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Inverted oscillations of a driven pendulum

1998; Royal Society; Volume: 454; Issue: 1979 Linguagem: Inglês

10.1098/rspa.1998.0282

1471-2946

Mike Clifford, Steven R. Bishop,

Advanced Differential Equations and Dynamical Systems

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.