Spatial twisted central configuration for Newtonian (2N+1)-body problem

Abstract

For a spatial twisted central configuration of the Newtonian ($ 2N $+1)-body problem where $ 2N $ masses are at the vertices of two paralleled regular $ N $-polygons with distance $ h > 0 $, and the twist angle between the two regular $ N $-polygons is $ 0\leq\theta < 2\pi $, we study the sufficient and necessary conditions for the existence of the spatial twisted central configuration. Additionally, we obtain the uniqueness of the spatial twisted central configuration.

Keywords

• newtonian ($ 2n $+1)-body problem
• spatial central configuration
• regular $ n $-polygons
• twist angle