Nouvelle version de l'animation : ajout du ciel étoilé par Manuel

diff --git a/gravitation/animation_satellite.pdf b/gravitation/animation_satellite.pdf
index 503a600..eb30122 100644 (file)
Binary files a/gravitation/animation_satellite.pdf and b/gravitation/animation_satellite.pdf differ

diff --git a/gravitation/animation_satellite.tex b/gravitation/animation_satellite.tex
index 931d118..524ca74 100644 (file)
--- a/gravitation/animation_satellite.tex
+++ b/gravitation/animation_satellite.tex
@@ -1,156 +1,202 @@
-\documentclass{article}
-\usepackage[a4paper,margin=2cm]{geometry}
-\usepackage[latin1]{inputenc}
-\usepackage{pstricks,pst-eqdf}
-\usepackage{animate}
-\newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.125,linecolor={[rgb]{1 0.5 0}}}
-\newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.7 1}}}
-\newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0.5 0}}}
-%%%%%%%%%%%%%%%%%%
-\title{Animation du mouvement d'un satellite}
-\date{23 juin 2\,012}
-%timeline
-\begin{filecontents}{satellite.dat}
-::0x0
-::1
-::2
-::3
-::4
-::5
-::6
-::7
-::8
-::9
-::10
-::11
-::12
-::13
-::14
-::15
-::16
-::17
-::18
-::19
-::20
-::21
-::22
-::23
-::24
-::25
-::26
-::27
-::28
-::29
-::30
-::31
-::32
-::33
-::34
-::35
-::36
-::37
-::38
-::39
-::40
-::41
-::42
-::43
-::44
-::45
-::46
-::47
-::48
-::49
-::50
-::51
-::52
-\end{filecontents}
-\newcommand{\Jupiter}{%
-  \psclip{\pscircle[fillstyle=solid,fillcolor=yellow]{1.5}}
-  \psset{fillstyle=solid,fillcolor={[cmyk]{0 0.2 0.4 0}},linestyle=none}
-    \psframe(-2,.6)(2,1)
-    \psframe(-2,0.45)(2,0.52)
-    \psframe(-2,.05)(2,.3)
-    \psframe(-2,-0.35)(2,-0.2)
-    \psframe(-2,-0.9)(2,-.5)
-  \endpsclip
-  \psellipse[fillstyle=solid,fillcolor={[cmyk]{0 0.4 0.6 0}},linestyle=none](-0.3,-0.6)(0.35,0.2)
-  \pscircle{1.5}}
-\begin{document}
-\def\eqsatellite{%
-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)}%
-\begin{center}
-%\begin{pspicture}(-10,-10)(6,6)
-\def\nFrames{50}% 50 images
-\begin{animateinline}[controls,loop,timeline=satellite.dat,%
-                     begin={\begin{pspicture}(-10,-10)(6,6)},
-                     end={\end{pspicture}}]{5}% 5 images/s
-%\uput[r](0,3){$y$}\uput[u](3,0){$x$}
-%\psset{unit=2}
-\psframe*[linecolor={[rgb]{0 0 0.5}}](-10,-10)(6,6)
-\pstVerb{/tabXiYi [(XiYi.dat) run] def}%
-\pstVerb{/GM 1 def
-    /theta0 30 def
-    /r0 2 def
-    /x0 r0 theta0 cos mul def
-    /y0 r0 theta0 sin mul def
-    /v0 0.85 def
-    /v0x v0 theta0 sin mul neg def
-    /v0y v0 theta0 cos mul def
-    /Lc r0 v0 mul def % moment cinetique
-    /par Lc dup mul GM div def % paramètre de l'ellipse
-% excentricité
-    /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
-%%%%%%%%%%%%%%
-    /a_2 par 1 exc dup mul sub div def % demi-grand axe
-    /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe
-    /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def}%
-\psequadiff[method=rk4,
-            plotpoints=1000,
-            algebraic,
-            whichabs=0,
-            whichord=1,
-            tabname=XiYi,
-%            saveData,filename=XiYi.dat
-]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
-\listplot[linecolor=gray,unit=2]{XiYi aload pop}
-\psequadiff[method=rk4,
-            plotpoints=1000,
-            algebraic,
-            whichabs=2,
-            whichord=3,
-            tabname=vxvy,
-%            saveData,filename=vxvy.dat
-]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%
-%\listplot[unit=2,linecolor=red]{vxvy aload pop}
-% on dessine la vitesse un point sur 50
-%\pscircle[fillcolor=gray!70,fillstyle=solid,unit=2](0,0){0.4}
-\Jupiter%
-%\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt,unit=2](-5,-5)(3,3)
-%\psline[arrowinset=0.05,arrowsize=0.1,unit=2]{<->}(3,0)(0,0)(0,3)
-\newframe
-\multiframe{\nFrames}{i=0+40}{
-\psset{unit=2}%
-\pstVerb{/tabXYpartiel {
-          2 2 \i\space {/I exch def
-          tabXiYi I get
-          tabXiYi I 1 add get
-          } for
-          } def
-         /vX vxvy \i\space get def
-         /vY vxvy \i\space 1 add get def
-         /xi tabXiYi \i\space get def
-         /yi tabXiYi \i\space 1 add get def
-         /ri3 xi dup mul yi dup mul add sqrt 3 exp def
-         /Fx xi ri3 div neg def
-         /Fy yi ri3 div neg def}%
-\listplot[linecolor=red,linewidth=0.05]{tabXYpartiel}
-\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)}}
-\newframe
-\listplot[linecolor=gray,unit=2]{XiYi aload pop}
-\listplot[linecolor=red,unit=2,linewidth=0.05]{XiYi aload pop}
-\psset{unit=2}%
-\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)}
-\end{animateinline}
-\end{center}
-\end{document}
+\documentclass{article}\r
+\usepackage[a4paper,margin=2cm]{geometry}\r
+\usepackage[latin1]{inputenc}\r
+\usepackage{pstricks,pst-eqdf}\r
+\usepackage{animate}\r
+\newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.125,linecolor={[rgb]{1 0.5 0}}}\r
+\newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.7 1}}}\r
+\newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0.5 0}}}\r
+%%%%%%%%%%%%%%%%%%\r
+\title{Animation du mouvement d'un satellite}\r
+\date{23 juin 2\,012}\r
+%timeline\r
+\begin{filecontents}{satellite.dat}\r
+::0x0\r
+::1\r
+::2\r
+::3\r
+::4\r
+::5\r
+::6\r
+::7\r
+::8\r
+::9\r
+::10\r
+::11\r
+::12\r
+::13\r
+::14\r
+::15\r
+::16\r
+::17\r
+::18\r
+::19\r
+::20\r
+::21\r
+::22\r
+::23\r
+::24\r
+::25\r
+::26\r
+::27\r
+::28\r
+::29\r
+::30\r
+::31\r
+::32\r
+::33\r
+::34\r
+::35\r
+::36\r
+::37\r
+::38\r
+::39\r
+::40\r
+::41\r
+::42\r
+::43\r
+::44\r
+::45\r
+::46\r
+::47\r
+::48\r
+::49\r
+::50\r
+::51\r
+::52\r
+\end{filecontents}\r
+\newcommand{\Jupiter}{%\r
+  \psclip{\pscircle[fillstyle=solid,fillcolor=yellow]{1.5}}\r
+  \psset{fillstyle=solid,fillcolor={[cmyk]{0 0.2 0.4 0}},linestyle=none}\r
+    \psframe(-2,.6)(2,1)\r
+    \psframe(-2,0.45)(2,0.52)\r
+    \psframe(-2,.05)(2,.3)\r
+    \psframe(-2,-0.35)(2,-0.2)\r
+    \psframe(-2,-0.9)(2,-.5)\r
+  \endpsclip\r
+  \psellipse[fillstyle=solid,fillcolor={[cmyk]{0 0.4 0.6 0}},linestyle=none](-0.3,-0.6)(0.35,0.2)\r
+  \pscircle{1.5}}\r
+\makeatletter\r
+%% adapté de \psRandom du package pstricks-add\r
+%% pour rendre aléatoire la taille des étoiles\r
+%% Manuel Luque\r
+\newdimen\pssizeStar\r
+\def\psset@sizeStar#1{\pssetlength\pssizeStar{#1}}\r
+\psset@sizeStar{1pt}\r
+\define@key[psset]{pst-eqd}{randomPoints}[1000]{\def\psk@randomPoints{#1}}\r
+\psset[pst-eqd]{randomPoints=1000}\r
+\define@boolkey[psset]{pst-eqd}[Pst@]{color}[true]{}\r
+\psset[pst-eqd]{color=false}\r
+\def\psRandomStar{\pst@object{psRandomStar}}%\r
+\def\psRandomStar@i{\@ifnextchar({\psRandomStar@ii}{\psRandomStar@iii(0,0)(1,1)}}\r
+\def\psRandomStar@ii(#1){\@ifnextchar({\psRandomStar@iii(#1)}{\psRandomStar@iii(0,0)(#1)}}\r
+\def\psRandomStar@iii(#1)(#2)#3{%\r
+  \def\pst@tempA{#3}%\r
+  \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi\r
+  \pst@getcoor{#1}\pst@tempA\r
+  \pst@getcoor{#2}\pst@tempB\r
+  \begin@SpecialObj\r
+  \addto@pscode{\r
+    \pst@tempA\space /yMin exch def\r
+    /xMin exch def\r
+    \pst@tempB\space /yMax exch def\r
+    /xMax exch def\r
+    /dy yMax yMin sub def\r
+    /dx xMax xMin sub def\r
+    rrand srand                 % initializes the random generator\r
+    /getRandReal { rand 2147483647 div } def\r
+     \psk@randomPoints {\r
+    /DS \pst@number\pssizeStar\space getRandReal mul def\r
+    \@nameuse{psds@\psk@dotstyle}\r
+     \ifPst@color getRandReal 1 1 sethsbcolor \fi\r
+     getRandReal dx mul xMin add\r
+     getRandReal dy mul yMin add\r
+     Dot\r
+     \ifx\psk@fillstyle\psfs@solid fill \fi stroke\r
+    } repeat\r
+  }%\r
+  \end@SpecialObj\r
+  \endpsclip\r
+  \ignorespaces\r
+}\r
+\makeatother\r
+\begin{document}\r
+\def\eqsatellite{%\r
+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)}%\r
+\begin{center}\r
+%\begin{pspicture}(-10,-10)(6,6)\r
+\def\nFrames{50}% 50 images\r
+\begin{animateinline}[controls,loop,timeline=satellite.dat,%\r
+                     begin={\begin{pspicture}(-10,-10)(6,6)},\r
+                     end={\end{pspicture}}]{5}% 5 images/s\r
+%\uput[r](0,3){$y$}\uput[u](3,0){$x$}\r
+%\psset{unit=2}\r
+\psframe*[linecolor={[cmyk]{1 1 0 0.7}}](-10,-10)(6,6)\r
+\psRandomStar[linecolor={[rgb]{1,1,0.5}},\r
+    randomPoints=1000,sizeStar=1.25pt](-10,-10)(6,6){\psframe[linestyle=none](-10,-10)(6,6)}\r
+\pstVerb{/tabXiYi [(XiYi.dat) run] def}%\r
+\pstVerb{/GM 1 def\r
+    /theta0 30 def\r
+    /r0 2 def\r
+    /x0 r0 theta0 cos mul def\r
+    /y0 r0 theta0 sin mul def\r
+    /v0 0.85 def\r
+    /v0x v0 theta0 sin mul neg def\r
+    /v0y v0 theta0 cos mul def\r
+    /Lc r0 v0 mul def % moment cinetique\r
+    /par Lc dup mul GM div def % paramètre de l'ellipse\r
+% excentricité\r
+    /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\r
+%%%%%%%%%%%%%%\r
+    /a_2 par 1 exc dup mul sub div def % demi-grand axe\r
+    /b_2 par 1 exc dup mul sub sqrt div def % demi-petit axe\r
+    /periode 2 3.1416 dup mul a_2 3 exp mul GM div sqrt mul def}%\r
+\psequadiff[method=rk4,\r
+            plotpoints=1000,\r
+            algebraic,\r
+            whichabs=0,\r
+            whichord=1,\r
+            tabname=XiYi,\r
+%            saveData,filename=XiYi.dat\r
+]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%\r
+\listplot[linecolor=gray,unit=2]{XiYi aload pop}\r
+\psequadiff[method=rk4,\r
+            plotpoints=1000,\r
+            algebraic,\r
+            whichabs=2,\r
+            whichord=3,\r
+            tabname=vxvy,\r
+%            saveData,filename=vxvy.dat\r
+]{0}{43}{x0 y0 v0x v0y}{\eqsatellite}%\r
+%\listplot[unit=2,linecolor=red]{vxvy aload pop}\r
+% on dessine la vitesse un point sur 50\r
+%\pscircle[fillcolor=gray!70,fillstyle=solid,unit=2](0,0){0.4}\r
+\Jupiter%\r
+%\psgrid[subgriddiv=2,gridcolor=lightgray,gridlabels=8pt,unit=2](-5,-5)(3,3)\r
+%\psline[arrowinset=0.05,arrowsize=0.1,unit=2]{<->}(3,0)(0,0)(0,3)\r
+\newframe\r
+\multiframe{\nFrames}{i=0+40}{\r
+\psset{unit=2}%\r
+\pstVerb{/tabXYpartiel {\r
+          2 2 \i\space {/I exch def\r
+          tabXiYi I get\r
+          tabXiYi I 1 add get\r
+          } for\r
+          } def\r
+         /vX vxvy \i\space get def\r
+         /vY vxvy \i\space 1 add get def\r
+         /xi tabXiYi \i\space get def\r
+         /yi tabXiYi \i\space 1 add get def\r
+         /ri3 xi dup mul yi dup mul add sqrt 3 exp def\r
+         /Fx xi ri3 div neg def\r
+         /Fy yi ri3 div neg def}%\r
+\listplot[linecolor=red,linewidth=0.05]{tabXYpartiel}\r
+\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)}}\r
+\newframe\r
+\listplot[linecolor=gray,unit=2]{XiYi aload pop}\r
+\listplot[linecolor=red,unit=2,linewidth=0.05]{XiYi aload pop}\r
+\psset{unit=2}%\r
+\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)}\r
+\end{animateinline}\r
+\end{center}\r
+\end{document}\r