An existence proof of a symmetric periodic orbit in the octahedral six-body problem
Anete S. Cavalcanti
Discrete & Continuous Dynamical Systems - A 2017, 37(4): 1903-1922 doi: 10.3934/dcds.2017080

We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the lagrangian action functional on a well chosen class of symmetric loops.

keywords: Celestial mechanics octahedral six body problem periodic solutions symmetric orbits

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