Families / Choreographies
Simó’s choreographies
Carles Simó’s catalogue of three-body choreographies with nonzero angular momentum, the curves that made choreographies famous. All unstable except the figure-eight.
Simó’s choreographies are periodic solutions of the planar three-body problem. The atlas holds 343 of them, with periods from 1.556 to 17.3, all with equal masses; none is linearly stable. They come from Simó (2001), Dynamical properties of the figure eight solution of the three-body problem. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.
Simó (2001). Dynamical properties of the figure eight solution of the three-body problem. Contemporary Mathematics 292 (Celestial Mechanics, dedicated to Donald Saari) (doi)