On the dynamics of the Euler equations on so(4)

摘要

This paper deals with the Euler equations on the Lie Algebra so(4). These equations are given by a polynomial differential system in R~6. We prove that this differential system has four 3-dimensional invariant manifolds and we give a complete description of its dynamics on these invariant manifolds. In particular, each of these invariant manifolds are fulfilled by periodic orbits except in a zero Lebesgue measure set.