An energy perturbation approach to limit cycle analysis in legged locomotion systems

The energy-balance method, originally developed for systems whose behaviors are described by a single continuous differential equation, is extended to hopping systems, where the equations of motion are discontinuous from one phase to the other. Specifically, the perturbation and energy-balance methods were combined to study the existence and stability of the limit cycle behavior of a vertical hopper system. Estimated values of the limit cycles obtained using the proposed method are compared with the true (simulated) values for both the linear and the nonlinear models. The results confirm the validity of the proposed method