The various motions of hula-hoop were analyzed using the shooting method and ordinary numerical integration. The obtained solutions were verified by the experiment. The results are summarized as follows : There exist many types of motion depending on the ratio of vibration amplitude of supporting point and the length between the center of gravity and supporting point of hula-hoop, namely, synchronized rotation, synchronized subharmonic rotation, harmonic vibration, subharmonic vibration, chaos and so on. It is made clear that the velocity of rotation of the synchronized rotation is not constant, but fluctuates, the solution of synchronized rotation bifurcate to chaos after period doubling bifurcations. The experimental and the analytical results were qualitatively in good agreement with each other.
