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

作者：Diacu Florin^*

来源：Canadian Journal of Mathematics, 2017, 69(4): 790-806.

DOI：10.4153/CJM-2016-041-2

• N-body problem
• spaces of constant curvature

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 is an element of R. In previous studies, the equations of motion made sense only for k not equal 0. The system derived here does more than just include the Euclidean case in the limit k -> 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.

• 出版日期2017-8