Symmetry of Planar Four-Body Convex Central Configurations

Abstract

We study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

12 pages

References in corpus (3)

• Convex Four Body Central Configurations with Some Equal Masses
• Euler configurations and quasi-polynomial systems
• On some exceptional cases in the integrability of the three-body problem

Cited by in corpus (13)

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• Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
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• A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite
• Relative equilibria of four identical satellites
• Four-body Central Configurations with Adjacent Equal Masses
• Bifurcations of Central Configurations in the Four-Body Problem with some equal masses
• On the uniqueness of trapezoidal four-body central configurations
• Classifying Four-Body Convex Central Configurations
• Linear Instability of Elliptic Rhombus Solutions to the Planar Four-body Problem
• Planarity conditions and four-body central configurations equations with angles as coordinates
• Symmetric Central Configurations in the Concave 4-Body Problem with Two Pairs of Equal Masses