Integral manifolds of the \(N\)-body problem
type: Item
instance of: scholarly article
title: Integral manifolds of the \(N\)-body problem
zbMATH Open document ID: 0801.70008
DOI: 10.1007/BF01232677
author: Alain Albouy
published in: Inventiones Mathematicae
publication date: 1994-11-24T00:00:00Z
full work available at URL: https://eudml.org/doc/144155
review text: This paper is devoted to the study of level manifolds (for an ambient space of dimension greater than three) of angular momentum of a system of bodies and treats in a global way the question of reduction or elimination of the node. Two distinct phenomena are studied: critical points and critical points at infinity of the energy function restricted to the chosen level manifold of angular momentum; the critical points are relative equilibria of Lagrange type. In particular, in the 4-body problem the critical points at infinity produce at most 26 changes of topology. The last part of the paper gives a description of the integral manifold of the 3-body problem.
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 37N99
zbMATH DE Number: 549635
zbMATH Keywords: planar problem
zbMATH Keywords: spatial problem
zbMATH Keywords: angular momentum
zbMATH Keywords: reduction
zbMATH Keywords: critical points
zbMATH Keywords: critical points at infinity
zbMATH Keywords: energy function
reviewed by: Vasile Marinca
MaRDI profile type: Publication
cites work: Q4167627
cites work: On the integral manifolds of the n-body problem
cites work: Some topology of n-body problems
cites work: Characteristic Classes. (AM-76)
cites work: Central configurations of the N-body problem via equivariant Morse theory
cites work: A generalized Morse theory
cites work: From rotations and inclinations to zero configurational velocity surfaces, II. The best possible configurational velocity surfaces
cites work: Topology and mechanics. I
cites work: Topology and mechanics. II: The planar \(n\)-body problem
cites work: Q5780526
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description: scientific article; zbMATH DE number 549635