Interplay of Friction and Structural Asymmetry in Non-Reciprocal Dynamics of a Rolling Prism

TL;DR

This study explores how friction and structural asymmetry influence the non-reciprocal rolling behavior of a hexagonal prism, revealing that friction can both suppress and restore this asymmetric motion.

Contribution

It demonstrates that friction can induce non-reciprocal dynamics in asymmetric rolling objects, highlighting a nuanced role of friction in such systems.

Findings

Asymmetry causes non-reciprocal rolling behavior.

Friction generally suppresses non-reciprocity.

A specific friction range restores non-reciprocal motion.

Abstract

We investigate how the dynamics of a hexagonal prism rolling on a floor change with friction and structural asymmetry. It is shown that the asymmetry induces the non-reciprocal dynamics where the prism rolls only in one direction regardless of the direction of the initial velocity. While such behavior is primarily suppressed with increasing friction, we observe that there is a certain range of friction coefficient where the non-reciprocity is restored. This suggests that the friction not only diminishes the dynamics, but also assists it by exerting a torque to the prism.