Rotation of synchronous satellites: application to the Galilean satellites
type: Item
instance of: scholarly article
title: Rotation of synchronous satellites: application to the Galilean satellites
zbMATH Open document ID: 1160.70327
DOI: 10.1023/B:CELE.0000034515.57763.33
author: Jacques Henrard
author: Gabriel Schwanen
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-03-01T00:00:00Z
review text: The equations of the \(n\)-body problem (and particularly, \( n=3 \) case) written in Keplerian variables have singularities in cases of orbits with small eccentricities and inclinations. On the contrary the Poincaré and the Laplace variables are regular for orbits with small eccentricities and inclinations, and are thus well suited for studying the planetary problem in the case of our solar system. Here, first the Laplace and the Poincaré variables are introduced, then it is demonstrated that the Poincaré action-angle variables are closely related to the geometry of the group \(\text{SO}(3)\) and the Laplace variables -- to the geometry of the group \(\text{SU}(2)\) and, finally, an algorithm easily implementable on a computer is constructed. The algorithm called POINCARE program performs series developments and averaging processes and it is written in the MAPLE algorithmic language.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 2140052
zbMATH Keywords: celestial mechanics
zbMATH Keywords: \(n\)-body problem
zbMATH Keywords: Laplace variables
zbMATH Keywords: Poincaré variables
zbMATH Keywords: averaging process
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: b:cele.0000034515.57763.33
OpenAlex ID: W2095010243
description: scientific article; zbMATH DE number 2140052