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Choreography SC.334

From Simó (2001)

Choreography SC.334 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.828 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 22718), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0949 of each other at a top speed of 3.65, line up 72 times a period, and the computed loop closes to 2.9×10⁻²⁷.

Measured over one period

Period: 16.82765425
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1136
Closest approach: 0.09487
Top speed: 3.648
Path length: 82.217
Alignments per period: 72
Topology: (aaaaabAbAbAbAbABBBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.3×10¹⁹)
Loop closure: 2.9×10⁻²⁷

Neighbours on the map

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