A note on the Dziobek central configurations

Llibre, Jaume

doi:10.1090/S0002-9939-2015-12502-6

A note on the Dziobek central configurations
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Proc. Amer. Math. Soc. 143 (2015), 3587-3591 Request permission

Abstract:

For the Newtonian $n$-body problem in $\mathbb {R}^{n-2}$ with $n\geq 3$ we prove that the following two statements are equivalent.

[(a)] Let $x$ be a Dziobek central configuration having one mass located at the center of mass.

[(b)] Let $x$ be a central configuration formed by $n-1$ equal masses located at the vertices of a regular $(n-2)$-simplex together with an arbitrary mass located at its barycenter.

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