Finiteness of polygonal relative equilibria for generalised quasi-homogeneous n-body problems and n-body problems in spaces of constant curvature

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

关键词: Mathematical physics;    Celestial mechanics;    n-body problems;    Curvature;    Dynamical systems;    Ordinary differential equations;   

DOI  :  10.1016/j.jmaa.2016.04.004

来源: Elsevier

【 摘 要 】

We prove for generalisations of quasi-homogeneous n-body problems with centre of mass zero and n-body problems in spaces of negative constant Gaussian curvature that if the masses and rotation are fixed, there exists, for every order of the masses, at most one equivalence class of relative equilibria for which the point masses lie on a circle, as well as that there exists, for every order of the masses, at most one equivalence class of relative equilibria for which all but one of the point masses lie on a circle and rotate around the remaining point mass. The method of proof is a generalised version of a proof by J.M. Cors, G.R. Hall and G.E. Roberts on the uniqueness of co-circular central configurations for power-law potentials. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free