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Lectures on Celestial Mechanics

Reprint of the 1971 Edition

  • Carl Ludwig Siegel
  • Jürgen K. Moser

Part of the Grundlehren der mathematischen Wissenschaften book series (CLASSICS, volume 187)

Table of contents

  1. Front Matter
    Pages N1-XII
  2. Carl Ludwig Siegel, Jürgen K. Moser
    Pages 1-90
  3. Carl Ludwig Siegel, Jürgen K. Moser
    Pages 91-182
  4. Carl Ludwig Siegel, Jürgen K. Moser
    Pages 183-283
  5. Back Matter
    Pages 284-290

About this book

Introduction

The present book represents to a large extent the translation of the German "Vorlesungen über Himmelsmechanik" by C. L. Siegel. The demand for a new edition and for an English translation gave rise to the present volume which, however, goes beyond a mere translation. To take account of recent work in this field a number of sections have been added, especially in the third chapter which deals with the stability theory. Still, it has not been attempted to give a complete presentation of the subject, and the basic prganization of Siegel's original book has not been altered. The emphasis lies in the development of results and analytic methods which are based on the ideas of H. Poincare, G. D. Birkhoff, A. Liapunov and, as far as Chapter I is concerned, on the work of K. F. Sundman and C. L. Siegel. In recent years the measure-theoretical aspects of mechanics have been revitalized and have led to new results which will not be discussed here. In this connection we refer, in particular, to the interesting book by V. I. Arnold and A. Avez on "Problemes Ergodiques de la Mecanique Classique", which stresses the interaction of ergodic theory and mechanics. We list the points in which the present book differs from the German text. In the first chapter two sections on the tri pie collision in the three­ body problem have been added by C. L. Siegel.

Keywords

Celestial mechanics File in Springer catalogue at LSI Invariant Jacobi convergence derivative eXist equation fixed-point theorem function interaction presentation proof theorem transformation

Authors and affiliations

  • Carl Ludwig Siegel
    • 1
  • Jürgen K. Moser
    • 2
    • 3
  1. 1.Mathematisches InstitutUniversität GöttingenDeutschland
  2. 2.ETH Zentrum, MathematikZürichSchweiz
  3. 3.Courant Institute of Mathematical SciencesNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-87284-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58656-2
  • Online ISBN 978-3-642-87284-6
  • Series Print ISSN 1431-0821
  • Buy this book on publisher's site