Wednesday, June 13, 2012

1206.2481 (Anton O. Belyakov et al.)

Homoclinic, Subharmonic and Superharmonic Bifurcations for a Pendulum
with Periodically Varying Length

Anton O. Belyakov, Alexander P. Seyranian
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the simplest model of child's swing. Melnikov's analysis is carried out to find bifurcations of homoclinic, subharmonic oscillatory, and subharmonic rotational orbits. For the analysis of superharmonic rotational orbits the averaging method is used. The analytical results are compared with numerical simulation results.
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