Equivalence of linear stabilities of elliptic triangle solutions of the planar charged and classical three-body problems
arXiv:1510.06821 · doi:10.1016/j.jde.2015.01.045
Abstract
In this paper, we prove that the linearized system of elliptic triangle homographic solution of planar charged three-body problem can be transformed to that of the elliptic equilateral triangle solution of the planar classical three-body problem. Consequently, the results of Mart\'ınez, Samà and Simó ([15] in J. Diff. Equa.) of 2006 and results of Hu, Long and Sun ([6] in Arch. Ration. Mech.Anal.) of 2014 can be applied to these solutions of the charged three-body problem to get their linear stability.
24 pages, 2 figures,final version