On the uniqueness of trapezoidal four-body central configurations

Abstract

We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central configuration for each cyclic ordering of the masses.

arXiv admin note: substantial text overlap with arXiv:2302.10089

References in corpus (3)

• Convex Four Body Central Configurations with Some Equal Masses
• Classifying Four-Body Convex Central Configurations
• On the Uniqueness of Co-circular Four Body Central Configurations

Cited by in corpus (2)

• Symmetric Central Configurations in the Concave 4-Body Problem with Two Pairs of Equal Masses
• Relative Equilibria for Scaling Symmetries and Central Configurations