Dynamic Modeling and Stability Analysis of Mechanical Systems with Time-Varying Topologies

Abstract

A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of a Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of a dynamic model and a local stability analysis are presented.