Canonical Perturbation Theories: Degenerate Systems and Resonance

Sylvio Ferraz-Mello (auth.)9780387389004, 0387389008, 0387389059, 9780387389059

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.

Table of contents :
Front Matter….Pages I-XIV
The Hamilton-Jacobi Theory….Pages 1-27
Angle-Action Variables. Separable Systems….Pages 29-60
Classical Perturbation Theories….Pages 61-98
Resonance….Pages 99-125
Lie Mappings….Pages 127-138
Lie Series Perturbation Theory….Pages 139-159
Non-Singular Canonical Variables….Pages 161-180
Lie Series Theory for Resonant Systems….Pages 181-207
Single Resonance near a Singularity….Pages 209-230
Nonlinear Oscillators….Pages 231-261
Back Matter….Pages 262-341