| Description |
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) |
