Document Type

Article

Publication Date

2004

Department

Mathematics

Abstract

In 1970 Don Saari conjectured that the only solutions of the Newtonian n-body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture in the collinear case for any potential that involves only the mutual distances. Furthermore, in the case of homogeneous potentials, we show that the only collinear and non-zero angular momentum solutions are homographic motions with central configurations.

Comments

This article was originally published in Transactions of the American Mathematical Society, 357(10): 4215-4223. © 2004 American Mathematical Society.

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