Volume 22, Number 3, July-September 2016
|Page(s)||872 - 882|
|Published online||14 June 2016|
On the polynomial integrability of a system motivated by the Riemann ellipsoid problem
Departament de Matemàtiques, Universitat Autònoma de
Barcelona, 08193 Bellaterra,
Barcelona, Catalonia, Spain
2 Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal
Received: 13 October 2014
We consider differential systems obtained by coupling two Euler–Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals.
Mathematics Subject Classification: 34C05 / 34A34 / 34C14
Key words: Polynomial first integrals / homogeneous differential systems / Riemann ellipsoid problem / Euler–Poinsot systems / complete integrability
© EDP Sciences, SMAI 2016
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