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

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 $n>4$.

15 pages, LaTeX, minor stylistic changes in v2

Cited by in corpus (6)

• Stability of equilibria for the $\mathfrak{so}(4)$ free rigid body
• Stability in bi-Hamiltonian systems and multidimensional rigid body
• Algebraic geometry and stability for integrable systems
• On the stability problem for the $\mathfrak{so}(5)$ free rigid body
• A note on relative equilibria of multidimensional rigid body
• Energy methods in the stability problem for the $\mathfrak{so}(4)$ free rigid body