Three topologically nontrivial choreographic motions of three bodies

Abstract

Choreographies are periodic orbits in which all bodies move on the same trajectory with equal time delay. The best known three-body choreography is figure-eight orbit. Here we introduce a search method specialized for choreographies and present three new orbits with vanishing angular momentum that are the first clear examples of choreographies that cannot be described as k-th powers of the figure-eight solution, according to the topological classification of orbits. We have also found 17 new “powers of the eight” choreographies. According to our numerical computation, one of two distinct k = 7 choreographies is linearly stable.