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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)

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arxiv math-ph/9911047 v1 pith:SBQQSSUN submitted 1999-11-30 math-ph math.MPmath.SG

Vladimir Dragovic , Borislav Gajic This is my paper · ORCID
classification math-phmath.MPmath.SG
keywords casepairapelequationseuler-poissonintegrablesystemtheorem
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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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  1. Heavy rigid body with a gyroscope in $\mathbb R^n$

    math-ph 2026-01 accept novelty 6.0 of 10

    Multidimensional Lagrange, Euler, and totally symmetric heavy tops remain Liouville integrable after adding a gyroscope with angular momentum in the symmetry subalgebra, with new polynomial Lax representations.

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