Geodesic
On the polynomial integrability of a system motivated by the Riemann ellipsoid problem
Llibre, Jaume1  ; Valls, Clàudia2
1 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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 872-882

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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.

Reçu le :
DOI : 10.1051/cocv/2015035
Classification : 34C05, 34A34, 34C14
Keywords: Polynomial first integrals, homogeneous differential systems, Riemann ellipsoid problem, Euler–Poinsot systems, complete integrability

Llibre, Jaume 1 ; Valls, Clàudia 2

1 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 
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Llibre, Jaume; Valls, Clàudia. On the polynomial integrability of a system motivated by the Riemann ellipsoid problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 872-882. doi: 10.1051/cocv/2015035

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