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arXiv · 1405.0453

The classical N-body problem in the context of curved space

Florin Diacu
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Abstract

We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k nonzero. The system derived here does more than just include the Euclidean case in the limit when k tends to 0: it recovers the classical equations for k=0. This new expression of the laws of motion allows the study of the N-body problem in the context of constant curvature spaces and thus offers a natural generalization of the Newtonian equations that includes the classical case. We end the paper with remarks about the bifurcations of the first integrals.

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Florin Diacu. 2014-05-02. The classical N-body problem in the context of curved space. https://doi.org/10.4153/cjm-2016-041-2

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