Gordon E Swaters

Introduction to Hamiltonian Fluid Dynamics and Stability Theory

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: CRC Press
• Seitenzahl: 288
• Erscheinungstermin: 29. September 1999
• Englisch
• Abmessung: 242mm x 164mm x 22mm
• Gewicht: 572g
• ISBN-13: 9781584880233
• ISBN-10: 1584880236
• Artikelnr.: 21948606

Autorenporträt

Swaters, Gordon E

Inhaltsangabe

Introduction
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
Exercises