Halfway between Heaven and Hell

TL;DR

This paper explores fundamental questions about the classical N-body problem, examining the relationship between the virial theorem and the Jacobi-Maupertuis principle to deepen understanding of gravitational systems.

Contribution

It provides new insights into the connections between virial equations and variational formulations in the N-body problem, addressing unresolved questions.

Findings

Some questions about the N-body problem are answered.

New links between virial theorem and Jacobi-Maupertuis formulation are established.

The paper advances theoretical understanding of gravitational dynamics.

Abstract

We pose several questions for the classical N-body problem inspired by connections between the virial equation and the Jacobi-Maupertuis formulationof mechanics. We answer some.