The symmetry of steady-state solutions of non-smooth dynamical systems with two constraints

摘要

In this paper, the symmetry of steady-state solutions in non-smooth dynamical systems with two symmetrical constraints are investigated to obtain all possible stable and unstable motions. An invariant transformation exists in regular and chaotic motions relative to skew-symmetrical mapping pairs in symmetrical systems with harmonic excitations. This investigation provides a mathematical foundation for the symmetry of solutions in this class of non-smooth dynamical systems. The group structure of mapping combinations should be further investigated.