## Plotting ODE solutions in cylindrical coordinates

Posted February 07, 2013 at 09:00 AM | categories: ode | tags: | View Comments

Updated March 06, 2013 at 06:33 PM

It is straightforward to plot functions in Cartesian coordinates. It is less convenient to plot them in cylindrical coordinates. Here we solve an ODE in cylindrical coordinates, and then convert the solution to Cartesian coordinates for simple plotting.

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')

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