On a Strange Motion in the System with Anisotropic Dry Friction

TL;DR

This paper investigates a particle with anisotropic dry friction, revealing that it can exhibit complex motion where the trajectory circles infinitely often around a center within finite time.

Contribution

It introduces a novel analysis of particle motion under symmetric anisotropic dry friction, demonstrating the possibility of infinite rotations in finite time.

Findings

Particle can rotate infinitely many times in finite time

Motion is governed by anisotropic but symmetric friction

New dynamic behaviors identified under dry friction conditions

Abstract

We consider a particle on the horizontal plane with a dry friction. The friction is anisotropic but symmetric under the group of rotations of the plane. It turns out that the particle can move such that in the finite time the trajectory turns about the center of symmetry infinitely many times.