Classifying Four-Body Convex Central Configurations

Abstract

We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain $D$ that is the union of elementary regions in ${\mathbb{R}}^{{+}^3}$.

28 pages, 14 figures

References in corpus (5)

• Some Problems on the Classical N-Body Problem
• Symmetry of Planar Four-Body Convex Central Configurations
• Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
• A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite
• Four-body central configurations with one pair of opposite sides parallel

Cited by in corpus (2)

• On the uniqueness of trapezoidal four-body central configurations
• Symmetric Central Configurations in the Concave 4-Body Problem with Two Pairs of Equal Masses