Random walker with damping and inertia

rw_damping_inertia.py

import numpy as np

def xyindependent(x,b,c,dt,randomfun):
    for idx in range(2,len(x)):
        x[idx] =(2-b*dt)*x[idx-1] + (b*dt-c*dt*dt-1)*x[idx-2] + dt*dt*randomfun()
    return x

import matplotlib.pyplot as plt

x0 = np.zeros(100,)
y0 = np.zeros(100,)
dt = 0.01

damping = -0.5 # play around
mass = 1/3 # play around

x0 = xyindependent(x0,-damping,1./mass,dt, lambda : np.random.uniform(-0.1,0.5))
y0 = xyindependent(y0,-damping,1./mass,dt, lambda : np.random.uniform(-0.1,0.5))

fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(x0,y0,label="x/y")
ax.set_aspect(1)