New classes of spatial central configurations for the [formula omitted]-body problem

Abstract

In this paper, we show the existence of new families of spatial central configurations for the n + 3 -body problem, n ≥ 3 . We study spatial central configurations where n bodies are at the vertices of a regular n -gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T . The results have simple and analytic proofs.