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Locating oscillatory orbits of the parametrically-excited pendulum

Published online by Cambridge University Press:  17 February 2009

M. J. Clifford  and
S. R. Bishop
M. J. Clifford
Affiliation:
Centre for Nonlin. Dyn. and its Appl'ns, University College London, WC1E 6BT, U.K.
S. R. Bishop
Affiliation:
Centre for Nonlin. Dyn. and its Appl'ns, University College London, WC1E 6BT, U.K.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 3 , January 1996 , pp. 309 - 319
Copyright
Copyright © Australian Mathematical Society 1996

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