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 $$n=12$$ n = 12 . We show some exemplary balanced configurations in the case $$n=5$$ n = 5 , as well as some balanced configurations without any axis of symmetry in the cases $$n=4$$ n = 4 and $$n=10$$ n = 10 .