On the Existence of Central Configurations of p Nested n-gons

Abstract

In this paper we prove the existence of central configurations of the pnbody problem where the masses are at the vertices of p nested regular n-gons with a common center for all p ≥ 2 and n ≥ 2. In such configurations all the masses on the same n-gon are equal, but masses on different n-gons could be different.