1:2 resonant orbit
Hover over the image to preview the animation, or click to open it.
Unchained choreographies
Unchained 4
Spatial unchained choreographies for four bodies.
Overview
These unchained examples are spatial choreographies whose projection onto the $xy$-plane has winding number $l$ around a center and is invariant under rotations by $2\pi/m$.
The bodies form groups of $h$ polygons, where $h=\gcd(n,k)$. In contrast with the vertical Lyapunov families, the unchained family has a different reflection structure: the spatial orbit is symmetric under the combined reflection $(-y,-z)$ when the $x$-axis is chosen through the center of the orbit.
Gallery
1:6 resonant orbit
Hover over the image to preview the animation, or click to open it.