Classification of stacked central configurations in R^3

Abstract

We classify the extensions of n-body central configurations to (n + 1)-body central configurations in R 3 , in both the collinear case and the non-collinear case. We completely solve the two open questions posed by Hampton (Nonlinearity 18: 2299-2304. This classification is related with study on co-circular and co-spherical central configurations. We also obtain a general property of co-circular central configurations.