image thumbnail

Forced damped driven pendulum

version 1.0.0.0 (8.35 KB) by Adam Wyatt
A forced damped driven pendulum exhibits chaotic motion.

4.6K Downloads

Updated 23 Jul 2007

View License

This simulink model simulates the damped driven pendulum, showing it's chaotic motion.
theta = angle of pendulum
omega = (d/dt)theta = angular velocity
Gamma(t) = gcos(phi) = Force
omega_d = (d/dt) phi
Gamma(t) = (d/dt)omega + omega/Q + sin(theta)

Play with the initial conditions (omega_0, theta_0, phi_0 = omega(t=0), theta(t=0), phi(t=0)) and the system parameters (g, Q, omega_d) and the solver parameters/method.

Chaos can be seen for Q=2, omega_d=w/3.

The program outputs to Matlab time, theta(time) & omega(time).

Plot the phase space via:
plot(mod(theta+pi, 2*pi)-pi, omega, '.');

Plot the Poincare sections using:
t_P = (0:2*pi/omega_d:max(time))';
plot(mod(spline(time, theta+pi, t_P), 2*pi)-pi, spline(time, omega, t_P), '.');

System is described in:
"Fractal basin boundaries and intermittency in the driven damped pendulum"
E. G. Gwinn and R. M. Westervelt
PRA 33(6):4143 (1986)

Cite As

Adam Wyatt (2021). Forced damped driven pendulum (https://www.mathworks.com/matlabcentral/fileexchange/15656-forced-damped-driven-pendulum), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2007a
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!