Overview
- Each theory is presented as a complete recipe which can be followed towards practical application, including warnings against known difficulties
- Presents complete solutions and action-angle variables of the elementary integrable systems that serve as starting points in Perturbations Theory
- The only book which considers extensively the problem of overcoming the small divisors that appear when Perturbations Theory is used to construct solutions in the neighborhood of a resonance of the proper frequencies
Part of the book series: Astrophysics and Space Science Library (ASSL, volume 345)
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About this book
Canonical Perturbation Theories, Degenerate Systems and Resonance presents the foundations of Hamiltonian Perturbation Theories used in Celestial Mechanics, emphasizing the Lie Series Theory and its application to degenerate systems and resonance.
This book is the complete text on the subject including advanced topics in Hamiltonian Mechanics, Hori’s Theory, and the classical theories of Poincaré, von Zeipel-Brouwer, and Delaunay. Also covered are Kolmogorov’s frequency relocation method to avoid small divisors, the construction of action-angle variables for integrable systems, and a complete overview of some problems in Classical Mechanics.
Sylvio Ferraz-Mello makes these ideas accessible not only to Astronomers, but also to those in the related fields of Physics and Mathematics.
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Reviews
From the reviews:
"The book consists of 10 chapters and four appendices. … Undoubtedly, the monograph will be useful for postgraduate students." (Sergei Georgievich Zhuravlev, Zentralblatt MATH, Vol. 1122 (24), 2007)
"The book by Sylvio Ferraz-Mello provides a deep insight in perturbation theories. … the mathematical presentation of the different facets is always accompanied by a number of case studies and examples. Such peculiarity makes the book unique … . Thanks to the … author, the book is recommended for both teaching and research purposes: the didactical and self-contained aspects address the book to advanced undergraduate students; the researchers in Dynamical Systems and Celestial Mechanics will certainly enjoy the excellent and deep presentation of perturbation theories." (Alessandra Celletti, Celestial Mechanics and Dynamical Astronomy, Vol. 100 (4), 2008)
"The purpose of this book is … ‘to deal with the perturbation theories used in Celestial Mechanics, but they should be presented in a universal way, so as to be understandable by investigators and students from related fields of science.’ In other words, one does not need a special background in astronomy to read and understand the book. … a large number of the examples will be of interest to people working in Hamiltonian theory. … a valuable source of material on conservative systems." (Ferdinand Verhulst, SIAM Review, Vol. 50 (2), 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Canonical Perturbation Theories
Book Subtitle: Degenerate Systems and Resonance
Authors: Sylvio Ferraz-Mello
Series Title: Astrophysics and Space Science Library
DOI: https://doi.org/10.1007/978-0-387-38905-9
Publisher: Springer New York, NY
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag New York 2007
Hardcover ISBN: 978-0-387-38900-4Published: 16 January 2007
Softcover ISBN: 978-1-4419-2285-4Published: 24 November 2010
eBook ISBN: 978-0-387-38905-9Published: 30 May 2007
Series ISSN: 0067-0057
Series E-ISSN: 2214-7985
Edition Number: 1
Number of Pages: XIV, 346
Number of Illustrations: 60 b/w illustrations
Topics: Astrophysics and Astroparticles, Theoretical, Mathematical and Computational Physics, Astronomy, Observations and Techniques, Applications of Mathematics