Stability of relative equilibria of multidimensional rigid body

TL;DR

This paper generalizes Euler's classical stability results for torque-free rigid body rotations from three dimensions to multidimensional bodies, analyzing the stability of their relative equilibria.

Contribution

It extends the classical stability analysis of rigid body rotations to higher dimensions, providing new insights into the stability of multidimensional rigid bodies.

Findings

Rotation about certain axes remains stable in higher dimensions.

Rotation about other axes becomes unstable in multidimensional cases.

The stability criteria depend on the body's inertia properties.

Abstract

It is a classical result of Euler that the rotation of a torque-free three-dimensional rigid body about the short or the long axis is stable, whereas the rotation about the middle axis is unstable. This result is generalized to the case of a multidimensional body.