Von Zeipel's theorem on singularities in celestial mechanics
type: Item
instance of: scholarly article
title: Von Zeipel's theorem on singularities in celestial mechanics
zbMATH Open document ID: 0622.70005
author: Richard McGehee
published in: Expositiones Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: The classification of the singularities which can arise in the solutions of the classical n-body problem given by Painlevé (collisions and pseudocollisions) is used for the rigorous proof of Zeipel's theorem [\textit{H. von Zeipel}, Ark. Mat. Astron. Fys. 4, 32, 1-4 (1908)]. This theorem asserts that a noncollision singularity (a pseudocollision) can occur only if the system of particles (bodies) becomes unbounded in finite time. In the present paper von Zeipel's proof of the mentioned theorem is translated into modern mathematical notation and terminology. So the von Zeipel's remarkable original ideas become more readily available to current researchers.
reviewed by: V.Ureche
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70F35
Mathematics Subject Classification ID: 31B99
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 4009869
zbMATH Keywords: classification of the singularities
zbMATH Keywords: Zeipel's theorem
zbMATH Keywords: noncollision singularity
zbMATH Keywords: pseudocollision
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4009869