FM 00-19

Author: M. V. Bartuccelli, G. Gentile , K.V. Georgiou

Title: On the Dynamics of a Vertically Driven Damped Planar Pendulum
 
Abstract: Results on the dynamics of the planar pendulum with parametric vertical time-periodic forcing are reviewed and extended. Numerical methods are employed to study the various dynamical features of the system about its equilibrium positions. Furthermore the dynamics of the system far from its equilibrium points is systematically investigated by using phase portraits and Poincare' sections. The attractors and the associated basins of attraction are computed. We also calculate the Lyapunov exponents to show that for some parameter values the dynamics of the pendulum shows sensitivity to initial conditions.

Keywords: Basins of attraction, attractors, Poincare' sections, Lyapunov exponents.

Michele Bartuccelli
Department of Mathematics and Statistics,
University of Surrey
Guildford, GU2 7XH
e-mail: m.bartuccelli@eim.surrey.ac.uk

Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@matrm3.mat.uniroma3.it

Kyriakos G. Georgiou
Department of Mathematics and Statistics,
University of Surrey
Guildford, GU2 7XH
e-mail: k.georgiou@eim.surrey.ac.uk