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Three bouncing

From Sheen (2016)

Three bouncing is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 1.251 time units, published by Sheen (2016). A dozen orbits Matthew Sheen found in 2016 with a root finder and hand-picked starting guesses while a teaching assistant on Cornell’s dynamics course, named for what they look like; six hang in the Belgrade gallery. Most of them carry angular momentum. His loop-ended triangles turned out to be Broucke and Boggs’s S4 of 1975, mirrored, and is listed under that name. It is unstable (largest Floquet multiplier 1.6186e+21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000889 of each other at a top speed of 2345, line up 2 times a period, and the computed loop closes to 9.8×10⁻⁵.

Measured over one period

Period: 1.250992581
Masses: 1 : 1 : 1
Energy: -2.51285
Angular momentum: 2.5×10⁻⁶
Closest approach: 8.9×10⁻⁶
Top speed: 2.3×10⁵
Path length: 3.4267
Alignments per period: 2
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1.6×10²¹)
Loop closure: 9.8×10⁻⁵

Neighbours on the map

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