Montserrat Corbera and Jaume Llibre have published a new paper proving the existence of a new family of central configurations in a special case of the spatial (2n+2) body problem with n>=4. These central configurations consist of n equal masses at the vertices of a regular n-gon, n additional equal masses at the vertices of another n-gon whose vertices are the midpoints of the edges of the initial n-gon, and two equal masses on the straight line orthogonal to the plane containing the two n-gons passing through their barycenters.

The peculiarity of these central configurations is that they are convex but non-strictly convex.

 

 

Corbera, M., Llibre, J. (2019) Spatial convex but non-strictly convex double-pyramidal central configurations of the (2n+2)-body problem. Journal of Dymanics and Differential Equations. DOI: 10.1007/s10884-019-09798-3