00-408 Michele V. Bartuccelli, Guido Gentile, Kyriakos V. Georgiou

On the dynamics of a vertically driven damped planar pendulum (4603K, Postscript) Oct 18, 00

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Abstract. The dynamics of the planar pendulum with parametric vertical time-periodic forcing is considered. Analytical and numerical methods are employed to study the various dynamical features of the system. A rigorous analysis is presented in order to show that, in presence of friction, the upward equilibrium position becomes asymptotically stable when the period of the forcing is below an appropriate threshold; this is illustrated by performing numerical computations and advanced visualization techniques. Also the dynamics of the system far from its equilibrium points is systematically investigated by using Poincare' sections and phase portraits. The attractors and the associated basins of attraction are computed. Furthermore we calculate the Lyapunov exponents to show that for some parameter values the dynamics of the pendulum shows sensitivity to initial conditions.

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