Processing math: 100%

7 bodies 8 bodies 9 bodies n+1 bodies

4 bodies 6 bodies 8 bodies 9 bodies n+1 bodies

4 bodies 6 bodies 8 bodies

4 bodies 6 bodies 7 bodies 8 bodies 9 bodies n+1 bodies

Planar 9

Each choreography is winding

$l$ times around a center and invariant by rotations of

$2\pi/m$ . Also, the bodies move in groups of

$h$ polygons, where

$h$ is maximum common divisor of

$n$ and

$k$ . In addition, these choreographies are symmetric by a reflection in the plane.

5 : 2 resonant orbit for k = 4
2 : 1 resonant orbit for k = 5
4 : 3 resonant orbit for k = 3
5 : 3 resonant orbit for k = 6
5 : 1 resonant orbit for k = 2
5 : 1 resonant orbit for k = 2