Energy methods in the stability problem for the $\mathfrak{so}(4)$ free rigid body

Abstract

For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a Lyapunov function. These Lyapunov functions are linear combinations of Mishchenko's constants of motion.

Preprint of a paper accepted for publication in International Journal of Bifurcation and Chaos

References in corpus (3)

• Stability of equilibria for the $\mathfrak{so}(4)$ free rigid body
• Stability problem for the torque-free gyrostat by using algebraic methods
• On the stability problem for the $\mathfrak{so}(5)$ free rigid body