Periodic impact motions at resonance of a particle bouncing on spheres and cylinders

TL;DR

This paper studies periodic impact trajectories of a particle under central forces hitting spheres or cylinders, providing new resonance conditions and extending results to impact oscillators at double resonance.

Contribution

It introduces new resonance conditions for impact trajectories and adapts these results to impact oscillators at double resonance.

Findings

Existence of periodic impact trajectories under specific resonance conditions

Development of Landesman-Lazer type conditions for nonlinear impact problems

Extension of results to impact oscillators at double resonance

Abstract

We investigate the existence of periodic trajectories of a particle, subject to a central force, which can hit a sphere, or a cylinder. We will provide also a Landesman-Lazer type of condition in the case of a nonlinearity satisfying a double resonance condition. Afterwards, we will show how such a result can be adapted to obtain a new result for the impact oscillator at double resonance.