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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.
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
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
- No. of pages:
- © Academic Press 1982
- 28th January 1982
- Academic Press
- eBook ISBN:
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