The chiral knife edge: a simplified rattleback to illustrate spin inversion

TL;DR

The paper introduces the chiral knife edge rattleback, a simplified model demonstrating spin inversion, with analytical and numerical analysis revealing its connection to the Chaplygin sleigh and providing insights into non-holonomic systems.

Contribution

It presents a simplified rattleback model that captures the physics of spin inversion and uncovers a novel link to the Chaplygin sleigh, enhancing understanding of non-holonomic dynamics.

Findings

Analytical solutions for the simplified model

Numerical results matching previous inversion time estimates

Connection between spin inversion and Chaplygin sleigh dynamics

Abstract

We present the chiral knife edge rattleback, an alternative version of previously presented systems that exhibit spin inversion. We offer a full treatment of the model using qualitative arguments, analytical solutions as well as numerical results. We treat a reduced, one--mode problem which not only contains the essence of the physics of spin inversion, but that also exhibits an unexpected connection to the Chaplygin sleigh, providing new insight into the non-holonomic structure of the problem. We also present exact results for the full problem together with estimates of the time between inversions that agree with previous results in the literature.