Inverted oscillations of a driven pendulum

Inverted oscillations of a parametrically driven planar pendulum are considered, together with their relationship to the inverted solution. In particular, a horseshoe structure of the associated manifolds is identified which explains the similarity between the bifurcations of the inverted position a...

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Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 1998-11, Vol.454 (1979), p.2811-2817
Hauptverfasser: Clifford, M. J., Bishop, S. R.
Format: Artikel
Sprache:eng
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Zusammenfassung:Inverted oscillations of a parametrically driven planar pendulum are considered, together with their relationship to the inverted solution. In particular, a horseshoe structure of the associated manifolds is identified which explains the similarity between the bifurcations of the inverted position and the hanging position. This allows us to apply a large body of existing knowledge to the dynamics enabling a lower bound on the forcing required to achieve inverted oscillations to be established.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.1998.0282