Generic uniqueness of the minimal Moulton central configuration

TL;DR

This paper proves that for most mass distributions in the collinear N-body problem, there is a unique minimal Moulton configuration, characterized by a single critical point of the potential function.

Contribution

It establishes the generic uniqueness of the minimal Moulton configuration for the collinear N-body problem, showing that typically only one such configuration exists.

Findings

For generic masses, the potential function has N!/2 critical points.

There is a unique minimal Moulton configuration for generic mass choices.

The result applies to the Newtonian collinear N-body problem.

Abstract

We prove that, for generic (open and dense) values of the masses, the Newtonian potential function of the collinear N-body problem has $N!/2$ critical values when restricted to a fixed inertia level. In particular, we prove that for generic masses, there is only one minimal Moulton configuration.