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

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

2010-10-02

arxiv.org/abs/1010.0295v3

Mathematics

Dynamical Systems

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

Scientific paper

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.

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