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
Recommended Citation
Xie, Z.,
Johnson, W.
(2020). Super Central Configurations In the Collinear 5-Body Problem. Applied Mathematics and Computation, 381.
Available at: https://aquila.usm.edu/fac_pubs/18222