Dynamics of Hula-Hoop in Horizontal Plane: Periodic Solutions and Chaos

The motions of hula-hoop were widely analyzed about the non-dimensional parameters related to damping and vibration amplitude of fulcrum using ordinary numerical integration and the shooting method. There exist many types of motion depending on the damping and the amplitude of fulcrum, namely, symmetrical and unsymmetrical rotation, symmetrical and unsymmetrical subharmonic vibration, rotation superior and vibration superior type chaos and so on. It is made clear that each periodic solution bifurcates from symmetrical motion to unsymmetrical motion, and bifurcates to chaos after period doubling bifurcations. The obtained solutions were verified by the experiment, and the results were qualitatively in good agreement with each other. Lastly, the motions of hula-hoop were evaluated from the viewpoint of the kinetic energy of the hula-hoop.