Planar choreographies

Planar 7

Planar resonant choreographies for seven equal masses.

7 bodies6 examples

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 $h=\gcd(n,k)$. These planar examples are also symmetric under a reflection in the plane.

Gallery

3 : 2 resonant orbit for k = 3

Animation: 3 : 2 resonant orbit for k = 3

3 : 2 resonant orbit for k = 3

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5 : 1 resonant orbit for k = 3

Animation: 5 : 1 resonant orbit for k = 3

5 : 1 resonant orbit for k = 3

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4 : 1 resonant orbit for k = 2

Animation: 4 : 1 resonant orbit for k = 2

4 : 1 resonant orbit for k = 2

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5 : 3 resonant orbit for k = 2

Animation: 5 : 3 resonant orbit for k = 2

5 : 3 resonant orbit for k = 2

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15 : 4 resonant orbit for k = 4

Animation: 15 : 4 resonant orbit for k = 4

15 : 4 resonant orbit for k = 4

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2 : 1 resonant orbit for k = 4

Animation: 2 : 1 resonant orbit for k = 4

2 : 1 resonant orbit for k = 4

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