We classify the set of central configurations lying on a common circle in the Newtonian
four-body problem. Using mutual distances as coordinates, we show that the set of four-body
co-circular central configurations with positive masses is a two-dimensional surface, a graph
over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid,
are investigated extensively. We also prove that a co-circular central configuration requires a
specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to
the general four-body case, we show that if any two masses of a four-body co-circular central
configuration are equal, then the configuration has a line of symmetry.
CitationCors, J.; Roberts, G. Four-body co-circular central configurations. "Nonlinearity", Febrer 2012, vol. 25, núm. 2, p. 343-370.
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