3-Body-Problem/yT.py at main · galavashubhang/3-Body-Problem · GitHub

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import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp
import time

# ------------------------------------------------------------------- #

m1 = 1.0
m2 = 1.0
m3 = 1.0

# Position
inital_position_1 =  [-0.5,  0.0,  0.0]
inital_position_2 =  [0.5,  0.0,  0.0]
inital_position_3 =  [0.0,   0.001, 1.0]

# Velocity
inital_velocity_1 =  [0.0, 0.347111, 0]
inital_velocity_2 =  [0.0, -0.347111, 0.0]
inital_velocity_3 =  [0.0, 0.0, -0.1]

initial_conditions = np.array([
    inital_position_1, inital_position_2, inital_position_3,
    inital_velocity_1, inital_velocity_2, inital_velocity_3
]).ravel()

# ------------------------------------------------------------------- #

def system_odes(t, S, m1, m2, m3):
    p1, p2, p3 = S[0:3], S[3:6], S[6:9]
    dp1_dt, dp2_dt, dp3_dt = S[9:12], S[12:15], S[15:18]

    f1, f2, f3 = dp1_dt, dp2_dt, dp3_dt

    df1_dt = m3*(p3 - p1)/np.linalg.norm(p3 - p1)**3 + m2*(p2 - p1)/np.linalg.norm(p2 - p1)**3
    df2_dt = m3*(p3 - p2)/np.linalg.norm(p3 - p2)**3 + m1*(p1 - p2)/np.linalg.norm(p1 - p2)**3
    df3_dt = m1*(p1 - p3)/np.linalg.norm(p1 - p3)**3 + m2*(p2 - p3)/np.linalg.norm(p2 - p3)**3

    return np.array([f1, f2, f3, df1_dt, df2_dt, df3_dt]).ravel()

# ------------------------------------------------------------------- #


time_s, time_e = 0, 7
t_points = np.linspace(time_s, time_e, 2001)

t1 = time.time()
solution = solve_ivp(
    fun=system_odes,
    t_span=(time_s, time_e),
    y0=initial_conditions,
    t_eval=t_points,
    args=(m1, m2, m3)
)
t2 = time.time()
print(f"Solved in: {t2-t1:.3f} [s]")


t_sol = solution.t
p1x_sol = solution.y[0]
p1y_sol = solution.y[1]
p1z_sol = solution.y[2]

p2x_sol = solution.y[3]
p2y_sol = solution.y[4]
p2z_sol = solution.y[5]

p3x_sol = solution.y[6]
p3y_sol = solution.y[7]
p3z_sol = solution.y[8]

# ------------------------------------------------------------------- #

fig, ax = plt.subplots(subplot_kw={"projection":"3d"})

planet1_plt, = ax.plot(p1x_sol, p1y_sol, p1z_sol, 'green', label='Planet 1', linewidth=1)
planet2_plt, = ax.plot(p2x_sol, p2y_sol, p2z_sol, 'red', label='Planet 2', linewidth=1)
planet3_plt, = ax.plot(p3x_sol, p3y_sol, p3z_sol, 'blue',label='Planet 3', linewidth=1)

planet1_dot, = ax.plot([p1x_sol[-1]], [p1y_sol[-1]], [p1z_sol[-1]], 'o', color='green', markersize=6)
planet2_dot, = ax.plot([p2x_sol[-1]], [p2y_sol[-1]], [p2z_sol[-1]], 'o', color='red', markersize=6)
planet3_dot, = ax.plot([p3x_sol[-1]], [p3y_sol[-1]], [p3z_sol[-1]], 'o', color='blue', markersize=6)


ax.set_title("The 3-Body Problem")
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
plt.grid()
plt.legend()

# ------------------------------------------------------------------- #


from matplotlib.animation import FuncAnimation

# -------  Animating the solutions ------- #

def update(frame):
    lower_lim = max(0, frame - 300)
    print(f"Progress: {(frame+1)/len(t_points):.1%} | 100.0 %", end='\r')

    x_current_1 = p1x_sol[lower_lim:frame+1]
    y_current_1 = p1y_sol[lower_lim:frame+1]
    z_current_1 = p1z_sol[lower_lim:frame+1]

    x_current_2 = p2x_sol[lower_lim:frame+1]
    y_current_2 = p2y_sol[lower_lim:frame+1]
    z_current_2 = p2z_sol[lower_lim:frame+1]

    x_current_3 = p3x_sol[lower_lim:frame+1]
    y_current_3 = p3y_sol[lower_lim:frame+1]
    z_current_3 = p3z_sol[lower_lim:frame+1]

    planet1_plt.set_data(x_current_1, y_current_1)
    planet1_plt.set_3d_properties(z_current_1)

    planet1_dot.set_data([x_current_1[-1]], [y_current_1[-1]])
    planet1_dot.set_3d_properties([z_current_1[-1]])


    planet2_plt.set_data(x_current_2, y_current_2)
    planet2_plt.set_3d_properties(z_current_2)

    planet2_dot.set_data([x_current_2[-1]], [y_current_2[-1]])
    planet2_dot.set_3d_properties([z_current_2[-1]])


    planet3_plt.set_data(x_current_3, y_current_3)
    planet3_plt.set_3d_properties(z_current_3)

    planet3_dot.set_data([x_current_3[-1]], [y_current_3[-1]])
    planet3_dot.set_3d_properties([z_current_3[-1]])


    return planet1_plt, planet1_dot, planet2_plt, planet2_dot, planet3_plt, planet3_dot

animation = FuncAnimation(fig, update, frames=range(0, len(t_points), 2), interval=10, blit=True)
plt.show()