The Kitchin Research Group

import numpy as np
from scipy.integrate import odeint

def dfdt(F, t):
    rho, theta, z = F
    drhodt = 0   # constant radius
    dthetadt = 1 # constant angular velocity
    dzdt = -1    # constant dropping velocity
    return [drhodt, dthetadt, dzdt]

# initial conditions
rho0 = 1
theta0 = 0
z0 = 100

tspan = np.linspace(0, 50, 500)
sol = odeint(dfdt, [rho0, theta0, z0], tspan)

rho = sol[:,0]
theta = sol[:,1]
z = sol[:,2]

# convert cylindrical coords to cartesian for plotting.
X = rho * np.cos(theta)
Y = rho * np.sin(theta)

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(X, Y, z)
plt.savefig('images/ode-cylindrical.png')