Analytic formula for the Geometric Phase of an Asymmetric Top

TL;DR

This paper derives an explicit formula for the geometric phase of a force-free asymmetric top, providing new insights into its classical dynamics and illustrating the concept with a spinning handle example.

Contribution

It presents a closed-form expression for the geometric phase of an asymmetric top, linking classical mechanics with the concept of Berry phase.

Findings

Derived a closed-form formula for the geometric phase.

Explored implications using a spinning handle example.

Connected classical asymmetric top dynamics to Berry phase concepts.

Abstract

The motion of a handle spinning in space has an odd behavior. It seems to unexpectedly flip back and forth in a periodic manner as seen in a popular YouTube video. As an asymmetrical top, its motion is completely described by the Euler equations and the equations of motion have been known for more than a century. However, recent concepts of the geometric phase have allowed a new perspective on this classical problem. Here we explicitly use the equations of motion to find a closed form expression for total phase and hence the geometric phase of the force-free asymmetric top and explore some consequences of this formula with the particular example of the spinning handle for demonstration purposes. As one of the simplest dynamical systems, the asymmetric top should be a canonical example to explore the classical analog of Berry phase.