Unchained 8
The projections in the $xy$-plane of these choreography has winding
number $l$ around a center and is invariant by rotations of
$2\pi/m$; and the bodies make groups of $h$ polygons, where $h$ is
maximum common divisor of $n$ and $k$.
The spatial choreographies along the vertical Lyapunov families are
symmetric by the two reflections $-y$ and $-z$, while the spatial
choreographies along the axial family are symmetric only by the
reflections $(-y,-z)$, when the $x$-axis is chosen to pass through
the "center" of the orbit.
1:4 resonant
orbit |
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3:4 resonant
orbit |
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