Dynamical Systems with Frictions

Abstract

In this chapter, two dynamical systems connected with frictions will be presented, and such two discontinuous dynamical systems possess a moving boundary. For such a problem, the analytical conditions for motion switching and sliding on the time-varying boundary will be developed. Based on the time-varying boundary, the basic mappings are introduced and the mapping structures for periodic motions will be developed. From a certain mapping structure, the corresponding periodic motions will be predicted analytically and the corresponding local stability and bifurcation analysis will be completed. To understand the singularity and switchability of motions to the time-varying boundary in such a two-mass system, illustrations of periodic motions will be given from analytical predictions. The relative forces will be presented for illustration of the analytical conditions.