problème à trois corps

examples/trois_corps.py

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+import sys
+import os
+sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+
+import legrandchien as lgc
+import matplotlib.pyplot as plt
+import matplotlib.animation as animation
+import numpy as np
+
+x1 = lgc.Var()
+y1 = lgc.Var()
+x2 = lgc.Var()
+y2 = lgc.Var()
+x3 = lgc.Var()
+y3 = lgc.Var()
+
+m1 = lgc.Const(1)
+m2 = lgc.Const(1)
+m3 = lgc.Const(1)
+G = 1
+
+T = 0.5 * m1 * (x1.diff()**2 + y1.diff()**2)
+T += 0.5 * m2 * (x2.diff()**2 + y2.diff()**2)
+T += 0.5 * m3 * (x3.diff()**2 + y3.diff()**2)
+
+r12 = ((x1 - x2)**2 + (y1 - y2)**2)**0.5
+r13 = ((x1 - x3)**2 + (y1 - y3)**2)**0.5
+r23 = ((x2 - x3)**2 + (y2 - y3)**2)**0.5
+
+V = -G * m1 * m2 / r12
+V += -G * m1 * m3 / r13
+V += -G * m2 * m3 / r23
+
+L = T - V
+
+init = {
+    x1: [1, -0.5],
+    y1: [1, 0.5],
+    x2: [-1, -0.25],
+    y2: [-0.5, 0.5],
+    x3: [0, 0.5],
+    y3: [0, -1],
+}
+
+dt = 0.01
+data = L.solve(init, 10, dt)
+
+# Extraire les positions
+times = sorted(data.keys())
+positions = [data[t] for t in times]
+
+x1_positions = [p["x1"] for p in positions]
+y1_positions = [p["y1"] for p in positions]
+x2_positions = [p["x2"] for p in positions]
+y2_positions = [p["y2"] for p in positions]
+x3_positions = [p["x3"] for p in positions]
+y3_positions = [p["y3"] for p in positions]
+
+fps = 25
+frame_skip = max(1, int(1 / (fps * dt)))
+
+display_indices = list(range(0, len(x1_positions), frame_skip))
+x1_display = [x1_positions[i] for i in display_indices]
+y1_display = [y1_positions[i] for i in display_indices]
+x2_display = [x2_positions[i] for i in display_indices]
+y2_display = [y2_positions[i] for i in display_indices]
+x3_display = [x3_positions[i] for i in display_indices]
+y3_display = [y3_positions[i] for i in display_indices]
+
+# Créer la figure
+fig, ax = plt.subplots(figsize=(8, 8))
+ax.set_xlim(-3, 3)
+ax.set_ylim(-3, 3)
+ax.set_xlabel("X")
+ax.set_ylabel("Y")
+ax.grid(True)
+
+point1, = ax.plot([], [], 'o', markersize=10, label='Corps 1')
+point2, = ax.plot([], [], 'o', markersize=10, label='Corps 2')
+point3, = ax.plot([], [], 'o', markersize=10, label='Corps 3')
+
+def animate(frame):
+    point1.set_data([x1_display[frame]], [y1_display[frame]])
+    point2.set_data([x2_display[frame]], [y2_display[frame]])
+    point3.set_data([x3_display[frame]], [y3_display[frame]])
+    return point1, point2, point3
+
+ax.legend()
+anim = animation.FuncAnimation(fig, animate, frames=len(x1_display), interval=1000//fps, blit=True, repeat=True)
+
+plt.show()