Stability analysis of some integrable Euler equations for SO(n)

TL;DR

This paper analyzes the stability of specific integrable Euler equations on so(n), identifying equilibria, their stability, and heteroclinic orbits, with complete results for n=4 and partial for larger n.

Contribution

It provides a detailed stability analysis of special integrable Euler equations on so(n), including equilibrium points and heteroclinic orbits, extending understanding of these systems.

Findings

Equilibrium points are identified and their stability is analyzed.

Heteroclinic orbits connecting unstable equilibria are constructed.

Complete results are achieved for n=4, partial for n>4.

Abstract

A family of special cases of the integrable Euler equations on $so(n)$ introduced by Manakov in 1976 is considered. The equilibrium points are found and their stability is studied. Heteroclinic orbits are constructed that connect unstable equilibria and are given by the orbits of certain 1-parameter subgroups of SO(n). The results are complete in the case $n=4$ and incomplete for $n>4$.