A note on the Dziobek central configurations

Abstract

Abstract. For the Newtonian n-body problem in R n−2 with n ≥ 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 configurations 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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