J Austral Math Soc Ser B 37 pp309--319, 1996.

Locating oscillatory orbits of the parametrically-excited pendulum

M. J. Clifford and S. R. Bishop

Abstract

A method is considered for locating oscillating, nonrotating solutions for the parametrically-excited pendulum by inferring that a particular horseshoe exists in the stable and unstable manifolds of the local saddles. In particular, odd-periodic solutions are determined which are difficult to locate by alternative numerical techniques. A pseudo-Anosov braid is also located which implies the existence of a countable infinity of periodic orbits without the horseshoe assumption being necessary.

Browse the article

Authors

M. J. Clifford

S. R. Bishop

Centre for Nonlin. Dyn. and its Appl'ns, University College London, WC1E 6BT, U.K.