An existence proof of a symmetric periodic orbit in the octahedral\n six-body problem

2016/05/12 by Anete Soares Cavalcanti, Cavalcanti, Anete Soares
Physics and Astronomy · Engineering · #Astro and Planetary Science #Spacecraft Dynamics and Control #Nuclear physics research studies

paper · pdf · doi:10.48550/arxiv.1605.03816

Abstract

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

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