Saari's Conjecture for Elliptical Type N-Body Problem and An Application

2013/08/11 by Xiang Yu, Yu, Xiang, Shiqing Zhang +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1308.2376

arXiv admin note: substantial text overlap with arXiv:1306.1047; and text overlap with arXiv:0909.4991 by other authors

openalex publication_date 2013/08/11 · arxiv created 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

By using an arithmetic fact, we will firstly prove Saari's conjecture in a particular case, which is called the Elliptical Type N-Body Problem, and then we apply it to prove that the variational minimal solution of the planar Newtonian N-body problem is precisely a relative equilibrium solution whose configuration minimizes the function IU², it's worth noticing that we don't need the hypothesis of Finiteness of Central Configurations. In the Planetary Restricted Problem (which ignore all the mutual gravitational interactions between the planets), the corresponding Saari's conjecture is stated and proved.

Citations

• Saari's Conjecture and Variational Minimal Solutions for N-Body Problems
• Saari's Homographic Conjecture of the Three-Body Problem

Cited by

• Action Minimizing Solutions of The One-Dimensional N-Body Problem With Equal Masses

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