gravitation/lancer_incline_distiller.tex

   1 \documentclass{article}
   2 \usepackage[a4paper,margin=2cm]{geometry}
   3 \usepackage[latin1]{inputenc}
   4 \usepackage{pstricks-add,pst-eqdf,pst-func}
   5 \usepackage{array,amsmath}
   6
   7 %%%%%%%%%%%%%%%%%%
   8 \def\datRoot{C:/Users/J\"{u}rgen/Desktop/gravitation/}
   9
  10 \begin{document}
  11
  12 \def\eqlancerA{%
  13 y[2]|y[3]|-d0/m0*y[2]|-d0/m0*y[3]-g0}%
  14 \def\eqlancerB{%
  15 y[2]|y[3]|0|-g0}%
  16
  17 \section{Un lancer inclin\'{e} avec du frottement}
  18
  19 Les \'{e}quations diff\'{e}rentielles sont :
  20 \begin{align*}
  21 \ddot{x}&=-\frac{d}{m}\dot{x}\\
  22 \ddot{y}&=-\frac{d}{m}\dot{y}-g
  23 \end{align*}
  24
  25 \begin{center}
  26 \begin{pspicture}(-0.5,-0.5)(10,6)
  27 \pstVerb{
  28     /m0 1 def
  29     /d0 0.75 def
  30     /theta0 60 def
  31     /x0 0 def
  32     /y0 1 def
  33     /v0 10 def
  34     /v0x v0 theta0 cos mul def
  35     /v0y v0 theta0 sin mul def
  36     /g0 9.81 def
  37 }%
  38 \psaxes[labels=none,ticks=none]{->}(0,0)(0,0)(10,5)
  39 \uput[0](10,0){$x$}
  40 \uput[90](0,5){$y$}
  41 \rput(!0 y0){%
  42 \psline[linecolor=gray]{->}(0;0)(!2 theta0 cos mul 2 theta0 sin mul)
  43 \psline[linestyle=dashed](0,0)(1.5,0)
  44 \psarc{->}(0,0){1}{0}{!theta0}
  45 \rput(!2.2 theta0 cos mul 2.2 theta0 sin mul){$\vec{v}_0$}
  46 \rput(!0.5 theta0 2 div cos mul 0.5 theta0 2 div sin mul){$\alpha$}
  47 }
  48 \psequadiff[method=rk4,
  49             plotpoints=1000,
  50             algebraic,
  51             whichabs=0,
  52             whichord=1,
  53             tabname=XiAYiA
  54 %           ,saveData,filename=XiYi.dat
  55 ]{0}{5}{x0 y0 v0x v0y}{\eqlancerA}%
  56 \listplot[linecolor=blue]{XiAYiA aload pop}
  57 \psequadiff[method=rk4,
  58             plotpoints=1000,
  59             algebraic,
  60             whichabs=0,
  61             whichord=1,
  62             tabname=XiBYiB
  63 %           ,saveData,filename=XiYi.dat
  64 ]{0}{5}{x0 y0 v0x v0y}{\eqlancerB}%
  65 \listplot[linecolor=red]{XiBYiB aload pop}
  66
  67 \end{pspicture}
  68 \end{center}
  69
  70
  71
  72 \end{document}