An L-A pair for the Apel'rot system and a new integrable case for the Euler-Poisson equations on so(4)xso(4)
Mathematical Physics
2007-05-23 v1 math.MP
Symplectic Geometry
Abstract
We present an L-A pair for the Apel'rot case of a heavy rigid 3-dimensional body. Using it we give an algebro-geometric integration procedure. Generalizing this L-A pair, we obtain a new completely integrable case of the Euler-Poisson equations in dimension four. Explicit formulae for integrals which are in involution are given. This system is a counterexample to one well known Ratiu's theorem. Corrected version of this classification theorem is proved.
Cite
@article{arxiv.math-ph/9911047,
title = {An L-A pair for the Apel'rot system and a new integrable case for the Euler-Poisson equations on so(4)xso(4)},
author = {Vladimir Dragovic and Borislav Gajic},
journal= {arXiv preprint arXiv:math-ph/9911047},
year = {2007}
}
Comments
14 pages