Dynamic Analysis of a Hula-Hoop System

This paper presents a theoretical and experimental study into the dynamics of a hula-hoop system, in which a free-rotating mass mimicking the ring is hinged on a main mass that simulates the human body and performs translational reciprocating motion under external excitations. The physical model of the hula-hoop system was first constructed and the equations governing the motions of the main mass and the free-rotating mass were, then, derived. The approximate steady-state solutions were obtained by employing homotopy perturbation method and the stabilities of which were analyzed by using Floquet theory. Good agreement between the results obtained from stability analysis and numerical simulation implied that the approximate solutions were adequate for the dynamic analysis of the proposed model. Finally, an experimental rig consisting of a semicircular thin plate hinged on the top of a linear-motor stage was devised to mimic the hula-hoop motion based on the analytical analysis.