Super central configurations in the collinear 5-body problem

Zhifu Xie and William Johnson

Applied Mathematics and Computation, 2020, vol. 381, issue C

Abstract: This paper studies the existence and classifications of super central configurations of the collinear 5-body problem. A super central configuration is a central configuration q for a mass vector m such that q is also a central configuration for at least one different arrangement m(τ) of the same mass vector m. Instead of investigating case by case as in previous papers for the collinear 3-body or 4-body problems, we first prove some properties of necessary conditions for super central conditions that exclude impossible cases. After excluding those impossible cases from total 120 permutations of the collinear 5-body problem, there are only 18 pairs of derangements which are possible for super central configurations. We further prove that a super central configuration has at most one different arrangement in the collinear 5-body problem. We provide numerical examples for such possible arrangements.

Keywords: Skew symmetric matrix; Pfaffian; Central configurations; Super central configurations; n-body problem (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320301636

DOI: 10.1016/j.amc.2020.125194

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