In this paper we prove the existence of central configurations of the n + 2-body problem where n equal masses are located at the vertices of a regular n-gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n-gon passing through its center. Here this kind of central configurations is called bi-pyramidal central configurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the configuration is central. We give explicitly those relations.
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 1 Jan 2013|
- Bi-pyramidal central configurations
- N+2-body problem
- Spatial central configurations