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Newton’s cradle

From Sheen (2016)

Newton’s cradle is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 3.5509 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 weakly unstable (largest Floquet multiplier 1.860), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0018 of each other at a top speed of 23.6, line up 4 times a period, and the computed loop closes to 8.0×10⁻²⁷.

Measured over one period

Period: 3.550944093
Masses: 1 : 1 : 1
Energy: -1.98984
Angular momentum: -0.17325
Closest approach: 0.001803
Top speed: 23.56
Path length: 8.7763
Alignments per period: 4
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: weakly unstable (|λ|max 1.860)
Loop closure: 8.0×10⁻²⁷

Neighbours on the map

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