Chaos in a Magnetic Pendulum Subjected to Tilted Excitation and Parametric Damping

Abstract

The effect of tilted harmonic excitation and parametric damping on the chaotic dynamics in an asymmetric magnetic pendulum is investigated in this paper. The Melnikov method is used to derive a criterion for transition to nonperiodic motion in terms of the Gauss hypergeometric function. The regular and fractal shapes of the basin of attraction are used to validate the Melnikov predictions. In the absence of parametric damping, the results show that an increase of the tilt angle of the excitation causes the lower bound for chaotic domain to increase and produces a singularity at the vertical position of the excitation. It is also shown that the presence of parametric damping without a periodic fluctuation can enhance or suppress chaos while a parametric damping with a periodic fluctuation can increase the region of regular motions significantly.