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OverviewHamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton.T he book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book. Full Product DetailsAuthor: Gordon E Swaters (University of Alberta, Edmonton, Canada) , Alan Jeffrey (University of Newcastle upon Tyne, UK) , Haim Brezis , Ronald G. Douglas (Texas A & M University)Publisher: Taylor & Francis Inc Imprint: Chapman & Hall/CRC Volume: 102 Dimensions: Width: 15.60cm , Height: 2.20cm , Length: 23.40cm Weight: 0.690kg ISBN: 9781584880233ISBN 10: 1584880236 Pages: 288 Publication Date: 29 September 1999 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction The Nonlinear Pendulum Model Formulation Canonical Hamiltonian Formulation Least Action Principle Symplectic Hamiltonian Formulation Mathematical Properties of the J Matrix Poisson Bracket Formulation Steady Solutions of a Canonical Hamiltonian System Linear Stability of a Steady Solution Nonlinear Stability of a Steady Solution The Two Dimensional Euler Equations Vorticity Equation Formulation Hamiltonian Structure for Partial Differential Equations Hamiltonian Structure of the Euler Equations Reduction of the Canonical Poisson Bracket Casimir Functionals and Noether's Theorem Exercises Stability of Steady Euler Flows Steady Solutions of the Vorticity Equation Linear Stability Problem Normal Mode Equations for Parallel Shear Flows Linear Stability Theorems Nonlinear Stability Theorems Andrews' Theorem Flows with Special Symmetries Exercises The Charney-Hasegawa-Mima Equation A Derivation of the CHM Equation Hamiltonian Structure Steady Solutions Stability of Steady Solutions Steadily-Travelling Solutions Exercises The KdV Equation A Derivation of the KdV Equation Hamiltonian Structure Periodic and Soliton Solutions Variational Principles Linear Stability Nonlinear Stability ExercisesReviewsa refreshingly non-technical stylethis is a well-written introduction to Hamiltonian fluid dynamics and basic stability results. --S. Reich, Edinburgh Mathematical Society, Vol. 44 Author InformationSwaters, Gordon E Tab Content 6Author Website:Countries AvailableAll regions |
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