import legrandchien as lgc
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import numpy as np
import cProfile
import pstats

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, 5, 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()