Permanent configurations in the $n$-body problem

Central configurations and relative equilibria in the n–body problem

The N-body Problem

New Classes of Spatial Central Configurations for N + N + 2 - Body Problem

and Applied Analysis 3 Recently, Hampton and Santoprete 17 provided new examples of stacked spatial central configurations—central configurations for theN-body problemwhere a proper subset of the N bodies are already on a central configuration—for the 7-body problem where the bodies are arranged as concentric threeand two-dimensional simplex. New classes of stacked spatial central configuration...

The quantum N-body problem

This selective review is written as an introduction to the mathematical theory of the Schro ̈dinger equation for N particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect are described by giving full proofs of...

Stacked Central Configurations for the Spatial Nine-Body Problem

We show the existence of the twisted stacked central configurations for the 9-body problem. More precisely, the position vectors x₁, x₂, x₃, x₄, and x₅ are at the vertices of a square pyramid Σ; the position vectors x₆, x₇, x₈, and x₉ are at the vertices of a square Π.