On the central configurations of the n-body problem

Abstract

We present a brief survey on some classes of central configurations of the n-body problem. We put special emphasis on the central configurations of the 1+n-body problem also called the coorbital satellite problem, and on the nested central configurations formed by either regular n-gons, or regular polyhedra. We also present some conjectures.

On the Newton–Raphson basins of convergence associated with the libration points in the axisymmetric restricted five-body problem: The concave configuration

“…These research topics have various practical applications in the field of planetary physics and in galactic dynamics. Therefore, the general extension of N −body problem is the study of problem of N -bodies for N > 4 (e.g., [16]). In few decades, the restricted problem of N = 5 bodies has fascinated many researchers and scientists.…”

The Circular Hill Problem Regarding Arbitrary Disturbing Forces: The Periodic Solutions that are Emerging from the Equilibria

“…The Hill problem is an example of this. There are many studies on the Hill problem [1][2][3][4][5][6][7][8][9][10][11], and many modifications of this classic problem have appeared in the mathematical, astronomical, and mechanical literature. For example, in [6], Markellos and Roy introduced a photogravitational Hill problem as a simplified, non-trivial form of the photogravitational restricted three-body problem.…”