This is a post-peer-review, pre-copyedit version of an article published in Qualitative Theory of Dynamical Systems. The final authenticated version is available online at: http://dx.doi.org/10.1007/s12346-017-0238-z.
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.
Corbera, M., Cors, J., Roberts, G. A four-body convex central configuration with perpendicular diagonals is necessarily a kite. "Qualitative theory of dynamical systems", 1 Juliol 2018, vol. 17, núm. 2, p. 367-374.