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

摘要

Dynamic behavior of a weightless rod with a point mass sliding along the rodaxis according to periodic law is studied. This is the simplest model ofchild's swing. Melnikov's analysis is carried out to find bifurcations ofhomoclinic, subharmonic oscillatory, and subharmonic rotational orbits. For theanalysis of superharmonic rotational orbits the averaging method is used andstability of obtained approximate solution is checked. The analytical resultsare compared with numerical simulation results.