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On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base
Corbera Subirana, Montserrat; Llibre, Jaume
Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n{gon passing through its center. Here this kind of central con gurations is called bi{pyramidal central con gurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the con guration is central. We give explicitly those relations.
(c) American Institute of Mathematical Science
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American Institute of Mathematical Science

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