Authors: Dragović, Vladimir 
Gajić, Borislav 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: An L-A pair for the Hess-Apel'rot system and a new integrable case for the Euler-Poisson equations on so(4) x so (4)
Journal: Royal Society of Edinburgh - Proceedings A
Volume: 131
Issue: 4
First page: 845
Last page: 855
Issue Date: 1-Jan-2001
Rank: M22
ISSN: 0308-2105
DOI: 10.1017/S0308210500001141
We present an L-A pair for the Hess-Apel'rot case of a heavy rigid three-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 that are in involution are given. This system is a counterexample to one of Ratiu's theorems. A corrected version of this classification theorem is proved.
Publisher: Cambridge University Press
Project: Ministry of Science and Technology of Serbia, Project 04M03

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