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

Published online by Cambridge University Press:  12 July 2007

Vladimir Dragović  and
Borislav Gajić
Vladimir Dragović
Affiliation:
Mathematical Institute SANU, Kneza Mihaila 35, 11000 Beograd, Yugoslavia ([email protected])
Borislav Gajić
Affiliation:
Mathematical Institute SANU, Kneza Mihaila 35, 11000 Beograd, Yugoslavia ([email protected])
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 845 - 855
Copyright
Copyright © Royal Society of Edinburgh 2001

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