Dynamical Systems and Microphysics

Geometry and Mechanics

1st Edition - January 28, 1982
Author: Andre Avez
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 3 9 5 2 - 6

Dynamical Systems and Microphysics: Geometry and Mechanics contains the proceedings of the Second International Seminar on Mathematical Theory of Dynamical Systems and Microphysics… Read more

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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.

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

Non-equilibrium Entropy for Kolmogorov Dynamical Systems

Bimetric Machian Gravitation: General Theory and Cosmology

Mechanics and the Notion of Observables

The Meaning of the Lagrangian

A Classical Theory of Extended Particles with the Pauli Exclusion Principle

Some Remarks on State Reversibility and Irreversibility in System Theory

Symplectic Structures, Energy-Momentum Functions, and Hamilton Equations Theories of Gravity

Stochastic Calculus of Variations, Stochastic Control, and Quantum Dynamics