© 2017, Springer-Verlag Berlin Heidelberg. We study the convex central configurations of the 4-body problem assuming that they have two pairs of equal masses located at two adjacent vertices of a convex quadrilateral. Under these assumptions we prove that the isosceles trapezoid is the unique central configuration.
Fernandes, A. C., Llibre, J., & Mello, L. F. (2017). Convex Central Configurations of the 4-Body Problem with Two Pairs of Equal Adjacent Masses. Archive for Rational Mechanics and Analysis, 226(1), 303-320. https://doi.org/10.1007/s00205-017-1134-z