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

2016/04/04 by Pieter Tibboel, Tibboel, Pieter
Physics and Astronomy · Earth and Planetary Sciences · #Astro and Planetary Science #Geophysics and Gravity Measurements #Cosmology and Gravitation Theories

paper · pdf · doi:10.48550/arxiv.1604.01107

Abstract

We prove for generalisations of quasi-homogeneous n-body problems with\ncenter of mass zero and n-body problems in spaces of negative constant\nGaussian curvature that if the masses and rotation are fixed, there exists, for\nevery order of the masses, at most one equivalence class of relative equilibria\nfor which the point masses lie on a circle, as well as that there exists, for\nevery order of the masses, at most one equivalence class of relative equilibria\nfor which all but one of the point masses lie on a circle and rotate around the\nremaining point mass. The method of proof is a generalised version of a proof\nby J.M. Cors, G.R. Hall and G.E. Roberts on the uniqueness of co-circular\ncentral configurations for power-law potentials.\n

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