Some insights from total collapse in the N-body problem

Abstract

Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.We discuss the Sundman-Weierstrass theorem of total collapse in its historical context. This remarkable and relatively simple result, a type of stability criterion, is at the crossroads of some interesting developments in the gravitational N-body problem. We use it as motivation to explore the connections to such important concepts as integrability, singularities, and typicality in order to gain insight into the transition from a predominantly quantitative to a novel qualitative approach to dynamical problems that took place at the end of the 19th century.