Abstract
In this thesis, the concept and definition of hula-hoop motion will be introduced. The hula-hoop system is constructed simply by a main mass and a free-moving mass. By mimicking the motion characteristics of the hula-hoop, which is commonly regarded as the circular oscillations where a ring spins around a moving human body. The main mass that performs reciprocating motion is considered as the human body while the free-moving mass that rotates around the main mass simulates the ring. Considering the impulsive excitation as the external force, the governing nonlinear equations are first formulated based upon Lagrange’s equation. Then, a thorough dynamic analysis is performed to understand the relation between the varied system parameters and the chance of occurrence of hula-hoop motion. The possibility of existence of the approximate analytical solutions can be evaluated by stability analysis. The numerical simulation is also performed by using direct integration method to verify the aforementioned qualitative analysis. Finally, Phase plane and Poincaré section are used to analyze the dynamic response. On the basis of the obtained results, the design guidelines for initial conditions to ensure the occurrence of hula-hoop motions are distilled and can be applied to the micro-generator.