Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 2: 309 - 321

DOI: https://doi.org/10.1007/s11464-016-0514-2

RESEARCH ARTICLE

Geometric characterizations for variational minimizing solutions of charged 3-body problems

  • Wentian KUANG 1 ,
  • Yiming LONG , 1,2
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  • 1. Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
  • 2. Key Laboratory of Pure Mathematics and Combinatorics of the Ministry of Education, Nankai University, Tianjin 300071, China

Received date: 30 Nov 2015

Accepted date: 04 Jan 2016

Published date: 18 Apr 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We study the charged 3-body problem with the potential function being (-α)-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the π2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.

Key words： Charged 3-body problem; variational minimizer; geometric characterization

Cite this article

Wentian KUANG , Yiming LONG . Geometric characterizations for variational minimizing solutions of charged 3-body problems[J]. Frontiers of Mathematics in China, 2016 , 11(2) : 309 -321 . DOI: 10.1007/s11464-016-0514-2

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