Super Central Configurations In the Collinear 5-Body Problem
Mathematics and Natural Sciences
©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.
Applied Mathematics and Computation
(2020). Super Central Configurations In the Collinear 5-Body Problem. Applied Mathematics and Computation, 381.
Available at: https://aquila.usm.edu/fac_pubs/18222