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Chapitre D'ouvrage Année : 2016

Integrability and Non Integrability of Some n Body Problems

Résumé

We prove the non integrability of the colinear 3 and 4 body problem, for any positive masses. To deal with resistant cases, we present strong integrability criterions for 3 dimensional homogeneous potentials of degree −1, and prove that such cases cannot appear in the 4 body problem. Following the same strategy, we present a simple proof of non integrability for the planar n body problem. Eventually, we present some integrable cases of the n body problem restricted to some invariant vector spaces.

Dates et versions

hal-01514125 , version 1 (25-04-2017)

Identifiants

Citer

Thierry Combot. Integrability and Non Integrability of Some n Body Problems. Bernard Bonnard ; Monique Chyba Recent Advances in Celestial and Space Mechanics, 23, Springer International Publishing, pp.1-30, 2016, Mathematics for Industry, 978-3-319-27462-1, 978-3-319-27464-5. ⟨10.1007/978-3-319-27464-5_1⟩. ⟨hal-01514125⟩
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