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Planar choreographies
Planar n+1
A curated gallery of numerically continued choreographies and their animated trajectories.
Overview
These are planar choreographies obtained along resonant Lyapunov orbits. For an $l:m$ resonance, the choreography winds $l$ times around a center and is invariant under rotations by $2\pi/m$.
The $n$ bodies move in groups of $h$ polygons, where $h=\gcd(n,k)$. The examples below illustrate the geometry produced by different resonances and symmetry classes.
Gallery
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Hover over the image to preview the animation, or click to open it.