is)_S 1500 6969 _m
(greatly)_S 67 _t
(amplified)_S 67 _t
(over)_S 67 _t
(the)_S 67 _t
(passage)_S 67 _t
(of)_S 67 _t
(time.)_S 134 _t
(Proper)_S 67 _t
(conversion)_S 67 _t
(from)_S 67 _t
(local)_S 67 _t
(inertial)_S 1500 6620 _m
(reference)_S 67 _t
(frames)_S 67 _t
(to)_S 67 _t
(geostationary)_S 67 _t
(or)_S 67 _t
(geocentric)_S 67 _t
(inertial)_S 67 _t
(reference)_S 67 _t
(frames)_S 67 _t
(is)_S 67 _t
(also)_S 1500 6271 _m
(necessary)_S 67 _t
(\(Maloney)_S 67 _t
(88\).)_S 134 _t
(Additional)_S 67 _t
(errors)_S 67 _t
(and)_S 67 _t
(correction)_S 67 _t
(factors)_S 67 _t
(all)_S 67 _t
(can)_S 67 _t
(raise)_S 67 _t
(the)_S 1500 5922 _m
(complexity)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(sensor)_S 67 _t
(and)_S 67 _t
(its)_S 67 _t
(model.)_S 1980 5573 _m
(Electromechanical)_S 67 _t
(and)_S 67 _t
(inertial)_S 67 _t
(sensors)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(precisely)_S 67 _t
(modeled)_S 67 _t
(by)_S 67 _t
(perfect)_S 1500 5224 _m
("virtual)_S 67 _t
(sensors")_S 67 _t
(using)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(model.)_S 134 _t
(This)_S 67 _t
(is)_S 67 _t
(very)_S 67 _t
(useful)_S 67 _t
(for)_S 67 _t
(initial)_S 1500 4875 _m
(experimentation)_S 67 _t
(with)_S 67 _t
(navigation)_S 67 _t
(functions)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(robot.)_S 134 _t
(For)_S 67 _t
(realistic)_S 67 _t
(modeling,)_S 1500 4526 _m
(however,)_S 67 _t
(accurate)_S 67 _t
(distributions)_S 67 _t
(for)_S 67 _t
(sensor)_S 67 _t
(bias,)_S 67 _t
(error)_S 67 _t
(and)_S 67 _t
(variance)_S 67 _t
(are)_S 67 _t
(needed.)_S 134 _t
(Such)_S 1500 4177 _m
(distributions)_S 67 _t
(can)_S 67 _t
(only)_S 67 _t
(be)_S 67 _t
(meaningfully)_S 67 _t
(applied)_S 67 _t
(using)_S 67 _t
(specifications)_S 67 _t
(and)_S 67 _t
(test)_S 67 _t
(results)_S 67 _t
(for)_S 1500 3828 _m
(actual)_S 67 _t
(hardware.)_S 134 _t
(Error)_S 67 _t
(models)_S 67 _t
(are)_S 67 _t
(feasible)_S 67 _t
(\(Pappas)_S 67 _t
(91\))_S 67 _t
(\(Brancart)_S 67 _t
(94\))_S 67 _t
(and)_S 67 _t
(can)_S 67 _t
(be)_S 1500 3479 _m
(modeled)_S 67 _t
(statistically)_S 67 _t
(\(Law,)_S 67 _t
(Kelton)_S 67 _t
(91\).)_S 134 _t
(Simulating)_S 67 _t
("virtual)_S 67 _t
(sensors")_S 67 _t
(using)_S 67 _t
(the)_S 1500 3130 _m
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(is)_S 67 _t
(of)_S 67 _t
(particular)_S 67 _t
(usefulness)_S 67 _t
(when)_S 67 _t
(evaluating)_S 67 _t
(robust)_S 67 _t
(vehicle)_S 1500 2781 _m
(control)_S 67 _t
(under)_S 67 _t
(variable)_S 67 _t
(operating)_S 67 _t
(conditions)_S 67 _t
(\(especially)_S 67 _t
(simulated)_S 67 _t
(sensor)_S 67 _t
(failure\).)_S 134 _t
(The)_S 1500 2432 _m
(key)_S 67 _t
(to)_S 67 _t
(success)_S 67 _t
(when)_S 67 _t
(producing)_S 67 _t
(such)_S 67 _t
(simulations)_S 67 _t
(will)_S 67 _t
(be)_S 67 _t
(incorporating)_S 67 _t
(statistically)_S 1500 2083 _m
(valid)_S 67 _t
(error)_S 67 _t
(models.)_S 4950 1288 _m
(167)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1500 11705 _m
/Times-BoldR 600 _ff
(I.)_S 1980 11705 _m
(SPECIAL)_S 67 _t
(EFFECTS)_S 67 _t
(AND)_S 67 _t
(FUTURE)_S 67 _t
(WORK:)_S 134 _t
(ROBUST)_S 67 _t
(CONTROL,)_S 1980 11356 _m
(TETHER,)_S 67 _t
(OCEAN)_S 67 _t
(SURFACE,)_S 67 _t
(COLLISION)_S 67 _t
(DETECTION)_S /Times-RomanR 600 _ff
1980 11007 _m
(The)_S 67 _t
(networked)_S 67 _t
(real-time)_S 67 _t
(availability)_S 67 _t
(of)_S 67 _t
(this)_S 67 _t
(model)_S 67 _t
(enables)_S 67 _t
(further)_S 67 _t
(work)_S 67 _t
(in)_S 1500 10658 _m
(several)_S 67 _t
(important)_S 67 _t
(research)_S 67 _t
(areas.)_S 134 _t
(The)_S 67 _t
(analysis)_S 67 _t
(and)_S 67 _t
(design)_S 67 _t
(of)_S 67 _t
(robust)_S 67 _t
(controllers)_S 67 _t
(focuses)_S 1500 10309 _m
(on)_S 67 _t
(producing)_S 67 _t
(stable)_S 67 _t
(performance)_S 67 _t
(when)_S 67 _t
(controlling)_S 67 _t
(multivariable)_S 67 _t
(systems)_S 67 _t
(with)_S 1500 9960 _m
(significant)_S 67 _t
(uncertainty)_S 67 _t
(\(Dorato)_S 67 _t
(87\).)_S 134 _t
(Ordinarily)_S 67 _t
(this)_S 67 _t
(includes)_S 67 _t
(fixed)_S 67 _t
(control)_S 67 _t
(systems)_S 67 _t
(that)_S 1500 9611 _m
(meet)_S 67 _t
(performance)_S 67 _t
(measure)_S 67 _t
(criteria)_S 67 _t
(for)_S 67 _t
(specified)_S 67 _t
(uncertainty)_S 67 _t
(bounds.)_S 134 _t
(Example)_S 67 _t
(linear)_S 1500 9262 _m
(control)_S 67 _t
(algorithms)_S 67 _t
(used)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(robot)_S 67 _t
(for)_S 67 _t
(posture)_S 67 _t
(control)_S 67 _t
(are)_S 67 _t
(included)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(robot)_S 1500 8913 _m
(architecture)_S 67 _t
(chapter)_S 67 _t
(of)_S 67 _t
(this)_S 67 _t
(work.)_S 134 _t
(More)_S 67 _t
(sophisticated)_S 67 _t
(controller)_S 67 _t
(analysis)_S 67 _t
(appears)_S 67 _t
(in)_S 1500 8564 _m
(\(Yoerger)_S 67 _t
(85,)_S 67 _t
(90\))_S 67 _t
(\(Papoulias)_S 67 _t
(89,)_S 67 _t
(91\))_S 67 _t
(\(Cristi)_S 67 _t
(89\))_S 67 _t
(\(Healey)_S 67 _t
(89,)_S 67 _t
(92b,)_S 67 _t
(93,)_S 67 _t
(94a\))_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 1500 8215 _m
(and)_S 67 _t
(numerous)_S 67 _t
(other)_S 67 _t
(references.)_S 134 _t
(Adaptive)_S 67 _t
(control)_S 67 _t
(methods)_S 67 _t
(and)_S 67 _t
(application)_S 67 _t
(of)_S 67 _t
(machine)_S 1500 7866 _m
(learning)_S 67 _t
(techniques)_S 67 _t
(to)_S 67 _t
(control)_S 67 _t
(are)_S 67 _t
(active)_S 67 _t
(areas)_S 67 _t
(of)_S 67 _t
(research)_S 67 _t
(\(Goheen)_S 67 _t
(87\).)_S 134 _t
(This)_S 67 _t
(work)_S 67 _t
(is)_S 1500 7517 _m
(of)_S 67 _t
(particular)_S 67 _t
(interest)_S 67 _t
(given)_S 67 _t
(the)_S 67 _t
(paramount)_S 67 _t
(importance)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(stability)_S 67 _t
(despite)_S 67 _t
(any)_S 1500 7168 _m
(potentially)_S 67 _t
(chaotic)_S 67 _t
(\(nonlinear)_S 67 _t
(instability\))_S 67 _t
(behavior)_S 67 _t
(which)_S 67 _t
(may)_S 67 _t
(emerge)_S 67 _t
(due)_S 67 _t
(to)_S 1500 6819 _m
(unforeseen)_S 67 _t
(interactions)_S 67 _t
(between)_S 67 _t
(multiple)_S 67 _t
(active)_S 67 _t
(controllers.)_S 134 _t
(The)_S 67 _t
(ability)_S 67 _t
(to)_S 67 _t
(repeatedly)_S 1500 6470 _m
(test)_S 67 _t
(controllers)_S 67 _t
(for)_S 67 _t
(yaw,)_S 67 _t
(depth,)_S 67 _t
(pitch,)_S 67 _t
(tracking)_S 67 _t
(and)_S 67 _t
(hovering)_S 67 _t
(while)_S 67 _t
(they)_S 67 _t
(are)_S 67 _t
(operating)_S 1500 6121 _m
(simultaneously)_S 67 _t
(on)_S 67 _t
(vehicle)_S 67 _t
(hardware)_S 67 _t
(in)_S 67 _t
(real)_S 67 _t
(time)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(laboratory)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(tremendous)_S 1500 5772 _m
(research)_S 67 _t
(tool)_S 67 _t
(provided)_S 67 _t
(by)_S 67 _t
(this)_S 67 _t
(model)_S 67 _t
(and)_S 67 _t
(the)_S 67 _t
(networked)_S 67 _t
(virtual)_S 67 _t
(world.)_S 1980 5423 _m
(Although)_S 67 _t
(a)_S 67 _t
(tether)_S 67 _t
(is)_S 67 _t
(not)_S 67 _t
(ordinarily)_S 67 _t
(used)_S 67 _t
(on)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV,)_S 67 _t
(employment)_S 67 _t
(of)_S 67 _t
(a)_S 1500 5074 _m
(tether)_S 67 _t
(for)_S 67 _t
(power)_S 67 _t
(supply,)_S 67 _t
(task-level)_S 67 _t
(mission)_S 67 _t
(control)_S 67 _t
(or)_S 67 _t
(telemetry)_S 67 _t
(feedback)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(very)_S 1500 4725 _m
(useful)_S 67 _t
(during)_S 67 _t
(vehicle)_S 67 _t
(testing.)_S 134 _t
(Tethers)_S 67 _t
(can)_S 67 _t
(also)_S 67 _t
(be)_S 67 _t
(a)_S 67 _t
(good)_S 67 _t
(way)_S 67 _t
(to)_S 67 _t
(prepare)_S 67 _t
(for)_S 67 _t
(using)_S 1500 4376 _m
(acoustic)_S 67 _t
(links,)_S 67 _t
(or)_S 67 _t
(to)_S 67 _t
(reliably)_S 67 _t
(test)_S 67 _t
(a)_S 67 _t
(vehicle)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(open)_S 67 _t
(ocean)_S 67 _t
(prior)_S 67 _t
(to)_S 67 _t
(autonomous)_S 1500 4027 _m
(control.)_S 134 _t
(It)_S 67 _t
(is)_S 67 _t
(important)_S 67 _t
(to)_S 67 _t
(note)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(operational)_S 67 _t
(characteristics)_S 67 _t
(of)_S 67 _t
(remotely)_S 67 _t
(operated)_S 1500 3678 _m
(vehicles)_S 67 _t
(are)_S 67 _t
(often)_S 67 _t
(dominated)_S 67 _t
(by)_S 67 _t
(tether)_S 67 _t
(dynamics.)_S 134 _t
(Incorporation)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(tether)_S 67 _t
(injects)_S 1500 3329 _m
(significant)_S 67 _t
(forces)_S 67 _t
(and)_S 67 _t
(moments)_S 67 _t
(into)_S 67 _t
(the)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion,)_S 67 _t
(but)_S 67 _t
(tether)_S 67 _t
(forces)_S 67 _t
(can)_S 67 _t
(be)_S 1500 2980 _m
(realistically)_S 67 _t
(modeled)_S 67 _t
(\(Abel)_S 67 _t
(72\))_S 67 _t
(\(Brancart)_S 67 _t
(94\))_S 67 _t
(\(Hover)_S 67 _t
(94\).)_S 134 _t
(Addition)_S 67 _t
(of)_S 67 _t
(a)_S 67 _t
(general)_S 67 _t
(tether)_S 1500 2631 _m
(model)_S 67 _t
(into)_S 67 _t
(this)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(valuable)_S 67 _t
(subject)_S 67 _t
(for)_S 1500 2282 _m
(future)_S 67 _t
(work.)_S 4950 1288 _m
(168)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
     }bdef
1980 11855 _m
(Modeling)_S 67 _t
(ocean)_S 67 _t
(waves)_S 67 _t
(and)_S 67 _t
(surface)_S 67 _t
(interactions)_S 67 _t
(are)_S 67 _t
(also)_S 67 _t
(interesting)_S 67 _t
(areas)_S 67 _t
(for)_S 1500 11506 _m
(future)_S 67 _t
(work.)_S 134 _t
(Model)_S 67 _t
(complexity)_S 67 _t
(ranges)_S 67 _t
(from)_S 67 _t
(simple)_S 67 _t
(sinusoids)_S 67 _t
(to)_S 67 _t
(sophisticated)_S 1500 11157 _m
(numerical)_S 67 _t
(models)_S 67 _t
(obtained)_S 67 _t
(from)_S 67 _t
(supercomputer)_S 67 _t
(programs)_S 67 _t
(analyzing)_S 67 _t
(years)_S 67 _t
(of)_S 67 _t
(empirical)_S 1500 10808 _m
(oceanographic)_S 67 _t
(data)_S 67 _t
(\(Covington)_S 67 _t
(94\))_S 67 _t
(\(Fossen)_S 67 _t
(94\))_S 67 _t
(\(Musker)_S 67 _t
(88\))_S 67 _t
(\(Blumberg)_S 67 _t
(94\).)_S 134 _t
(Usually)_S 1500 10459 _m
(the)_S 67 _t
(principle)_S 67 _t
(of)_S 67 _t
(superposition)_S 67 _t
(permits)_S 67 _t
(wave)_S 67 _t
(and)_S 67 _t
(current)_S 67 _t
(effects)_S 67 _t
(to)_S 67 _t
(be)_S 67 _t
(injected)_S 67 _t
(into)_S 67 _t
(the)_S 1500 10110 _m
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(solution)_S 67 _t
(at)_S 67 _t
(the)_S 67 _t
(last)_S 67 _t
(algorithmic)_S 67 _t
(step,)_S 67 _t
(implying)_S 67 _t
(that)_S 67 _t
(highly)_S 1500 9761 _m
(complex)_S 67 _t
(ocean)_S 67 _t
(wave)_S 67 _t
(and)_S 67 _t
(circulation)_S 67 _t
(models)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(solved)_S 67 _t
(off-line)_S 67 _t
(or)_S 67 _t
(in)_S 67 _t
(parallel.)_S 67 _t
1500 9412 _m
(Incorporation)_S 67 _t
(of)_S 67 _t
(high-resolution)_S 67 _t
(ocean)_S 67 _t
(current)_S 67 _t
(models)_S 67 _t
(over)_S 67 _t
(computer)_S 67 _t
(networks)_S 67 _t
(is)_S 67 _t
(yet)_S 1500 9063 _m
(another)_S 67 _t
(worthy)_S 67 _t
(area)_S 67 _t
(for)_S 67 _t
(future)_S 67 _t
(research.)_S 1980 8714 _m
(The)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(presented)_S 67 _t
(here)_S 67 _t
(does)_S 67 _t
(not)_S 67 _t
(include)_S 67 _t
(collision)_S 67 _t
(effects.)_S 67 _t
1500 8365 _m
(Abrupt)_S 67 _t
(changes)_S 67 _t
(in)_S 67 _t
(body)_S 67 _t
(acceleration)_S 67 _t
(and)_S 67 _t
(velocity)_S 67 _t
(may)_S 67 _t
(require)_S 67 _t
(extensions)_S 67 _t
(to)_S 67 _t
(the)_S 1500 8016 _m
(temporal)_S 67 _t
(integration)_S 67 _t
(algorithm.)_S 134 _t
(Detecting)_S 67 _t
(collisions)_S 67 _t
(and)_S 67 _t
(points)_S 67 _t
(of)_S 67 _t
(contact)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(highly)_S 1500 7667 _m
(populated)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(is)_S 67 _t
(a)_S 67 _t
(separate)_S 67 _t
(active)_S 67 _t
(research)_S 67 _t
(problem)_S 67 _t
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(an)_S 67 _t
(extremely)_S 67 _t
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(degree)_S 67 _t
(of)_S 67 _t
(computational)_S 67 _t
(complexity.)_S 134 _t
(Properly)_S 67 _t
(adapting)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(algorithm)_S 1500 6969 _m
(to)_S 67 _t
(include)_S 67 _t
(realistic)_S 67 _t
(collision)_S 67 _t
(effects)_S 67 _t
(can)_S 67 _t
(be)_S 67 _t
(done)_S 67 _t
(meaningfully)_S 67 _t
(if)_S 67 _t
(performed)_S 67 _t
(in)_S 1500 6620 _m
(conjunction)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(more)_S 67 _t
(general)_S 67 _t
(virtual)_S 67 _t
(world)_S 67 _t
(collision)_S 67 _t
(detection)_S 67 _t
(problem.)_S 134 _t
(This)_S 67 _t
(is)_S 1500 6271 _m
(another)_S 67 _t
(important)_S 67 _t
(area)_S 67 _t
(for)_S 67 _t
(future)_S 67 _t
(research.)_S 1500 5772 _m
/Times-BoldR 600 _ff
(J.)_S 1980 5772 _m
(SUMMARY)_S /Times-RomanR 600 _ff
1980 5423 _m
(The)_S 67 _t
(requirements)_S 67 _t
(for)_S 67 _t
(a)_S 67 _t
(general)_S 67 _t
(networked)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(six)_S 1500 5074 _m
(degree-of-freedom)_S 67 _t
(hydrodynamics)_S 67 _t
(model)_S 67 _t
(are)_S 67 _t
(outlined)_S 67 _t
(for)_S 67 _t
(a)_S 67 _t
(robot)_S 67 _t
(connected)_S 67 _t
(to)_S 67 _t
(a)_S 1500 4725 _m
(virtual)_S 67 _t
(world.)_S 134 _t
(An)_S 67 _t
(overall)_S 67 _t
(comparison)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(in)_S 67 _t
(other)_S 67 _t
(environments)_S 1500 4376 _m
(shows)_S 67 _t
(that)_S 67 _t
(the)_S 67 _t
(underwater)_S 67 _t
(vehicle)_S 67 _t
(case)_S 67 _t
(is)_S 67 _t
(among)_S 67 _t
(the)_S 67 _t
(most)_S 67 _t
(difficult)_S 67 _t
(and)_S 67 _t
(crucial.)_S 67 _t
1500 4027 _m
(No)_S 67 _t
(rigorous)_S 67 _t
(general)_S 67 _t
(model)_S 67 _t
(was)_S 67 _t
(previously)_S 67 _t
(available)_S 67 _t
(from)_S 67 _t
(a)_S 67 _t
(single)_S 67 _t
(source)_S 67 _t
(which)_S 67 _t
(is)_S 1500 3678 _m
(computationally)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(real-time)_S 67 _t
(simulation)_S 67 _t
(of)_S 67 _t
(submerged)_S 67 _t
(vehicle)_S 67 _t
(hydrodynamics.)_S 67 _t
1500 3329 _m
(The)_S 67 _t
(primary)_S 67 _t
(intended)_S 67 _t
(contributions)_S 67 _t
(of)_S 67 _t
(the)_S 67 _t
(hydrodynamic)_S 67 _t
(model)_S 67 _t
(developed)_S 67 _t
(here)_S 67 _t
(are)_S 1500 2980 _m
(clarity,)_S 67 _t
(correctness,)_S 67 _t
(generality,)_S 67 _t
(standardized)_S 67 _t
(nomenclature)_S 67 _t
(and)_S 67 _t
(suitability)_S 67 _t
(for)_S 67 _t
(real-time)_S 1500 2631 _m
(simulation.)_S 4950 1288 _m
(169)_S _ep
_bp /Times-RomanR 600 _ff
0 13200 10200 _ornt 
/_r      { sflg {/_t {0 rmoveto}bdef /ron false def}
         { /_S /show load def /_t {0 rmoveto}bdef /ron false def}ifelse
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1980 11855 _m
(Coordinate)_S 67 _t
(systems,)_S 67 _t
(variable)_S 67 _t
(definitions)_S 67 _t
(and)_S 67 _t
(coefficient)_S 67 _t
(nomenclature)_S 67 _t
(are)_S 1500 11506 _m
(explicitly)_S 67 _t
(defined.)_S 134 _t
(Kinematics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(reveal)_S 67 _t
(constraints)_S 67 _t
(between)_S 1500 11157 _m
(representations)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(body)_S 67 _t
(coordinate)_S 67 _t
(frame)_S 67 _t
(and)_S 67 _t
(world)_S 67 _t
(coordinate)_S 67 _t
(frame.)_S 134 _t
(Restrictions)_S 1500 10808 _m
(on)_S 67 _t
(Euler)_S 67 _t
(angles)_S 67 _t
(when)_S 67 _t
(pointing)_S 67 _t
(vertically)_S 67 _t
(are)_S 67 _t
(examined.)_S 134 _t
(Defining)_S 67 _t
(the)_S 67 _t
(underwater)_S 1500 10459 _m
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(problem)_S 67 _t
(as)_S 67 _t
(a)_S 67 _t
(function)_S 67 _t
(of)_S 67 _t
(vehicle)_S 67 _t
(state)_S 67 _t
(vector)_S 67 _t
(and)_S 67 _t
(hydrodynamics)_S 1500 10110 _m
(state)_S 67 _t
(vector)_S 67 _t
(provides)_S 67 _t
(precise)_S 67 _t
(specifications)_S 67 _t
(of)_S 67 _t
(algorithm)_S 67 _t
(inputs)_S 67 _t
(and)_S 67 _t
(outputs.)_S 134 _t
(Dynamics)_S 1500 9761 _m
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(derived)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(form)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(temporal)_S 67 _t
(integration)_S 67 _t
(in)_S 1500 9412 _m
(real)_S 67 _t
(time.)_S 134 _t
(Dimensionless)_S 67 _t
(coefficient)_S 67 _t
(values)_S 67 _t
(are)_S 67 _t
(presented)_S 67 _t
(for)_S 67 _t
(the)_S 67 _t
(NPS)_S 67 _t
(AUV)_S 67 _t
(and)_S 1500 9063 _m
(methods)_S 67 _t
(are)_S 67 _t
(discussed)_S 67 _t
(for)_S 67 _t
(determining)_S 67 _t
(coefficients)_S 67 _t
(of)_S 67 _t
(other)_S 67 _t
(vehicles.)_S 134 _t
(After)_S 67 _t
(extending)_S 1500 8714 _m
(previous)_S 67 _t
(work,)_S 67 _t
(a)_S 67 _t
(full)_S 67 _t
(set)_S 67 _t
(of)_S 67 _t
(component)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 67 _t
(are)_S 67 _t
(presented,)_S 1500 8365 _m
(including)_S 67 _t
(mass)_S 67 _t
(and)_S 67 _t
(inertia)_S 67 _t
(matrix)_S 67 _t
(determination.)_S 134 _t
(The)_S 67 _t
(dynamics)_S 67 _t
(equations)_S 67 _t
(of)_S 67 _t
(motion)_S 1500 8016 _m
(are)_S 67 _t
(in)_S 67 _t
(a)_S 67 _t
(form)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(most)_S 67 _t
(existing)_S 67 _t
(underwater)_S 67 _t
(vehicles.)_S 134 _t
(Techniques)_S 67 _t
(are)_S 1500 7667 _m
(demonstrated)_S 67 _t
(for)_S 67 _t
(modifying)_S 67 _t
(these)_S 67 _t
(general)_S 67 _t
(equations)_S 67 _t
(to)_S 67 _t
(accommodate)_S 67 _t
(different)_S 67 _t
(vehicle)_S 1500 7318 _m
(physical)_S 67 _t
(configurations.)_S 134 _t
(Since)_S 67 _t
(the)_S 67 _t
(equations)_S 67 _t
(are)_S 67 _t
(written)_S 67 _t
(to)_S 67 _t
(run)_S 67 _t
(in)_S 67 _t
(real)_S 67 _t
(time,)_S 67 _t
(it)_S 67 _t
(may)_S 67 _t
(be)_S 1500 6969 _m
(computationally)_S 67 _t
(feasible)_S 67 _t
(to)_S 67 _t
(embed)_S 67 _t
(them)_S 67 _t
(in)_S 67 _t
(the)_S 67 _t
(robot)_S 67 _t
(execution)_S 67 _t
(logic)_S 67 _t
(as)_S 67 _t
(an)_S 67 _t
(onboard)_S 1500 6620 _m
(hydrodynamics)_S 67 _t
(response)_S 67 _t
(predictor)_S 67 _t
(for)_S 67 _t
(improved)_S 67 _t
(physical)_S 67 _t
(control.)_S 1980 6271 _m
(Quaternion)_S 67 _t
(methods)_S 67 _t
(are)_S 67 _t
(examined)_S 67 _t
(as)_S 67 _t
(a)_S 67 _t
(possible)_S 67 _t
(alternative)_S 67 _t
(to)_S 67 _t
(Euler)_S 67 _t
(angle)_S 1500 5922 _m
(representations.)_S 134 _t
(The)_S 67 _t
(use)_S 67 _t
(of)_S 67 _t
(Distributed)_S 67 _t
(Interactive)_S 67 _t
(Simulation)_S 67 _t
(\(DIS\))_S 67 _t
(network)_S 67 _t
(protocols)_S 1500 5573 _m
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(communication)_S 67 _t
(between)_S 67 _t
(virtual)_S 67 _t
(worlds)_S 67 _t
(imposes)_S 67 _t
(special)_S 67 _t
(considerations)_S 67 _t
(on)_S 67 _t
(the)_S 1500 5224 _m
(hydrodynamic)_S 67 _t
(model.)_S 134 _t
(An)_S 67 _t
(object-oriented)_S 67 _t
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(rigid)_S 67 _t
(body)_S 67 _t
(dynamics)_S 67 _t
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(hierarchy)_S 67 _t
(illuminates)_S 67 _t
(the)_S 67 _t
(design)_S 67 _t
(and)_S 67 _t
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(of)_S 67 _t
(the)_S 67 _t
(hydrodynamics)_S 67 _t
(model.)_S 67 _t
1500 4526 _m
(This)_S 67 _t
(class)_S 67 _t
(hierarchy)_S 67 _t
(may)_S 67 _t
(also)_S 67 _t
(be)_S 67 _t
(suitable)_S 67 _t
(for)_S 67 _t
(other)_S 67 _t
(types)_S 67 _t
(of)_S 67 _t
(networked)_S 67 _t
(vehicle)_S 67 _t
(models.)_S 67 _t
1500 4177 _m
(Simulation)_S 67 _t
(of)_S 67 _t
(virtual)_S 67 _t
(sensors,)_S 67 _t
(robust)_S 67 _t
(control,)_S 67 _t
(tether)_S 67 _t
(considerations,)_S 67 _t
(ocean)_S 67 _t
(surface)_S 1500 3828 _m
(modeling)_S 67 _t
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(collision)_S 67 _t
(detection)_S 67 _t
(are)_S 67 _t
(all)_S 67 _t
(examined)_S 67 _t
(as)_S 67 _t
(possible)_S 67 _t
(components)_S 67 _t
(of)_S 67 _t
(the)_S 1500 3479 _m
(hydrodynamics)_S 67 _t
(model.)_S 134 _t
(Numerous)_S 67 _t
(considerations)_S 67 _t
(in)_S 67 _t
(these)_S 67 _t
(many)_S 67 _t
(areas)_S 67 _t
(are)_S 67 _t
(pointed)_S 67 _t
(out)_S 1500 3130 _m
(as)_S 67 _t
(useful)_S 67 _t
(candidates)_S 67 _t
(for)_S 67 _t
(future)_S 67 _t
(research,)_S 67 _t
(with)_S 67 _t
(the)_S 67 _t
(expectation)_S 67 _t
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(each)_S 67 _t
(can)_S 67 _t
(be)_S 1500 2781 _m
(implemented)_S 67 _t
(as)_S 67 _t
(compatible)_S 67 _t
(networked)_S 67 _t
(real-time)_S 67 _t
(extensions)_S 67 _t
(to)_S 67 _t
(the)_S 67 _t
(general)_S 67 _t
(underwater)_S 1500 2432 _m
(vehicle)_S 67 _t
(dynamics)_S 67 _t
(model.)_S 4950 1288 _m
(170)_S _ep
_ed end end
%-12345X