On Periodic Solutions of Some Problem With Dry Friction

TL;DR

This paper proves the existence of periodic solutions for a point mass on a moving plane with Coulomb friction, demonstrating that the mass's velocity can be a continuous periodic function under certain conditions.

Contribution

It establishes an existence theorem for periodic solutions in a system with dry friction, extending understanding of motion under Coulomb friction.

Findings

Existence of periodic solutions with continuous velocity functions.

Motion of the point mass can be periodic despite dry friction.

Mathematical proof via differential inclusion analysis.

Abstract

We consider a point mass on a horizontal plane. The motion of the plane is given. The plane moves periodically such that all its points have congruent closed trajectories. There is the Coulomb friction between the point mass and the plane. We show that there exists a motion of the point mass such that the velocity of the point mass is an absolutely continuous periodic function. Mathematically the result is expressed as an existence theorem for a periodic solution to some differential inclusion.