Saari's Conjecture and Variational Minimal Solutions for N-Body Problems

2013/06/05 by Yu Xiang, Xiang, Yu, Zhang Shiqing +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1306.1047

arXiv admin note: text overlap with arXiv:0909.4991 by other authors

arxiv created 2013/06/08 · arxiv updated 2013/06/11

Abstract

In this paper, we will prove Saari's conjecture in a particular case by using a arithmetic fact, and then, apply it to prove that for any given positive masses, the variational minimal solutions of the N-body problem in ℝ² are precisely a relative equilibrium solution whose configuration minimizes the function IU² in ℝ².

Citations

• Saari's Homographic Conjecture of the Three-Body Problem

Cited by

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

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