Motion near the unit circle in the three-body problem
type: Item
instance of: scholarly article
title: Motion near the unit circle in the three-body problem
zbMATH Open document ID: 0960.70009
DOI: 10.1023/A:1008371719238
author: Roger A. Broucke
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2001-05-10T00:00:00Z
review text: The author investigates the motion near the unit circle \((r=1)\) by expanding the Lagrangian of the restricted problem up to different orders of \(\varepsilon\) \((r=1 +\varepsilon,\;\varepsilon\ll 1)\). The Clohessy-Wiltshire equations are analysed in perturbed and unperturbed form, and a new symmetric property with respect to the unit circle is discovered. It is also revealed that the \(L_3,L_4,L_5\) libration points are retained even in the case of the lowest-order models.
Mathematics Subject Classification ID: 70F07
zbMATH DE Number: 1442270
zbMATH Keywords: perturbation analysis
zbMATH Keywords: unit circle
zbMATH Keywords: Lagrangian
zbMATH Keywords: Clohessy-Wiltshire equations
zbMATH Keywords: symmetric property
zbMATH Keywords: libration points
zbMATH Keywords: lowest-order models
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
full work available at URL: a:1008371719238
OpenAlex ID: W4252852175
description: scientific article; zbMATH DE number 1442270