Many Body Symmetrical Dynamical Systems

TL;DR

This paper explores the stability and analytical solutions of symmetrical multi-body dynamical systems, specifically focusing on four and five body problems, providing new stability criteria and numerical analyses.

Contribution

It introduces new analytical solutions and stability criteria for symmetric four and five body problems, including the CS5BP and CSNBP configurations.

Findings

Derived analytical solutions for the four body problem

Established a stability criterion valid for all time for the CS5BP

Numerically investigated hierarchical stability of the CS5BP

Abstract

We investigate the stability of few body symmetrical dynamical systems which include four and five body symmetrical dynamical systems. Research presented in this thesis includes the following original investigations: determination of some analytical solutions of the four body problem; stability analysis of the near symmetric coplanar CSFBP ; derivation of the analytical stability criterion valid for all time for a special symmetric configuration of the general five-body problem, the CS5BP, which exhibits many of the salient characteristics of the general five body problem; numerical investigation of the hierarchical stability of the CS5BP and derivation of the stability criterion for the CSNBP.