Convex central configurations for the n-body problem

Central configurations and relative equilibria in 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...

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.

Convex Four Body Central Configurations with Some Equal Masses

We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such central configuration posses a symmetry line and it is a kite shaped quadrilateral. We also show that there is exactly on...

Central Configurations and Total Collisions for Quasihomogeneous N-body Problems

We consider n-body problems given by potentials of the form α r + β r with a, b, α, β constants, 0 ≤ a < b. To analyze the dynamics of the problem, we first prove some properties related to central configurations, including a generalization of Moulton’s theorem. Then we obtain several qualitative properties for collision and near-collision orbits in the Manev-type case a = 1. At the end we poin...