Symplectic Step

Problem

Take one velocity Verlet (symplectic) step for the oscillator with potential 0.5 * k * x ** 2.

Set x_new = x + dt * v - 0.5 * dt ** 2 * k * x, v_half = v - 0.5 * dt * k * x, and v_new = v_half - 0.5 * dt * k * x_new. Return [x_new, v_new].

Hint

Velocity Verlet splits the kick into two half-steps around the drift.

case 1

in: [1,0,1,0.1]

expected: [0.995,-0.09975]

case 2

in: [0,1,2,0.5]

expected: [0.5,0.75]

case 3

in: [2,-1,0.5,0.2]

expected: [1.78,-1.189]

Starter codePython

def symplectic_step(x, v, k, dt):
    # Returns [x_new, v_new]
    # Your code here
    pass

3 test cases · run your code against them in the editor