A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem

Abstract

A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem is presented. We find a comprehensive list of equal mass central configurations satisfying the Morse equality up to n=12. We show some exemplary balanced configurations in the case n=5, as well as some balanced configurations without any axis of symmetry in the cases n=4 and n=10.