Twisted Angles for Central Configurations Formed By Two Twisted Regular Polygons

TL;DR

This paper investigates the conditions for twisted angles in central configurations formed by two twisted regular polygons, establishing specific necessary and sufficient conditions for the angles in 2N-body problems.

Contribution

It proves that the twisted angles in such configurations must be either 0 or π/N, providing a precise characterization of these angles.

Findings

Twisted angles must be 0 or π/N in the studied configurations.

Provides necessary and sufficient conditions for twisted angles.

Enhances understanding of central configurations in N-body problems.

Abstract

In this paper, we study the necessary conditions and sufficient conditions for the twisted angles of the central configurations formed by two twisted regular polygons, specially, we prove that for the 2N-body problems, the twisted angles must be$\theta=0 {or} \theta=\pi/N$.