Super central configurations in the collinear 5-body problem

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摘要

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.

论文关键词:Skew symmetric matrix,Pfaffian,Central configurations,Super central configurations,n-body problem

论文评审过程:Received 5 February 2019, Revised 18 October 2019, Accepted 28 February 2020, Available online 8 May 2020, Version of Record 8 May 2020.

论文官网地址:https://doi.org/10.1016/j.amc.2020.125194