The nonlinear dynamics of hula hoop motion is deciphered in this study by nonlinear dynamic modeling techniques to find solution and stability analysis. This is different from the previous study , where a homotopy method is employed. The analysis results are capable of transforming linear reciprocating motion into rotational motion. The dynamic governing equations of the system are first successfully derived by force balance. The non-linear dynamic analysis is next applied to derive approximate, asymptotic solutions. Stabilities associated with all solution are determined by subsequent analysis on the derived asymptotic solutions. In addition, the transformer could be integrated with coils, magnets, and electric circuits to form a portable energy scavenging device. A novel front-end circuit is proposed in this work for harvesting human's energy. The situation of human's walking and running is simulated by a shaker. And the ac-like energy is processed by the novel energy harvesting circuit, transformed as a DC voltage suitable for devices successfully. The efficiency of the entire circuit is proven up to 60%, and is an input-powered circuit with no standby power. A complete experimental system is also designed and successfully confirm the existence of the stable nonlinear solutions found by analytical and numerical analysis.