国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ] 本书特色

This book contains a mathematical expositioof analogies betweeclassical (Hamiltonian) mechanics，geometrical optics，and hydrodynamics. This theory highlights several general mathematical ideas that appeared iHamiltoniamechanics，optics and hydrodynamics under different names. Iaddition，some interesting applications of the general theory of vortices are discussed ithe book such as applications inumerical methods，stability theory，and the theory of exact integratioof equations of dynamics. The investigatioof families of trajectories of Hamiltoniasystems cabe reduced to problems of multidimensional ideal fluid dynamics.For example，the well-knowHamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested imathematical physics，mechanics，and the theory of differential equations.

国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ] 内容简介

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国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ] 目录

Introduction
Descartes， Leibnitz， and Newton
Newtoand Bernoulli
Voltaire， Maupertuis， and Clairaut
Helmholtz and Thomson
About the Book

Chapter 1． Hydrodynamics， Geometric Optics， and Classical Mechanics
1． Vortex Motions of a Continuous Medium
2． Point Vortices othe Plane
3． Systems of Rays， Laws of Reflectioand Refraction， and the Malus Theorem
4． Fermat Principle， Canonical HamiltoEquations， and the Optical-Mechanical Analogy
5． HamiltoniaForm of the Equations of Motion
6． Actioithe Phase Space and the Poincare-CartaInvariant
7． Hamilton-Jacobi Method and Huygens Principle
8． Hydrodynamics of HamiltoniaSystems
9． Lamb Equations and the Stability Problem

Chapter 2． General Vortex Theory
1． Lamb Equations and HamiltoEquations
2． Reductioto the Autonomous Case
3． Invariant Volume Forms
4． Vortex Manifolds
5． Euler Equation
6． Vortices iDissipative Systems

Chapter 3． Geodesics oLie Groups with a Left-Invariant Metric
1． Euter-Poincare Equations
2． Vortex Theory of the Top
3． Haar Measure
4． PoissoBrackets
5． Casimir Functions and Vortex Manifolds

Chapter 4． Vortex Method for Integrating HamiltoEquations
1． Hamilton-Jacobi Method and the Liouville Theorem oComplete Integrability
2． Noncommutative Integratioof the HamiltoEquations
3． Vortex IntegratioMethod
4． Complete Integrability of the Quotient System
5． Systems with Three Degrees of Freedom

Supplement 1： Vorticity Invariants and Secondary Hydrodynamics
Supplement 2： Quantum Mechanics and Hydrodynamics
Supplement 3： Vortex Theory of Adiabatic Equilibrium Processes
References
Index

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自然科学 数学 数学理论

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