double pendule exemple

double_pendule.py

@@ -0,0 +1,70 @@
+import legrandchien as lgc
+import matplotlib.pyplot as plt
+import matplotlib.animation as animation
+import numpy as np
+
+g = lgc.Const(-10)
+m1 = lgc.Const(1)
+m2 = lgc.Const(1)
+r1 = lgc.Const(1)
+r2 = lgc.Const(1)
+
+theta1 = lgc.Var("theta1")
+theta2 = lgc.Var("theta2")
+
+x1 = r1 * lgc.cos(theta1)
+y1 = r1 * lgc.sin(theta1)
+
+x2 = x1 + r2 * lgc.cos(theta2)
+y2 = y1 + r2 * lgc.sin(theta2)
+
+T = 0.5 * m1 * (x1.diff()*x1.diff() + y1.diff()*y1.diff())
+T += 0.5 * m2 * (x2.diff()*x2.diff() + y2.diff()*y2.diff())
+
+V = m1 * g * x1
+V += m2 * g * x2
+
+L = T - V
+
+init = {
+    "theta1" : -3 * np.pi/4,
+    "d_theta1" : 0,
+    "theta2" : -np.pi/2,
+    "d_theta2" : 0
+}
+
+data = L.solve(init, 10, 0.01)
+
+# Extraire les positions
+times = sorted(data.keys())
+positions = [data[t] for t in times]
+
+x1_positions = [r1.value * np.sin(p["theta1"]) for p in positions]
+y1_positions = [r1.value * np.cos(p["theta1"]) for p in positions]
+
+x2_positions = [x1_positions[i] + r2.value * np.sin(p["theta2"]) for i, p in enumerate(positions)]
+y2_positions = [y1_positions[i] + r2.value * np.cos(p["theta2"]) for i, p in enumerate(positions)]
+
+# 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()
+
+line1, = ax.plot([], [], 'o-', lw=2, markersize=8, label='Pendule 1')
+line2, = ax.plot([], [], 'o-', lw=2, markersize=8, label='Pendule 2')
+trace, = ax.plot([], [], 'r-', alpha=0.3, lw=1, label='Trace')
+
+def animate(frame):
+    line1.set_data([0, x1_positions[frame]], [0, y1_positions[frame]])
+    line2.set_data([x1_positions[frame], x2_positions[frame]], [y1_positions[frame], y2_positions[frame]])
+    trace.set_data(x2_positions[:frame+1], y2_positions[:frame+1])
+    return line1, line2, trace
+
+ax.legend()
+anim = animation.FuncAnimation(fig, animate, frames=len(x1_positions), interval=50, blit=True, repeat=True)
+
+plt.show()