Numerical Exploration of the Limit Ring Problem

The aim of this work is to provide an insight of an idealized model of a planetary ring. The model is a limit case of the planar circular restricted 1 +  n body problem, where an infinitesimal particle moves under the gravitational influence of a large central body and n smaller bodies located on th...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems Vol. 12; no. 1; pp. 25 - 52
Main Authors: Barrabés, E., Cors, J. M., Hall, G. R.
Format: Journal Article Publication
Language:English
Published: Basel SP Birkhäuser Verlag Basel 01.04.2013
Subjects:
37 Dynamical systems and ergodic theory
37N Applications
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
70K Nonlinear dynamics
Anells planetaris
Celestial mechanics
Classificació AMS
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Many-body problem
Matemàtiques i estadística
Mathematics
Mathematics and Statistics
Mecànica celest
N body problem
Planetary rings
Problema dels cossos múltiples
Àrees temàtiques de la UPC
70F45
body problem
Planetary rings
37N05
70F15
70K43
Celestial Mechanics
70K42
ISSN:1575-5460, 1662-3592
Online Access:Get full text
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Summary:The aim of this work is to provide an insight of an idealized model of a planetary ring. The model is a limit case of the planar circular restricted 1 +  n body problem, where an infinitesimal particle moves under the gravitational influence of a large central body and n smaller bodies located on the vertices of a regular n -gon. When considering n tending to infinity, a model depending on one parameter is obtained. We study the main important structures of the problem depending on this parameter (equilibria, Hill’s regions, linear stability, …). We use Poincaré maps, for different values of the parameter, in order to predict the width of the ring and the richness of the dynamics that occur is discussed. This work is a continuation of the work presented in Barrabés by (SIAM J Appl Dyn Syst 9:634–658, 2010 ).
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-012-0082-0