| Introduction Descartes， Leibnitz， and Newton Newton and 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 on the Plane 3.Systems of Rays， Laws of Reflection and Refraction， and the Malus Theorem 4.Fermat Principle， Canonical Hamilton Equations， and the Optical-Mechanical Analogy 5.Hamiltonian Form of the Equations of Motion 6.Action in the Phase Space and the Poincare-Cartan Invariant 7.Hamilton-Jacobi Method and Huygens Principle 8.Hydrodynamics of Hamiltonian Systems 9.Lamb Equations and the Stability Problem Chapter 2.General Vortex Theory 1.Lamb Equations and Hamilton Equations 2.Reduction to the Autonomous Case 3.Invariant Volume Forms 4.Vortex Manifolds 5.Euler Equation 6.Vortices in Dissipative Systems Chapter 3.Geodesics on Lie Groups with a Left-Invariant Metric 1.Euter-Poincare Equations 2.Vortex Theory of the Top 3.Haar Measure 4.Poisson Brackets 5.Casimir Functions and Vortex Manifolds Chapter 4.Vortex Method for Integrating Hamilton Equations 1.Hamilton-Jacobi Method and the Liouville Theorem on Complete Integrability 2.Noncommutative Integration of the Hamilton Equations 3.Vortex Integration Method 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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