gravitation/animation_satellite.tex

   1 \documentclass{article}
   2 \usepackage[a4paper,margin=2cm]{geometry}
   3 \usepackage[latin1]{inputenc}
   4 \usepackage{pstricks,pst-eqdf}
   5 \usepackage{animate}
   6 \newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.125,linecolor={[rgb]{1 0.5 0}}}
   7 \newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.7 1}}}
   8 \newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0.5 0}}}
   9 %%%%%%%%%%%%%%%%%%
  10 \title{Animation du mouvement d'un satellite}
  11 \date{23 juin 2\,012}
  12 %timeline
  13 \begin{filecontents}{satellite.dat}
  14 ::0x0
  15 ::1
  16 ::2
  17 ::3
  18 ::4
  19 ::5
  20 ::6
  21 ::7
  22 ::8
  23 ::9
  24 ::10
  25 ::11
  26 ::12
  27 ::13
  28 ::14
  29 ::15
  30 ::16
  31 ::17
  32 ::18
  33 ::19
  34 ::20
  35 ::21
  36 ::22
  37 ::23
  38 ::24
  39 ::25
  40 ::26
  41 ::27
  42 ::28
  43 ::29
  44 ::30
  45 ::31
  46 ::32
  47 ::33
  48 ::34
  49 ::35
  50 ::36
  51 ::37
  52 ::38
  53 ::39
  54 ::40
  55 ::41
  56 ::42
  57 ::43
  58 ::44
  59 ::45
  60 ::46
  61 ::47
  62 ::48
  63 ::49
  64 ::50
  65 ::51
  66 ::52
  67 \end{filecontents}
  68 \newcommand{\Jupiter}{%
  69   \psclip{\pscircle[fillstyle=solid,fillcolor=yellow]{1.5}}
  70   \psset{fillstyle=solid,fillcolor={[cmyk]{0 0.2 0.4 0}},linestyle=none}
  71     \psframe(-2,.6)(2,1)
  72     \psframe(-2,0.45)(2,0.52)
  73     \psframe(-2,.05)(2,.3)
  74     \psframe(-2,-0.35)(2,-0.2)
  75     \psframe(-2,-0.9)(2,-.5)
  76   \endpsclip
  77   \psellipse[fillstyle=solid,fillcolor={[cmyk]{0 0.4 0.6 0}},linestyle=none](-0.3,-0.6)(0.35,0.2)
  78   \pscircle{1.5}}
  79 \makeatletter
  80 %% adapté de \psRandom du package pstricks-add
  81 %% pour rendre aléatoire la taille des étoiles
  82 %% Manuel Luque
  83 \newdimen\pssizeStar
  84 \def\psset@sizeStar#1{\pssetlength\pssizeStar{#1}}
  85 \psset@sizeStar{1pt}
  86 \define@key[psset]{pst-eqd}{randomPoints}[1000]{\def\psk@randomPoints{#1}}
  87 \psset[pst-eqd]{randomPoints=1000}
  88 \define@boolkey[psset]{pst-eqd}[Pst@]{color}[true]{}
  89 \psset[pst-eqd]{color=false}
  90 \def\psRandomStar{\pst@object{psRandomStar}}%
  91 \def\psRandomStar@i{\@ifnextchar({\psRandomStar@ii}{\psRandomStar@iii(0,0)(1,1)}}
  92 \def\psRandomStar@ii(#1){\@ifnextchar({\psRandomStar@iii(#1)}{\psRandomStar@iii(0,0)(#1)}}
  93 \def\psRandomStar@iii(#1)(#2)#3{%
  94   \def\pst@tempA{#3}%
  95   \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi
  96   \pst@getcoor{#1}\pst@tempA
  97   \pst@getcoor{#2}\pst@tempB
  98   \begin@SpecialObj
  99   \addto@pscode{
 100     \pst@tempA\space /yMin exch def
 101     /xMin exch def
 102     \pst@tempB\space /yMax exch def
 103     /xMax exch def
 104     /dy yMax yMin sub def
 105     /dx xMax xMin sub def
 106     rrand srand                 % initializes the random generator
 107     /getRandReal { rand 2147483647 div } def
 108      \psk@randomPoints {
 109     /DS \pst@number\pssizeStar\space getRandReal mul def
 110     \@nameuse{psds@\psk@dotstyle}
 111      \ifPst@color getRandReal 1 1 sethsbcolor \fi
 112      getRandReal dx mul xMin add
 113      getRandReal dy mul yMin add
 114      Dot
 115      \ifx\psk@fillstyle\psfs@solid fill \fi stroke
 116     } repeat
 117   }%
 118   \end@SpecialObj
 119   \endpsclip
 120   \ignorespaces
 121 }
 122 \makeatother
 123 \begin{document}
 124 \def\eqsatellite{%
 125 y[2]|y[3]|-GM*y[0]/((sqrt(y[0]^2+y[1]^2))^3)|-GM*y[1]/((sqrt(y[0]^2+y[1]^2))^3)}%
 126 \begin{center}
 127 %\begin{pspicture}(-10,-10)(6,6)
 128 \def\nFrames{50}% 50 images
 129 \begin{animateinline}[controls,loop,timeline=satellite.dat,%
 130                      begin={\begin{pspicture}(-10,-10)(6,6)},
 131                      end={\end{pspicture}}]{5}% 5 images/s
 132 %\uput[r](0,3){$y$}\uput[u](3,0){$x$}
 133 %\psset{unit=2}
 134 \psframe*[linecolor={[cmyk]{1 1 0 0.7}}](-10,-10)(6,6)
 135 \psRandomStar[linecolor={[rgb]{1,1,0.5}},
 136     randomPoints=1000,sizeStar=1.25pt](-10,-10)(6,6){\psframe[linestyle=none](-10,-10)(6,6)}
 137 \pstVerb{/tabXiYi [(XiYi.dat) run] def}%
 138 \pstVerb{/GM 1 def
 139     /theta0 30 def
 140     /r0 2 def
 141     /x0 r0 theta0 cos mul def
 142     /y0 r0 theta0 sin mul def
 143     /v0 0.85 def
 144     /v0x v0 theta0 sin mul neg def
 145     /v0y v0 theta0 cos mul def
 146     /Lc r0 v0 mul def % moment cinetique
 147     /par Lc dup mul GM div def % paramètre de l'ellipse
 148 % excentricité
 149     /exc 1 0.5 v0 4 exp mul r0 dup mul mul GM r0 mul v0 dup mul mul sub GM dup mul div 2 mul add sqrt def
 150 %%%%%%%%%%%%%%
 151     /a_2 par 1 exc dup mul sub div def % demi-grand axe
 152     /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
 153     /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def}%
 154 \psequadiff[method=rk4,
 155             plotpoints=1000,
 156             algebraic,
 157             whichabs=0,
 158             whichord=1,
 159             tabname=XiYi,
 160 %            saveData,filename=XiYi.dat
 161 ]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
 162 \listplot[linecolor=gray,unit=2]{XiYi aload pop}
 163 \psequadiff[method=rk4,
 164             plotpoints=1000,
 165             algebraic,
 166             whichabs=2,
 167             whichord=3,
 168             tabname=vxvy,
 169 %            saveData,filename=vxvy.dat
 170 ]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
 171 %\listplot[unit=2,linecolor=red]{vxvy aload pop}
 172 % on dessine la vitesse un point sur 50
 173 %\pscircle[fillcolor=gray!70,fillstyle=solid,unit=2](0,0){0.4}
 174 \Jupiter%
 175 %\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt,unit=2](-5,-5)(3,3)
 176 %\psline[arrowinset=0.05,arrowsize=0.1,unit=2]{<->}(3,0)(0,0)(0,3)
 177 \newframe
 178 \multiframe{\nFrames}{i=0+40}{
 179 \psset{unit=2}%
 180 \pstVerb{/tabXYpartiel {
 181           2 2 \i\space {/I exch def
 182           tabXiYi I get
 183           tabXiYi I 1 add get
 184           } for
 185           } def
 186          /vX vxvy \i\space get def
 187          /vY vxvy \i\space 1 add get def
 188          /xi tabXiYi \i\space get def
 189          /yi tabXiYi \i\space 1 add get def
 190          /ri3 xi dup mul yi dup mul add sqrt 3 exp def
 191          /Fx xi ri3 div neg def
 192          /Fy yi ri3 div neg def}%
 193 \listplot[linecolor=red,linewidth=0.05]{tabXYpartiel}
 194 \rput(!xi yi){\pscircle[fillstyle=solid,fillcolor=gray!50]{0.075}\psline[style=vecteurA]{->}(! vX 2 mul vY 2 mul)\psline[style=vecteurB]{->}(! Fx 5 mul Fy 5 mul)}}
 195 \newframe
 196 \listplot[linecolor=gray,unit=2]{XiYi aload pop}
 197 \listplot[linecolor=red,unit=2,linewidth=0.05]{XiYi aload pop}
 198 \psset{unit=2}%
 199 \rput(!x0 y0){\pscircle[fillstyle=solid,fillcolor=gray!50]{0.075}\psline[style=vecteurA]{->}(! v0x 2 mul v0y 2 mul)\psline[style=vecteurB]{->}(! x0 r0 3 exp div 5 mul neg y0 r0 3 exp div 5 mul neg)}
 200 \end{animateinline}
 201 \end{center}
 202 \end{document}