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arXiv · 1510.06821

Equivalence of linear stabilities of elliptic triangle solutions of the planar charged and classical three-body problems

Qinglong Zhou·Yiming Long
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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.

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Qinglong Zhou, Yiming Long. 2015-10-23. Equivalence of linear stabilities of elliptic triangle solutions of the planar charged and classical three-body problems. https://doi.org/10.1016/j.jde.2015.01.045

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