Families / Belgrade classes

Split figure-eights

Titov’s continuations of the figure-eight to a lighter third body, where the curve splits into two lobes.

Split figure-eights are periodic solutions of the planar three-body problem. The atlas holds 2 of them, with periods from 6.283 to 6.283, for several mass ratios; none is linearly stable. They come from Titov (2012), Periodic solutions of the three-body problem with unequal masses in the vicinity of the figure-eight. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Titov (2012). Periodic solutions of the three-body problem with unequal masses in the vicinity of the figure-eight. Russian Journal of Nonlinear Dynamics 8, 377–389 (doi)