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)

-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)