Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Meyer, Kenneth Ray (1937-....)
Titre(s) : Periodic solutions of the N-body problem [Texte électronique] / Kenneth R. Meyer
Publication : Berlin ; New York : Springer, cop. 1999
Description matérielle : 1 online resource (ix, 144 pages)
Collection : Lecture notes in mathematics ; 1719
Note(s) : Includes bibliographical references (pages 139-142) and index
The N-body problem is the classical prototype of a Hamiltonian system with a large
symmetry group and many first integrals. These lecture notes are an introduction to
the theory of periodic solutions of such Hamiltonian systems. From a generic point
of view the N-body problem is highly degenerate. It is invariant under the symmetry
group of Euclidean motions and admits linear momentum, angular momentum and energy
as integrals. Therefore, the integrals and symmetries must be confronted head on,
which leads to the definition of the reduced space where all the known integrals and
symmetries have been eliminated. It is on the reduced space that one can hope for
a nonsingular Jacobian without imposing extra symmetries. These lecture notes are
intended for graduate students and researchers in mathematics or celestial mechanics
with some knowledge of the theory of ODE or dynamical system theory. The first six
chapters develops the theory of Hamiltonian systems, symplectic transformations and
coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced
space etc. The remaining six chapters contain theorems which establish the existence
of periodic solutions of the N-body problem on the reduced space
Sujet(s) : Problème à N corps
Systèmes hamiltoniens
Mathématiques
Analyse globale (mathématiques)
Indice(s) Dewey :
510 (23e éd.) = Mathématiques ; 530.144 (23e éd.) = Problème à plusieurs corps
Identifiants, prix et caractéristiques : ISBN 9783540480730
Identifiant de la notice : ark:/12148/cb44692589c
Notice n° :
FRBNF44692589
(notice reprise d'un réservoir extérieur)
Table des matières : Introduction ; Equations of Celestial Mechanics ; Hamiltonian Systems ; Central
Configurations ; Symmetries ; Integrals and Reduction ; Theory of Periodic Solutions
; Satellite Orbits ; The Restricted Problem ; Lunar Orbits ; Comet Orbits ; Hill's
Lunar Equations ; The Elliptic Problem.
