Dynamical Systems and Microphysics

Dynamical Systems and Microphysics

Geometry and Mechanics

1st Edition - January 28, 1982

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  • Author: Andre Avez
  • eBook ISBN: 9780323139526

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Description

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

    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


Product details

  • No. of pages: 465
  • Language: English
  • Copyright: © Academic Press 1982
  • Published: January 28, 1982
  • Imprint: Academic Press
  • eBook ISBN: 9780323139526

About the Author

Andre Avez

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