Spatial n+1



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 \textquotedblleft center\textquotedblright of the orbit.

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. The mass of the central body is equal to $\mu =200$ for the case of 7+1 bodies and $\mu=300$ for the case of 8+1 bodies.


8:7 resonant
orbit for k = n
for 7+1 bodies
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15:14 resonant
orbit for k = n
for 7+1 bodies
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13:12 resonant
orbit for k = 4
for 8+1 bodies
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15:12 resonant
orbit for k = 4
for 8+1 bodies
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9:8 resonant
orbit for k = n
for 8+1 bodies
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17:16 resonant
orbit for k = n
for 8+1 bodies
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