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  • License: Freeware
  • Last update: 6 years ago
  • Total downloads: 286
  • Price: Free |
  • Operating system: Linux, Mac OS X, Win All, BSD, Solaris
  • Publisher: Adam Wyatt (10 other programs)
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scripts default iconForced damped driven pendulum (Scripts) Publisher's description

This simulink model simulates the damped driven pendulum, showing it's chaotic motion.

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)

System Requirements:

MATLAB 7.4 (R2007a)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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