Families / Choreographies

Nontrivial choreographies

Choreographies whose knot is not a power of the figure-eight’s: three bodies on one closed curve with a topology of its own. Computed to 180 digits; all unstable.

Nontrivial choreographies are periodic solutions of the planar three-body problem. The atlas holds 164 of them, with periods from 31.06 to 297.6, all with equal masses; none is linearly stable. They come from Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024), Nontrivial choreographies of the planar 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.

Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024). Nontrivial choreographies of the planar three-body problem. Physics of Particles and Nuclei 55, 495–497 (doi)