动力系统X pdf epub mobi txt 电子书下载 2025

简体网页||繁体网页

☆☆☆☆☆

出版者:科学

作者:科兹洛夫

出品人:

页数:184

译者:

出版时间:2009-1

价格:50.00元

装帧:

isbn号码:9787030234971

丛书系列:国外数学名著系列（影印版）

图书标签:

mathematics
动力系统
非线性动力学
混沌理论
控制理论
数学建模
工程应用
数值分析
微分方程
复杂系统
物理学

下载链接在页面底部

facebook linkedin mastodon messenger pinterest reddit telegram twitter viber vkontakte whatsapp 复制链接

想要找书就要到小美书屋

book.quotespace.org

立刻按 ctrl+D收藏本页

你会得到大惊喜!!

具体描述

《国外数学名著系列(续1)(影印版)54:动力系统10(旋涡的一般理论》contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics.For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations.

作者简介

目录信息

IntroductionDescartes, Leibnitz, and NewtonNewton and BernoulliVoltaire, Maupertuis, and ClairautHelmholtz and ThomsonAbout the BookChapter 1. Hydrodynamics, Geometric Optics, and Classical Mechanics1. Vortex Motions of a Continuous Medium2. Point Vortices on the Plane3. Systems of Rays, Laws of Reflection and Refraction, and the Malus Theorem4. Fermat Principle, Canonical Hamilton Equations, and the Optical-Mechanical Analogy5. Hamiltonian Form of the Equations of Motion6. Action in the Phase Space and the Poincare-Cartan Invariant7. Hamilton-Jacobi Method and Huygens Principle8. Hydrodynamics of Hamiltonian Systems9. Lamb Equations and the Stability ProblemChapter 2. General Vortex Theory1. Lamb Equations and Hamilton Equations2. Reduction to the Autonomous Case3. Invariant Volume Forms4. Vortex Manifolds5. Euler Equation6. Vortices in Dissipative SystemsChapter 3. Geodesics on Lie Groups with a Left-Invariant Metric1. Euter-Poincare Equations2. Vortex Theory of the Top3. Haar Measure4. Poisson Brackets5. Casimir Functions and Vortex ManifoldsChapter 4. Vortex Method for Integrating Hamilton Equations1. Hamilton-Jacobi Method and the Liouville Theorem on Complete Integrability2. Noncommutative Integration of the Hamilton Equations3. Vortex Integration Method4. Complete Integrability of the Quotient System5. Systems with Three Degrees of FreedomSupplement 1: Vorticity Invariants and Secondary HydrodynamicsSupplement 2: Quantum Mechanics and HydrodynamicsSupplement 3: Vortex Theory of Adiabatic Equilibrium ProcessesReferencesIndex
· · · · · · (收起)