Nonabelian ${\mathfrak so}_3$ Euler top

TL;DR

This paper develops an integrable matrix version of the classical Euler top on the Lie algebra so_3 using a nonabelianization procedure, extending the understanding of integrable systems in matrix form.

Contribution

It introduces a novel integrable matrix formulation of the Euler top on so_3 via nonabelianization, expanding the scope of integrable systems.

Findings

Derived an integrable matrix model of the Euler top on so_3

Demonstrated the nonabelianization procedure for integrable systems

Extended classical mechanics concepts to matrix Lie algebra setting

Abstract

Using the nonabilinization procedure, we find an integrable matrix version of the Euler top on $\mathfrak{so}_3$