Dynamical Systems and Microphysics - 1st Edition - ISBN: 9780120687206, 9780323139526

Dynamical Systems and Microphysics

1st Edition

Geometry and Mechanics

Authors: Andre Avez
eBook ISBN: 9780323139526
Imprint: Academic Press
Published Date: 28th January 1982
Page Count: 465
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Dynamical Systems and Microphysics: Geometry and Mechanics contains the proceedings of the Second International Seminar on Mathematical Theory of Dynamical Systems and Microphysics held at the International Center for Mechanical Sciences in Udine, Italy on September 1-11, 1981. Contributors explore the geometry and mechanics of dynamical systems and microphysics and cover topics ranging from Lagrangian submanifolds and optimal control theory to Hamiltonian mechanics, linear dynamical systems, and the quantum theory of measurement. This volume is organized into six sections encompassing 30 chapters and begins with an introduction to geometric structures, mechanics, and general relativity. It considers an approach to quantum mechanics through deformation of the symplectic structure, giving a striking insight into the correspondence principle. The chapters that follow focus on the gauge invariance of the Einstein field, group treatment of the space of orbits in the Kepler problem, and stable configurations in nonlinear problems arising from physics. This book is intended for researchers and graduate students in theoretical physics, mechanics, control and system theory, and mathematics. It will also be profitably read by philosophers of science and, to some extent, by persons who have a keen interest in basic questions of contemporary mechanics and physics and some background in the physical and mathematical sciences.

Table of Contents

Contributors Preface I. Geometric Structures, Mechanics, and General Relativity Lagrangian Submanifolds, Statics and Dynamics of Mechanical Systems Deformations and Quantization Lie Group Actions on Poisson and Canonical Manifolds Gauge Theories and Gravitation Riemannian Geometry and Mechanics: The Kepler Problem Confinement Problems in Mathematical Physics, Classical and Modern II. System Theory Approaches to Mechanics Optimality and Reachability with Feedback Control Optimization and Controllability in Problems of Relativistic Dynamics and of Geometrical Optics Some Relations between Optimal Control Theory and Classical Mechanics Modeling of Dynamical Systems using External and Internal Variables with Applications to Hamiltonian Systems III. Lagrangian and Hamiltonian Formulations of Mechanics Some Reflections on Hamiltonian Formalism On the Lagrange Representation of a System of Newton Equations Conservation Laws and a Hamilton-Jacobi-Like Method in Nonconservative Mechanics On the Validity Limits of Hamiltonian Mechanics and a Way of Going beyond Them IV. Perturbations Adiabatical Invariants in Linear Dynamical Systems Periodically Depending on Time, with an Application to the Statistical Fluctuations of Mathieu Oscillators Adiabatical Invariants in Nonlinear Dynamical Systems Periodically Depending on Time, with an Application to the Parametrical Resonance in a Physical (Nonlinear) Pendulum A Theorem on Phase-Locking in Two Interacting Clocks (The Huyghens Effect) Simple Closed Geodesics on Surfaces V. Some Problems in Quantum Mechanics Some Topics in the Quantum Theory of Measurement Light-Cone Quantization of Gauge Theories with Periodic Boundary Conditions VI. Contributed Papers Solutions of Generalized Theories of Gravitation Derived from a Modified Double Duality Condition Dynamical Systems and Microphysics: A Wish


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© Academic Press 1982
Academic Press
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Andre Avez

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