Introduction to Hamiltonian Fluid Dynamics and Stability Theory
Introduction to Hamiltonian Fluid Dynamics and Stability Theory
复制标题
哈密顿流体动力学和稳定性理论简介
DOI：
10.1201/9780203750087
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发表时间：
1999
影响因子：
3.7
通讯作者：
G. Swaters
中科院分区：
文献类型：
--
作者：
G. Swaters
非线性钟摆模型公式正则哈密顿公式最小作用原理辛哈密顿公式J矩阵的数学性质泊松支架公式正则哈密顿系统的稳定解线性稳定解非线性稳定解二维欧拉方程涡量方程哈密顿结构为偏微分方程哈密顿结构欧拉方程正则泊松托架卡西米尔泛函的化简和诺特定理的定常欧拉流的稳定性练习涡度方程的定常解线性稳定性问题平行剪切流的正模方程线性稳定性定理非线性稳定性定理安德鲁斯定理特殊对称性流动练习Charney-Hasegawa-Mima方程CHM方程的推导哈密顿结构的定常解解-稳定运动解练习KdV方程KdV方程的推导哈密顿结构周期解和孤子解变分原理线性稳定性非线性稳定性练习
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