TY - JOUR

T1 - Finiteness of polygonal relative equilibria for generalised quasi-homogeneous n-body problems and n-body problems in spaces of constant curvature

AU - Tibboel, Pieter

N1 - Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Celestial mechanics

KW - Curvature

KW - Dynamical systems

KW - Mathematical physics

KW - N-body problems

KW - Ordinary differential equations

UR - http://www.scopus.com/inward/record.url?scp=84963945564&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.04.004

DO - 10.1016/j.jmaa.2016.04.004

M3 - Article

AN - SCOPUS:84963945564

SN - 0022-247X

VL - 441

SP - 183

EP - 193

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -