Mixed global dynamics of forced vibro-impact oscillator with Coulomb friction

Abstract

This paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In the vast majority of the existing studies, this model included also viscous friction, and its global dynamics in the state space is governed by periodic, quasiperiodic, or chaotic attractors. We demonstrate that removal of the viscous friction leads to qualitative modification of the global dynamics, namely, the state space is divided into the regions with "regular" attraction to the aforementioned special solutions and the regions with profoundly Hamiltonian dynamics. The latter regions contain structures typical for forced Hamiltonian systems: stability islands, extended nonattractive chaotic regions, etc. We prove that such local Hamiltonian behavior should occur for phase trajectories with nonvanishing velocity. Stability analysis for the periodic orbits confirms the above statement. It is demonstrated that similar mixed global dynamics can be observed in a broader class of models.