Central Configurations of the Five-Body Problem with Equal Masses

Abstract

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.

References in corpus (3)

• Symmetry of Planar Four-Body Convex Central Configurations
• Convex Four Body Central Configurations with Some Equal Masses
• Seven-body central configurations: a family of central configurations in the spatial seven-body problem

Cited by in corpus (11)

• Some Problems on the Classical N-Body Problem
• Central configurations for the planar Newtonian Four-Body problem
• Central configurations in planar $n$-body problem with equal masses for $n=5,6,7$
• Existence of symmetric central configurations
• Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem
• On the planar central configurations of rhomboidal and triangular four- and five-body problems
• On the uniqueness of trapezoidal four-body central configurations
• Non integrability of the n body problem with non zero angular momentum
• Central configurations in spatial n-body problem for n = 5, 6 with equal masses
• Symmetric Central Configurations in the Concave 4-Body Problem with Two Pairs of Equal Masses
• On the equilateral pentagonal central configurations