Higher-dimensional Generalisations of the Euler Top Equations

TL;DR

This paper introduces higher-dimensional generalizations of Euler top equations that are integrable and relate to advanced topics like string theory, expanding classical mechanics into new mathematical and physical contexts.

Contribution

It proposes new higher-dimensional Euler top equations with sufficient conservation laws for integrability, connecting classical mechanics to modern theoretical physics.

Findings

Seven-dimensional Euler top example provided

Connections made to eight-dimensional self-dual equations

Potential implications for string theory developments

Abstract

Generalisations of the familiar Euler top equations in three dimensions are proposed which admit a sufficiently large number of conservation laws to permit integrability by quadratures. The usual top is a classical analogue of the Nahm equations. One of the examples discussed here is a seven-dimensional Euler top, which arises as a classical counterpart to the eight-dimensional self-dual equations which are currently believed to play a role in new developments in string theory.