FM 01-05

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

Title: On the Stability of the Upside-Down Pendulum with Damping}
 
Abstract: A rigorous analysis is presented in order to show that, in presence of friction, the upward equilibrium position of the vertically driven pendulum, with a small non-vanishing damping term, becomes asymptotically stable when the period of the forcing is below an appropriate threshold value. As a byproduct we obtain an analytic expression of the solution for initial data close enough to the equilibrium position.

Keywords: Pendulum, Mathieu's equation, perturbation theory, stability, basins of attraction

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