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# Forced damped driven pendulum 1.0

Date Added: May 10, 2013  |  Visits: 213

This simulink model simulates the damped driven pendulum, showing it's chaotic motion.theta = angle of pendulumomega = (d/dt)theta = angular velocityGamma(t) = gcos(phi) = Forceomega_d = (d/dt) phiGamma(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. WesterveltPRA 33(6):4143 (1986)

 Requirements: No special requirements Platforms: Matlab Keyword: Boundaries,  Gwinn,  Intermittency,  Matlab,  Omega,  Omegatimeplot,  Outputs,  Parametersmethodchaos,  Pendulumquote,  Phase,  Pipi,  Plot,  Poincare,  Program,  Sections,  Solver,  Space,  Thetatime,  Viaplotmodtheta Bpi Users rating: 0/10

 License: Freeware Size: 10 KB
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