Periodic Impact Motions at Resonance of a Particle Bouncing on Spheres and Cylinders

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 also provide a Landesman–Lazer-type 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.

Keywords

• keplerian problem
• periodic solutions
• impact
• resonance
• landesman–lazer condition
• 34b15
• 34c25