Chaotic motion of a horizontal impact pair

A theory for a system with discontinuities and applied to the impact analysis of a horizontal impact pair is presented. Mappings for four switch-planes are defined and from these several impact models are developed. As a case of special interest, the case of a steady state, periodic two-impacts/ N-cycles motion is studied in greater detail. Numerical simulations of the various models are also given. The results show that the ensuing chaotic behavior can be either regularwith period-doubling bifurcation or randomwith other types of bifurcation. The former refers to chaos, where its mathematical structure is regular, while the latter refers to one with a random mathematical structure.