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

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 ${\mathbb{R}}^2$ are precisely a relative equilibrium solution whose configuration minimizes the function $I{U}^2$ in ${\mathbb{R}}^2$.

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

References in corpus (1)

• A Counterexample to a Generalized Saari's Conjecture with a Continuum of Central Configurations