velocity_verlet_integration 1

Query

import numpy as np

def verlet_integrate(x0, v0, F, steps=1000, dt=0.001):
    """
    Integrates given force field with Velocity-Verlet integration
    """
    x_traj = np.zeros(steps)
    v_traj = np.zeros(steps)
    [insert]
    return x_traj, v_traj

Output

import numpy as np

def verlet_integrate(x0, v0, F, steps=1000, dt=0.001):
    """
    Integrates given force field with Velocity-Verlet integration
    """
    x_traj = np.zeros(steps)
    v_traj = np.zeros(steps)
    x_traj[0] = x0
    v_traj[0] = v0
    for i in range(steps-1):
        v_traj[i+1] = v_traj[i] + 0.5*dt*F(x_traj[i])
        x_traj[i+1] = x_traj[i] + dt*v_traj[i+1]
        v_traj[i+1] = v_traj[i+1] + 0.5*dt*F(x_traj[i+1])
    return x_traj, v_traj

Evaluate

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