Non-integrability of generalised Charlier and Saint-Germain problem

Andrzej J. Maciejewski and Maria Przybylska

Applied Mathematics and Computation, 2020, vol. 365, issue C

Abstract: Certain generalisation of a classical problem of celestial mechanics is considered. A material point moves in the potential force field that is a superposition of a radial force and a constant force. The potential of the central forces is proportional to an integer power −n of the distance from the origin. For all positive integers n except n=1 non-integrability in meromorphic functions is proved. Case n=1 is integrable. For negative integer n analysis is much more complex: for n=−1 non-integrability is proved, for n=−2 additional first integral is found, for n=−3 although the system meets the necessary integrability conditions Poincaré cross-sections show presence of chaotic layers in phase space.

Keywords: Non-integrability; Celestial mechanics; Generalised Kepler problem; Variational equations; Differential Galois group (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:365:y:2020:i:c:s009630031930712x

DOI: 10.1016/j.amc.2019.124720

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