国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ]
国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ]作者:-- 开 本:16开 书号ISBN:9787030234971 定价:98.0 出版时间:2016-01-01 出版社:科学出版社 |
国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ] 本书特色
This book contains a mathematical expositioof analogies betweeclassical (Hamiltonian) mechanics,geometrical optics,and hydrodynamics. This theory highlights several general mathematical ideas that appeared iHamiltoniamechanics,optics and hydrodynamics under different names. Iaddition,some interesting applications of the general theory of vortices are discussed ithe book such as applications inumerical methods,stability theory,and the theory of exact integratioof equations of dynamics. The investigatioof families of trajectories of Hamiltoniasystems cabe reduced to problems of multidimensional ideal fluid dynamics.For example,the well-knowHamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested imathematical physics,mechanics,and the theory of differential equations.
国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ] 内容简介
POD产品说明: 1. 本产品为按需印刷(POD)图书,实行先付款,后印刷的流程。您在页面购买且完成支付后,订单转交出版社。出版社根据您的订单采用数字印刷的方式,单独为您印制该图书,属于定制产品。 2. 按需印刷的图书装帧均为平装书(含原为精装的图书)。由于印刷工艺、彩墨的批次不同,颜色会与老版本略有差异,但通常会比老版本的颜色更准确。原书内容含彩图的,统一变成黑白图,原书含光盘的,统一无法提供光盘。 3. 按需印刷的图书制作成本高于传统的单本成本,因此售价高于原书定价。 4. 按需印刷的图书,出版社生产周期一般为15个工作日(特殊情况除外)。请您耐心等待。 5. 按需印刷的图书,属于定制产品,不可取消订单,无质量问题不支持退货。
国外数学名著系列(续一)(影印版):动力系统[ 旋涡的一般理论 Ⅹ] 目录
IntroductionDescartes, Leibnitz, and Newton
Newtoand Bernoulli
Voltaire, Maupertuis, and Clairaut
Helmholtz and Thomson
About the Book
Chapter 1. Hydrodynamics, Geometric Optics, and Classical Mechanics
1. Vortex Motions of a Continuous Medium
2. Point Vortices othe Plane
3. Systems of Rays, Laws of Reflectioand Refraction, and the Malus Theorem
4. Fermat Principle, Canonical HamiltoEquations, and the Optical-Mechanical Analogy
5. HamiltoniaForm of the Equations of Motion
6. Actioithe Phase Space and the Poincare-CartaInvariant
7. Hamilton-Jacobi Method and Huygens Principle
8. Hydrodynamics of HamiltoniaSystems
9. Lamb Equations and the Stability Problem
Chapter 2. General Vortex Theory
1. Lamb Equations and HamiltoEquations
2. Reductioto the Autonomous Case
3. Invariant Volume Forms
4. Vortex Manifolds
5. Euler Equation
6. Vortices iDissipative Systems
Chapter 3. Geodesics oLie Groups with a Left-Invariant Metric
1. Euter-Poincare Equations
2. Vortex Theory of the Top
3. Haar Measure
4. PoissoBrackets
5. Casimir Functions and Vortex Manifolds
Chapter 4. Vortex Method for Integrating HamiltoEquations
1. Hamilton-Jacobi Method and the Liouville Theorem oComplete Integrability
2. Noncommutative Integratioof the HamiltoEquations
3. Vortex IntegratioMethod
4. Complete Integrability of the Quotient System
5. Systems with Three Degrees of Freedom
Supplement 1: Vorticity Invariants and Secondary Hydrodynamics
Supplement 2: Quantum Mechanics and Hydrodynamics
Supplement 3: Vortex Theory of Adiabatic Equilibrium Processes
References
Index
自然科学 数学 数学理论
在线阅读
- 最新内容
- 相关内容
- 网友推荐
- 图文推荐
[家长教育] 孩子为什么会和父母感情疏离? (2019-07-14) |
[教师分享] 给远方姐姐的一封信 (2018-11-07) |
[教师分享] 伸缩门 (2018-11-07) |
[教师分享] 回家乡 (2018-11-07) |
[教师分享] 是风味也是人间 (2018-11-07) |
[教师分享] 一句格言的启示 (2018-11-07) |
[教师分享] 无规矩不成方圆 (2018-11-07) |
[教师分享] 第十届全国教育名家论坛有感(二) (2018-11-07) |
[教师分享] 贪玩的小狗 (2018-11-07) |
[教师分享] 未命名文章 (2018-11-07) |