Central configuration in the planar n + 1 body problem with generalized forces.

In this paper we consider a polygonal configuration for the planar (n + 1) body problem. When a newtonian field is considered, is well know that we have a central configuration. By introducting general functions that depends on distance, we prove that central configuration is preserved not only for a newtonian field but for any field wich depends on the inverse of distances. The Manev-type and the Schwarzschild-type fields are particular cases of our study.