Convex Four-Body Central Configurations with Some Equal Masses

Abstract

We prove that there is an unique convex noncollinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such a central configuration possesses a symmetry line and it is a kite-shaped quadrilateral. We also show that there is exactly one convex noncollinear central configuration when the opposite masses are equal. Such a central configuration also possesses a symmetry line and it is a rhombus.

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Correspondence to Ernesto Perez-Chavela.

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Communicated by P. Rabinowitz

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Perez-Chavela, E., Santoprete, M. Convex Four-Body Central Configurations with Some Equal Masses. Arch Rational Mech Anal 185, 481–494 (2007). https://doi.org/10.1007/s00205-006-0047-z

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Keywords

  • Relative Equilibrium
  • Body Problem
  • Equal Mass
  • Symmetry Line
  • Central Configuration