## Saari's Conjecture and Variational Minimal Solutions for \$N\$-Body Problems    [PDF]

Yu Xiang, Zhang Shiqing
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 \$IU^2\$ in \${{\mathbb{R}}}^2\$.
View original: http://arxiv.org/abs/1306.1047