A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite

TL;DR

This paper proves that any convex four-body central configuration with perpendicular diagonals must be a kite, extending the result to various potential functions including the four-vortex problem.

Contribution

It establishes a necessary condition for convex four-body configurations with perpendicular diagonals to be kites, generalizing previous results to broader potential functions.

Findings

Convex four-body configurations with perpendicular diagonals are necessarily kites.

The result applies to general power-law potential functions.

Includes implications for the planar four-vortex problem.

Abstract

We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.