rajout du pendule simple

pendule_simple.py

@@ -0,0 +1,64 @@
+import legrandchien as lgc
+import matplotlib.pyplot as plt
+import matplotlib.animation as animation
+import numpy as np
+
+g = lgc.Const(-10)
+m = lgc.Const(1)
+r = lgc.Const(1)
+
+theta = lgc.Var("theta")
+
+x = r * lgc.cos(theta)
+y = r * lgc.sin(theta)
+
+T = 0.5 * m * (x.diff()*x.diff() + y.diff()*y.diff())
+V = m * g * r * lgc.cos(theta)
+
+L = T - V
+
+init = {
+    "theta" : -3 * 3.14/4,
+    "d_theta" : 0,
+}
+
+dt = 0.01
+data = L.solve(init, 10, dt, True)
+
+# Extraire les positions
+times = sorted(data.keys())
+positions = [data[t] for t in times]
+
+x_positions = [r.value * np.sin(p["theta"]) for p in positions]
+y_positions = [r.value * np.cos(p["theta"]) for p in positions]
+
+# Calculer l'intervalle de frame pour 25 fps
+fps = 25
+frame_skip = max(1, int(1 / (fps * dt)))
+
+# Filtrer les frames
+display_indices = list(range(0, len(x_positions), frame_skip))
+x_display = [x_positions[i] for i in display_indices]
+y_display = [y_positions[i] for i in display_indices]
+
+# Créer la figure et l'axe
+fig, ax = plt.subplots(figsize=(8, 8))
+ax.set_xlim(-3, 3)
+ax.set_ylim(-3, 3)
+ax.set_xlabel("X (m)")
+ax.set_ylabel("Y (m)")
+ax.grid(True)
+ax.invert_yaxis()
+
+line, = ax.plot([], [], 'o-', lw=2, markersize=8, label='Pendule')
+trace, = ax.plot([], [], 'r-', alpha=0.3, lw=1, label='Trace')
+
+def animate(frame):
+    line.set_data([0, x_display[frame]], [0, y_display[frame]])
+    trace.set_data(x_display[:frame+1], y_display[:frame+1])
+    return line, trace
+
+ax.legend()
+anim = animation.FuncAnimation(fig, animate, frames=len(x_display), interval=40, blit=True, repeat=True)
+
+plt.show()