The Euler-Poisson equations: An elementary approach to integrability conditions

Sasho Popov; Jean-Marie Strelcyn

doi:10.3934/jgm.2018011

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2018, Volume 10, Issue 3: 293-329. Doi: 10.3934/jgm.2018011

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The Euler-Poisson equations: An elementary approach to integrability conditions

Sasho Popov^1, and
Jean-Marie Strelcyn^2, ,

1.
Institute of Metal Science, Equipment and Technologies, with Hydro- and Aerodynamics Centre "Acad. A. Balevski", Bulgarian Academy of Sciences, 67 Shipchenski Prohod Street, 1574 Sofia, Bulgaria
2.
Université Paris 13, Sorbonne Paris Cité, CNRS UMR 7539, Laboratoire Analyse, Geometrie et Aplications, 99 Av. J.-B. Clement, 93430 Villetaneuse, France

* Corresponding author
* Corresponding author

Received: April 2017

Revised: August 2018

Published: August 2018

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Abstract

We consider the Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point with parameters in a complex domain. We suppose that these equations admit a first integral functionally independent of the three already known integrals which does not depend on all the variables. We prove that this may happen only in the already known three integrable cases or in the trivial case of kinetic symmetry. We provide a method for finding such a fourth integral, when it exists.

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Mathematics Subject Classification: Primary: 70E17, 70E40; Secondary: 37J30, 37J35.

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