Classifying four-body convex central configurations - Corbera, Montserrat; Cors, Josep M.; Roberts, Gareth E. (Celestial mechanics and dynamical astronomy, 2019)
We classify the full set of convex central configurations in the Newtonian planar 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 R + 3 .