Title

Super Central Configurations In the Collinear 5-Body Problem

Document Type

Article

Publication Date

9-15-2020

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

©2020. 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.

Publication Title

Applied Mathematics and Computation

Volume

381

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