A Four-Body Convex Central Configuration with Perpendicular Diagonals is Necessarily a Kite - Corbera, Montserrat; Cors, Josep M.; Roberts, Gareth E. (Qualitative theory of dynamical systems, 2018)
We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.