الصفحة 1
الصفحة 1
Metamorphoses of Hamiltonian Systems with Symmetries
Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.
Mechanics : From Newton's Laws to Deterministic Chaos
This updated and revised fourth edition covers all topics in mechanics from elementary Newtonian mechanics, canonical and rigid body mechanics to relativistic mechanics and nonlinear dynamics. In particular, symmetries and invariance principles, geometrical structures and continuum mechanics play an important role. This book will enable the reader to develop general principles from which equations of motions may be derived, to understand the importance of symmetries as a basis for quantum mechanics and to get practice in using theoretical tools and concepts that are essential for all branches of physics. The book contains numerous problems with complete solutions, and some practical examples.This will be appreciated in particular by students using the text to accompnay lectures on mechanics. The book ends with some historical remarks on important pioneers in mechanics.
Lectures on Symplectic Geometry
Provides a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding.
Canonical Perturbation Theories, Degenerate Systems, and Resonance
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.
A Comparison of the Dynamical Evolution of Planetary Systems ; Proceedings of the Sixth Alexander von Humboldt Colloquium on Celestial Mechanics Bad Hofgastein (Austria), 21-27 March 2004
The papers in this volume cover a wide range of subjects covering the most recent developments in Celestial Mechanics from the theoretical point of nonlinear dynamical systems to the application to real problems. We emphasize the papers on the formation of planetary systems, their stability and also the problem of habitable zones in extrasolar planetary systems. A special topic is the stability of Trojans in our planetary system, where more and more realistic dynamical models are used to explain their complex motions: besides the important contribution from the theoretical point of view, the results of several numerical experiments unraveled the structure of the stable zone around the librations points. This volume will be of interest to astronomers and mathematicians interested in Hamiltonian mechanics and in the dynamics of planetary systems.
