Mathematics-Dynamical Systems

Periodic Solutions of the N-Body Problem

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Title (user) : Periodic Solutions of the N-Body ProblemISBN : 3540666303,9783540666301ISSN : 0075-8434DDC : 510 s,530.14/4LCC : QA3 .L28 no. 1719,QA614.83 .L28 no. 1719DOI : 10.1007/BFb0094677GoogleBook ID : crQF-Tc3ZWwCOpenLibrary ID : OL48295MEd...
Description

Title (user) : Periodic Solutions of the N-Body Problem

ISBN : 3540666303,9783540666301

ISSN : 0075-8434

DDC : 510 s,530.14/4

LCC : QA3 .L28 no. 1719,QA614.83 .L28 no. 1719

DOI : 10.1007/BFb0094677

GoogleBook ID : crQF-Tc3ZWwC

OpenLibrary ID : OL48295M

Edition : 1

Series : Lecture Notes in Mathematics 1719

Authors (user) : Kenneth R. Meyer (auth.)

Authors (google) : Kenneth R. Meyer

Publisher : Springer-Verlag Berlin Heidelberg

Language : English

Publication Date : 1999

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :

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.


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Description (google) :
Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.


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Table of contents :
Introduction....Pages 1-8
Equations of celestial mechanics....Pages 9-18
Hamiltonian systems....Pages 19-37
Central configurations....Pages 39-49
Symmetries, integrals, and reduction....Pages 51-70
Theory of periodic solutions....Pages 71-86
Satellite orbits....Pages 87-90
The restricted problem....Pages 91-103
Lunar orbits....Pages 105-110
Comet orbits....Pages 111-118
Hill’s lunar equations....Pages 119-127
The elliptic problem....Pages 129-137

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