| Introduction to Hamiltonian Fluid Dynamics and Stability Theory Contributor(s): Swaters, Gordon E. (Author) |
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ISBN: 1584880236 ISBN-13: 9781584880233 Publisher: CRC Press OUR PRICE: $209.00 Product Type: Hardcover - Other Formats Published: September 1999 Annotation: This monograph in applied mathematics provides an introduction to Hamiltonian fluid dynamics and stability theory -- the first book to combine the two topics. It takes a tutorial approach and introduces many of the ideas with a simple physical example -- the nonlinear pendulum. It examines Andrew's Theorem, derives and develops the CHM equation, presents an account of the Hamiltonian structure of the KdV equations, and discusses the stability theories for the KdV solution. |
| Additional Information |
| BISAC Categories: - Science | Mechanics - Dynamics - Science | Physics - Mathematical & Computational - Mathematics | Applied |
| Dewey: 532 |
| LCCN: 00501323 |
| Series: Monographs and Surveys in Pure and Applied Mathematics |
| Physical Information: 0.88" H x 6.47" W x 9.54" (1.26 lbs) 288 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Hamiltonian 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. The 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. |