Astronomy and Astrophysics Library

Theory of Orbits

Perturbative and Geometrical Methods

Authors: Boccaletti, Dino, Pucacco, Giuseppe

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  • ISBN 978-3-662-09240-8
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About this Textbook

Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry.
The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform. A whole chapter treats the theory of adiabatic invariants and its applications in celestial mechanics and stellar dynamics. Also the theory of resonances is illustrated and applications in both fields are shown. Classical and modern problems connected to periodic solutions are reviewed. The description of modern developments of the theory of chaos in conservative systems is the subject of a chapter in which an introduction is given to what happens in both near-integrable and non-integrable systems. The invaluable help provided by computers in the exploration of the long-time behaviour of dynamical systems is acknowledged in a final chapter, where some numerical algorithms and their applications both to systems with few degrees of freedom and to large N-body systems are illustrated.

Reviews

From the reviews
"The book is ... didactically written and contains topics from classical to most modern ones, treated rigorously by indicating where complete proofs are to be found."
Zentralblatt für Mathematik, 1999

Table of contents (7 chapters)

  • Classical Perturbation Theory in Celestial Mechanics. The Equations of Planetary Motion

    Boccaletti, Dino (et al.)

    Pages 1-67

  • Canonical Perturbation Theory

    Boccaletti, Dino (et al.)

    Pages 69-123

  • Lie Transform Perturbation Theory

    Boccaletti, Dino (et al.)

    Pages 125-178

  • The Theory of Adiabatic Invariants

    Boccaletti, Dino (et al.)

    Pages 179-233

  • Periodic Orbits and Resonances

    Boccaletti, Dino (et al.)

    Pages 235-295

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-662-09240-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-540-60355-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-642-08222-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Orbits
Book Subtitle
Perturbative and Geometrical Methods
Authors
Series Title
Astronomy and Astrophysics Library
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-09240-8
DOI
10.1007/978-3-662-09240-8
Hardcover ISBN
978-3-540-60355-9
Softcover ISBN
978-3-642-08222-1
Series ISSN
0941-7834
Edition Number
1
Number of Pages
XIV, 423
Number of Illustrations and Tables
62 b/w illustrations
Topics