# Aligned

Other configurations

### Two aligned rings $$C_{nv}(2R)$$

There is not much to say for these aligned rings: they are only stable if $$n<7$$ and if the rings are sufficiently far apart. They necessarily have vorticities of opposite signs.

In the diagram, the horizontal axis is θ0, the vertical is θ1 .

Lyapounov stable points in red elliptic ones in blue (none of the latter if n is even)

For $$n=4$$ one has,

If n is odd, there are very thin slivers of elliptic points around the curved edge of the Lyapounov stable regions, but too narrow to see at this scale.