The Classical N-body Problem in the Context of Curved Space

Diacu, Florin

Canadian journal of mathematics, Tome 69 (2017) no. 4, pp. 790-806

Résumé

We provide the differential equations that generalize the Newtonian $N$ -body problem of celestial mechanics to spaces of constant Gaussian curvature $\kappa $ , for all $\kappa \in \mathbb{R}$ . In previous studies, the equations of motion made sense only for $\kappa \ne 0$ . The system derived here does more than just include the Euclidean case in the limit $\kappa \to 0;$ it recovers the classical equations for $\kappa =0$ . 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 oòers 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.

Détail

DOI : 10.4153/CJM-2016-041-2

Mots-clés : N-body problem, spaces of constant curvature