Twisted stacked central configurations for the spatial seven-body problem

Abstract

In this paper, we show the existence of the twisted stacked central configurations for 7-body problem. More precisely, the position vectors x1,x2,x3 and x4 are at the vertices of a regular tetrahedron Σ; the position vectors x5,x6 and x7 are at the vertices of an equilateral triangle Π; the triangle (x1,x2,x3) and the triangle (x5,x6,x7) have twisted angle π3.