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931d118..524ca74 100644 --- 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} +\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}} +\makeatletter +%% adapté de \psRandom du package pstricks-add +%% pour rendre aléatoire la taille des étoiles +%% Manuel Luque +\newdimen\pssizeStar +\def\psset@sizeStar#1{\pssetlength\pssizeStar{#1}} +\psset@sizeStar{1pt} +\define@key[psset]{pst-eqd}{randomPoints}[1000]{\def\psk@randomPoints{#1}} +\psset[pst-eqd]{randomPoints=1000} +\define@boolkey[psset]{pst-eqd}[Pst@]{color}[true]{} +\psset[pst-eqd]{color=false} +\def\psRandomStar{\pst@object{psRandomStar}}% +\def\psRandomStar@i{\@ifnextchar({\psRandomStar@ii}{\psRandomStar@iii(0,0)(1,1)}} +\def\psRandomStar@ii(#1){\@ifnextchar({\psRandomStar@iii(#1)}{\psRandomStar@iii(0,0)(#1)}} +\def\psRandomStar@iii(#1)(#2)#3{% + \def\pst@tempA{#3}% + \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi + \pst@getcoor{#1}\pst@tempA + \pst@getcoor{#2}\pst@tempB + \begin@SpecialObj + \addto@pscode{ + \pst@tempA\space /yMin exch def + /xMin exch def + \pst@tempB\space /yMax exch def + /xMax exch def + /dy yMax yMin sub def + /dx xMax xMin sub def + rrand srand % initializes the random generator + /getRandReal { rand 2147483647 div } def + \psk@randomPoints { + /DS \pst@number\pssizeStar\space getRandReal mul def + \@nameuse{psds@\psk@dotstyle} + \ifPst@color getRandReal 1 1 sethsbcolor \fi + getRandReal dx mul xMin add + getRandReal dy mul yMin add + Dot + \ifx\psk@fillstyle\psfs@solid fill \fi stroke + } repeat + }% + \end@SpecialObj + \endpsclip + \ignorespaces +} +\makeatother +\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={[cmyk]{1 1 0 0.7}}](-10,-10)(6,6) +\psRandomStar[linecolor={[rgb]{1,1,0.5}}, + randomPoints=1000,sizeStar=1.25pt](-10,-10)(6,6){\psframe[linestyle=none](-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} -- 2.20.1