经典力学和天体力学中的数学论题（第2版英文版）

经典力学和天体力学中的数学论题（第2版英文版）

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作者: V 编 , I.Arnold 编 , V.V 编 , A.I.Neishtadt 编

出版社: 世界图书出版公司

出版时间: 2000-06

版次: 2

ISBN: 9787506247092

定价: 51.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 247页

正文语种: 英语

分类: 自然科学

4 张插图图片

　　Thisworkdescribesthefundamentalprinciples，problems，andmethodsofclassicalmechanicsfocussingonitsmathematicalaspects.Theauthorshavestriventogiveanexpositionstressingtheworkingapparatusofclassicalmechanics，ratherthanitsphysicalfoundationsorapplications.ThisapparatusisbasicallycontainedinChapters1，3，4and5.Chapter1isdevotedtothefundamentalmathematicalmodelswhichareusuallyemployedtodescribethemotionofrealmechanicalsystems.Specialconsiderationisgiventothestudyofmotionunderconstraints，andalsotoproblemsconcernedwiththerealizationofconstraintsindynamics.Thisworkdescribesthefundamentalprinciples，problems，andmethodsofclassicalmechanicsfocussingonitsmathematicalaspects.Theauthorshavestriventogiveanexpositionstressingtheworkingapparatusofclassicalmechanics，ratherthanitsphysicalfoundationsorapplications.ThisapparatusisbasicallycontainedinChapters1，3，4and5.Chapter1isdevotedtothefundamentalmathematicalmodelswhichareusuallyemployedtodescribethemotionofrealmechanicalsystems.Specialconsiderationisgiventothestudyofmotionunderconstraints，andalsotoproblemsconcernedwiththerealizationofconstraintsindynamics. Chapter1.BasicPrinciplesofClassicalMechanics
1.NewtonianMechanics
1.1.Space.Time.Motion
1.2.TheNewton-LaplacePrincipleofDeterminacy
1.3.ThePrincipleofRelativity
1.4.BasicDynamicalQuantities.ConservationLaws
2.LagrangianMechanics
2.1.PreliminaryRemarks
2.2.VariationsandExtremals
2.3.Lagrange'sEquations
2.4.Poincare'sEquations
2.5.ConstrainedMotion
3.HamiltonianMechanics
3.1.SymplecticStructuresandHamilton'sEquations
3.2.GeneratingFunctions
3.3.SymplecticStructureoftheCotangentBundle
3.4.TheProblemofnPointVortices
3.5.TheActionFunctionalinPhaseSpace
3.6.IntegralInvariants
3.7.ApplicationstotheDynamicsofIdealFluids
3.8.PrincipleorStationaryIsoenergeticAction
4.VakonomicMechanics
4.1.Lagrange'sProblem
4.2.VakonomicMechanics
4.3.ThePrincipleofDeterminacy
4.4.Hamilton'sEquationsinRedundantCoordinates
5.HamiltonianFormalismwithConstraints
5.1.Dirac'sProblem
5.2.Duality
6.RealizationofConstraints
6.1.VariousMethodsofRealizingConstraints
6.2.HolonomicConstraints
6.3.AnisotropicFriction
6.4.AdjoiningMasses
6.5.AdjoiningMassesandAnisotropicFriction
6.6.SmallMasses

Chapter2.Then-BodyProblem
1.TheTwo-BodyProblem
1.1.Orbits
1.2.Anomalies
1.3.CollisionsandRegularization
1.4.GeometryoftheKeplerProblem
2.CollisionsandRegularization
2.1.'NecessaryConditionsforStability
2.2.SimultaneousCollisions
2.3.BinaryCollisions
2.4.SingularitiesofSolutionsinthen-BodyProblem
3.ParticularSolutions
3.1.CentralConfigurations
3.2.HomographicSolutions
3.3.TheAmendedPotentialandRelativeEquilibria
4.FinalMotionsintheThree-BodyProblem
4.1.ClassificationofFinalMotionsAccordingtoChazy
4.2.SymmetryofPastandFuture
5.TheRestrictedThree-BodyProblem
5.1.EquationsofMotion.TheJacobiIntegral
5.2.RelativeEquilibriaandtheHillRegion
5.3.Hill'sProblem
6.ErgodicTheoremsinCelestiaIMechanics
6.1.StabilityintheSenseofPoisson
6.2.ProbabilityofCapture

Chapter3.SymmetryGroupsandReduction(LoweringtheOrder)
1.SymmetriesandLinearFirstIntegrals
1.1.E.Noether'sTheorem
1.2.SymmetriesinNonholonomicMechanics
……
Chapter4.IntegrableSystemsandIntegrationMethods
Chapter5.PerturbationTheoryforIntegrableSystems
Chapter6.NonintegrableSystems
Chapter7.TheoryofSmallOscillations
CommentsontheBibliography
RecommendedReading
Bibliography
Index
内容简介:
　　Thisworkdescribesthefundamentalprinciples，problems，andmethodsofclassicalmechanicsfocussingonitsmathematicalaspects.Theauthorshavestriventogiveanexpositionstressingtheworkingapparatusofclassicalmechanics，ratherthanitsphysicalfoundationsorapplications.ThisapparatusisbasicallycontainedinChapters1，3，4and5.Chapter1isdevotedtothefundamentalmathematicalmodelswhichareusuallyemployedtodescribethemotionofrealmechanicalsystems.Specialconsiderationisgiventothestudyofmotionunderconstraints，andalsotoproblemsconcernedwiththerealizationofconstraintsindynamics.Thisworkdescribesthefundamentalprinciples，problems，andmethodsofclassicalmechanicsfocussingonitsmathematicalaspects.Theauthorshavestriventogiveanexpositionstressingtheworkingapparatusofclassicalmechanics，ratherthanitsphysicalfoundationsorapplications.ThisapparatusisbasicallycontainedinChapters1，3，4and5.Chapter1isdevotedtothefundamentalmathematicalmodelswhichareusuallyemployedtodescribethemotionofrealmechanicalsystems.Specialconsiderationisgiventothestudyofmotionunderconstraints，andalsotoproblemsconcernedwiththerealizationofconstraintsindynamics.
目录:
Chapter1.BasicPrinciplesofClassicalMechanics
1.NewtonianMechanics
1.1.Space.Time.Motion
1.2.TheNewton-LaplacePrincipleofDeterminacy
1.3.ThePrincipleofRelativity
1.4.BasicDynamicalQuantities.ConservationLaws
2.LagrangianMechanics
2.1.PreliminaryRemarks
2.2.VariationsandExtremals
2.3.Lagrange'sEquations
2.4.Poincare'sEquations
2.5.ConstrainedMotion
3.HamiltonianMechanics
3.1.SymplecticStructuresandHamilton'sEquations
3.2.GeneratingFunctions
3.3.SymplecticStructureoftheCotangentBundle
3.4.TheProblemofnPointVortices
3.5.TheActionFunctionalinPhaseSpace
3.6.IntegralInvariants
3.7.ApplicationstotheDynamicsofIdealFluids
3.8.PrincipleorStationaryIsoenergeticAction
4.VakonomicMechanics
4.1.Lagrange'sProblem
4.2.VakonomicMechanics
4.3.ThePrincipleofDeterminacy
4.4.Hamilton'sEquationsinRedundantCoordinates
5.HamiltonianFormalismwithConstraints
5.1.Dirac'sProblem
5.2.Duality
6.RealizationofConstraints
6.1.VariousMethodsofRealizingConstraints
6.2.HolonomicConstraints
6.3.AnisotropicFriction
6.4.AdjoiningMasses
6.5.AdjoiningMassesandAnisotropicFriction
6.6.SmallMasses

Chapter2.Then-BodyProblem
1.TheTwo-BodyProblem
1.1.Orbits
1.2.Anomalies
1.3.CollisionsandRegularization
1.4.GeometryoftheKeplerProblem
2.CollisionsandRegularization
2.1.'NecessaryConditionsforStability
2.2.SimultaneousCollisions
2.3.BinaryCollisions
2.4.SingularitiesofSolutionsinthen-BodyProblem
3.ParticularSolutions
3.1.CentralConfigurations
3.2.HomographicSolutions
3.3.TheAmendedPotentialandRelativeEquilibria
4.FinalMotionsintheThree-BodyProblem
4.1.ClassificationofFinalMotionsAccordingtoChazy
4.2.SymmetryofPastandFuture
5.TheRestrictedThree-BodyProblem
5.1.EquationsofMotion.TheJacobiIntegral
5.2.RelativeEquilibriaandtheHillRegion
5.3.Hill'sProblem
6.ErgodicTheoremsinCelestiaIMechanics
6.1.StabilityintheSenseofPoisson
6.2.ProbabilityofCapture

Chapter3.SymmetryGroupsandReduction(LoweringtheOrder)
1.SymmetriesandLinearFirstIntegrals
1.1.E.Noether'sTheorem
1.2.SymmetriesinNonholonomicMechanics
……
Chapter4.IntegrableSystemsandIntegrationMethods
Chapter5.PerturbationTheoryforIntegrableSystems
Chapter6.NonintegrableSystems
Chapter7.TheoryofSmallOscillations
CommentsontheBibliography
RecommendedReading
Bibliography
Index

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