Details
Canonical Perturbation Theories
Degenerate Systems and ResonanceAstrophysics and Space Science Library, Band 345
149,79 € |
|
Verlag: | Springer |
Format: | |
Veröffentl.: | 30.05.2007 |
ISBN/EAN: | 9780387389059 |
Sprache: | englisch |
Anzahl Seiten: | 346 |
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Beschreibungen
The Hamilton-Jacobi Theory.- Angle-Action Variables. Separable Systems.- Classical Perturbation Theories.- Resonance.- Lie Mappings.- Lie Series Perturbation Theory.- Non-Singular Canonical Variables.- Lie Series Theory for Resonant Systems.- Single Resonance near a Singularity.- Nonlinear Oscillators.
<P>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.</P>
<P>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.</P>
<P>Sylvio Ferraz-Mello makes these ideas accessible not only to Astronomers, but also to those in the related fields of Physics and Mathematics.</P>
<P>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.</P>
<P>Sylvio Ferraz-Mello makes these ideas accessible not only to Astronomers, but also to those in the related fields of Physics and Mathematics.</P>
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