Hula-Hoop: An Example of Heteroparametric Excitation Available to Purchase

This paper considers the parametric excitation of a pendulum swinging in a horizontal plane. It is shown that there exist a number of different limit cycle motions, one of which is a steady rotation about the point of support. This motion is associated with the mechanism whereby a Hula-Hoop may be kept in rotation by an oscillatory motion of the point of support. The stability and dependence of this type of motion on the initial conditions are analyzed in detail.