ForcedPendulum

  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) )