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Chaotic Motion of Perturbed Pendulum

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From the Hamiltonian corresponding to a pendulum with a rotating point of suspension, this Demonstration calculates the phase portrait showing chaotic dynamics, whose most notable feature is the existence of a separatrix.

Contributed by: Enrique Zeleny (April 2013)
Open content licensed under CC BY-NC-SA

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Details

The Hamiltonian is

,

where is the frequency of small oscillations for the unperturbed case, is a dimensionless parameter of perturbation chosen to be small, and is the frequency.

Reference

[1] G. M. Zaslavsky, Physics of Chaos in Hamiltonian Systems, 2nd ed., London: Imperial College Press, 2007 pp. 14–17.

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