Remark on integrable deformations of the Euler top

TL;DR

This paper explores how the unique determination of the Euler top’s equations by its integrals allows for the construction of integrable deformations, expanding understanding of rigid body dynamics.

Contribution

It introduces a method to create integrable deformations of the Euler top using the property that its integrals uniquely determine its equations.

Findings

Constructed new integrable deformations of the Euler top.

Highlighted the role of first integrals in defining system dynamics.

Provided a framework for deforming integrable systems.

Abstract

The Euler top describes a free rotation of a rigid body about its center of mass and provides an important example of a completely integrable system. A salient feature of its first integrals is that, up to a reparametrization of time, they uniquely determine the dynamical equations themselves. In this note, this property is used to construct integrable deformations of the Euler top.