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

## TL;DR

This paper investigates how removing viscous friction from a forced vibro-impact oscillator with Coulomb friction causes the global dynamics to split into regions with regular attractors and Hamiltonian-like behavior, revealing complex mixed dynamics.

## Contribution

It demonstrates that eliminating viscous friction qualitatively changes the global dynamics, leading to coexistence of regular and Hamiltonian regions, which was not previously well understood.

## Key findings

- Removal of viscous friction causes mixed global dynamics.
- Hamiltonian regions contain stability islands and chaotic zones.
- Local Hamiltonian behavior occurs for trajectories with non-zero velocity.

## Abstract

The paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In 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 non-attractive chaotic regions etc. We prove that such local Hamiltonian behavior should occur for phase trajectories with non-vanishing velocity. Stability analysis for the periodic orbits confirms the above statement. It is demonstrated that similar mixed global dynamics can be observed in broader class of models.