书籍简介:

本书将会填补国内的空白，对数学物理、微分方程等领域的科研人员有很高的参考价值。

书籍目录:

Introduction

Descartes,Leibnitz,andNewton

NewtonandBernoulli

Voltaire,Maupertuis,andClairaut

HelmholtzandThomson

AbouttheBook

Chapter1.Hydrodynamics,GeometricOptics,andClassicalMechanics

1.VortexMotionsofaContinuousMedium

2.PointVorticesonthePlane

3.SystemsofRays,LawsofReflectionandRefraction,andtheMalusTheorem

4.FermatPrinciple,CanonicalHamiltonEquations,andtheOptical-MechanicalAnalogy

5.HamiltonianFormoftheEquationsofMotion

6.ActioninthePhaseSpaceandthePoincare-CartanInvariant

7.Hamilton-JacobiMethodandHuygensPrinciple

8.HydrodynamicsofHamiltonianSystems

9.LambEquationsandtheStabilityProblem

Chapter2.GeneralVortexTheory

1.LambEquationsandHamiltonEquations

2.ReductiontotheAutonomousCase

3.InvariantVolumeForms

4.VortexManifolds

5.EulerEquation

6.VorticesinDissipativeSystems

Chapter3.GeodesicsonLieGroupswithaLeft-InvariantMetric

1.Euter-PoincareEquations

2.VortexTheoryoftheTop

3.HaarMeasure

4.PoissonBrackets

5.CasimirFunctionsandVortexManifolds

Chapter4.VortexMethodforIntegratingHamiltonEquations

1.Hamilton-JacobiMethodandtheLiouvilleTheoremonCompleteIntegrability

2.NoncommutativeIntegrationoftheHamiltonEquations

3.VortexIntegrationMethod

4.CompleteIntegrabilityoftheQuotientSystem

5.SystemswithThreeDegreesofFreedom

Supplement1:VorticityInvariantsandSecondaryHydrodynamics

Supplement2:QuantumMechanicsandHydrodynamics

Supplement3:VortexTheoryofAdiabaticEquilibriumProcesses

References

Index

内容摘要:

　　Thisbookcontainsamathematicalexpositionofanalogiesbetweenclassical(Hamiltonian)mechanics,geometricaloptics,andhydrodynamics.ThistheoryhighlightsseveralgeneralmathematicalideasthatappearedinHamiltonianmechanics,opticsandhydrodynamicsunderdifferentnames.Inaddition,someinterestingapplicationsofthegeneraltheoryofvorticesarediscussedinthebooksuchasapplicationsinnumericalmethods,stabilitytheory,andthetheoryofexactintegrationofequationsofdynamics.TheinvestigationoffamiliesoftrajectoriesofHamiltoniansystemscanbereducedtoproblemsofmultidimensionalidealfluiddynamics.Forexample,thewell-knownHamilton-Jacobimethodcorrespondstothecaseofpotentialflows.Thebookwillbeofgreatinteresttoresearchersandpostgraduatestudentsinterestedinmathematicalphysics,mechanics,andthetheoryofdifferentialequations.

书籍规格:

书籍详细信息
书名	动力系统. 5，旋涡的一般理论站内查询相似图书
丛书名	国外数学名著系列
	9787030234971 如需购买下载《动力系统. 5，旋涡的一般理论》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN
出版地	北京	出版单位	科学出版社
版次	影印本	印次	1
定价(元)	50.0	语种	英文
尺寸	24	装帧	精装
页数		印数

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书籍信息归属:

动力系统. 5，旋涡的一般理论是科学出版社于2008.出版的中图分类号为 O175 的主题关于动力系统（数学）－英文的书籍。