Dziobek's configurations in restricted problems and bifurcation
type: Item
instance of: scholarly article
title: Dziobek's configurations in restricted problems and bifurcation
zbMATH Open document ID: 1143.70004
author: Alan Almeida Santos
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-02-28T00:00:00Z
review text: The author considers central configurations in the restricted \((n+1)\)-body problem and investigates symmetry properties of the restricted \((n+1)\)-body problem in the \((n-1)\)-dimensional space. In particular, the author analyzes five bodies in a three-dimensional configuration with four particles of equal masses \(m\) and a fifth unitary mass located in their convex hull. The following theorem is proved: if \( 0<m<1/16\), then every central configuration of this problem has a plane of symmetry. Some particular cases are discussed.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70G10
zbMATH DE Number: 2139805
zbMATH Keywords: restricted 5-body problem
zbMATH Keywords: central configurations
zbMATH Keywords: symmetries
MaRDI profile type: Publication
full work available at URL: s10569-004-0415-7
OpenAlex ID: W2005109704
cites work: The \(n\)-body problem and mutual distances
cites work: On the role and the properties ofn body central configurations
cites work: Four-body central configurations with some equal masses
cites work: Bifurcations of relative equilibria in the 4- and 5-body problem
cites work: Central configurations of four bodies with one inferior mass
cites work: Relative equilibrium solutions in the four body problem
DOI: 10.1007/S10569-004-0415-7
description: scientific article; zbMATH DE number 2139805