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An L-A pair for the Apel'rot system and a new integrable case for the Euler-Poisson equations on so(4)xso(4)

Vladimir Dragovic·Borislav Gajic
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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.

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Vladimir Dragovic, Borislav Gajic. 1999-11-30. An L-A pair for the Apel'rot system and a new integrable case for the Euler-Poisson equations on so(4)xso(4). https://arxiv.org/abs/math-ph/9911047

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