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
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  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 \begin{document}
  80 \def\eqsatellite{%
  81 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)}%
  82 \begin{center}
  83 %\begin{pspicture}(-10,-10)(6,6)
  84 \def\nFrames{50}% 50 images
  85 \begin{animateinline}[controls,loop,timeline=satellite.dat,%
  86                      begin={\begin{pspicture}(-10,-10)(6,6)},
  87                      end={\end{pspicture}}]{5}% 5 images/s
  88 %\uput[r](0,3){$y$}\uput[u](3,0){$x$}
  89 %\psset{unit=2}
  90 \psframe*[linecolor={[rgb]{0 0 0.5}}](-10,-10)(6,6)
  91 \pstVerb{/tabXiYi [(XiYi.dat) run] def}%
  92 \pstVerb{/GM 1 def
  93     /theta0 30 def
  94     /r0 2 def
  95     /x0 r0 theta0 cos mul def
  96     /y0 r0 theta0 sin mul def
  97     /v0 0.85 def
  98     /v0x v0 theta0 sin mul neg def
  99     /v0y v0 theta0 cos mul def
 100     /Lc r0 v0 mul def % moment cinetique
 101     /par Lc dup mul GM div def % paramètre de l'ellipse
 102 % excentricité
 103     /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
 104 %%%%%%%%%%%%%%
 105     /a_2 par 1 exc dup mul sub div def % demi-grand axe
 106     /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
 107     /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def}%
 108 \psequadiff[method=rk4,
 109             plotpoints=1000,
 110             algebraic,
 111             whichabs=0,
 112             whichord=1,
 113             tabname=XiYi,
 114 %            saveData,filename=XiYi.dat
 115 ]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
 116 \listplot[linecolor=gray,unit=2]{XiYi aload pop}
 117 \psequadiff[method=rk4,
 118             plotpoints=1000,
 119             algebraic,
 120             whichabs=2,
 121             whichord=3,
 122             tabname=vxvy,
 123 %            saveData,filename=vxvy.dat
 124 ]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
 125 %\listplot[unit=2,linecolor=red]{vxvy aload pop}
 126 % on dessine la vitesse un point sur 50
 127 %\pscircle[fillcolor=gray!70,fillstyle=solid,unit=2](0,0){0.4}
 128 \Jupiter%
 129 %\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt,unit=2](-5,-5)(3,3)
 130 %\psline[arrowinset=0.05,arrowsize=0.1,unit=2]{<->}(3,0)(0,0)(0,3)
 131 \newframe
 132 \multiframe{\nFrames}{i=0+40}{
 133 \psset{unit=2}%
 134 \pstVerb{/tabXYpartiel {
 135           2 2 \i\space {/I exch def
 136           tabXiYi I get
 137           tabXiYi I 1 add get
 138           } for
 139           } def
 140          /vX vxvy \i\space get def
 141          /vY vxvy \i\space 1 add get def
 142          /xi tabXiYi \i\space get def
 143          /yi tabXiYi \i\space 1 add get def
 144          /ri3 xi dup mul yi dup mul add sqrt 3 exp def
 145          /Fx xi ri3 div neg def
 146          /Fy yi ri3 div neg def}%
 147 \listplot[linecolor=red,linewidth=0.05]{tabXYpartiel}
 148 \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)}}
 149 \newframe
 150 \listplot[linecolor=gray,unit=2]{XiYi aload pop}
 151 \listplot[linecolor=red,unit=2,linewidth=0.05]{XiYi aload pop}
 152 \psset{unit=2}%
 153 \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)}
 154 \end{animateinline}
 155 \end{center}
 156 \end{document}