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Choreography SC.332

From Simó (2001)

Choreography SC.332 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.812 time units, published by Simó (2001). Carles Simó’s catalogue of three-body choreographies with nonzero angular momentum, the curves that made choreographies famous. All unstable except the figure-eight. It is unstable (largest Floquet multiplier 53763), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0803 of each other at a top speed of 3.95, line up 66 times a period, and the computed loop closes to 2.0×10⁻²⁸.

Measured over one period

Period: 16.81205194
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1082
Closest approach: 0.08033
Top speed: 3.949
Path length: 81.853
Alignments per period: 66
Topology: (aaaaabAbAbAbAbABBBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 5.4×10¹⁶)
Loop closure: 2.0×10⁻²⁸

Neighbours on the map

All Simó’s choreographies, the families of periodic three-body orbits, or the atlas map.