Analytical Predication of Complex Motion of a Ball in a Periodically Shaken Horizontal Impact Pair

Abstract

In this paper, complex motions of a ball in the horizontal impact pair with a periodic excitation are studied analytically using the theory of discontinuous dynamical system. Analytical conditions for motion switching caused by impacts are developed, and generic mapping structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic and chaotic motions are given.