约束力学系统动力学（英文版）

图书标准信息

• 作者 梅凤翔、吴惠彬 著
• 出版社 北京理工大学出版社
• 出版时间 2009-04
• 版次 1
• ISBN 9787564021689
• 定价 90.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 604页
• 字数 1191千字
• 正文语种 英语

【内容简介】

约束力学系统的变分原理、运动方程、相关专门问题的理论与应用、积分方法、对称性与守恒量等内容，具有很高的学术价值，为方便国际学术交流，译成英文出版。全书共分为六个部分：第一部分：约束力学系统的基本概念。本部分包含6章，介绍分析力学的主要基本概念；第二部分：约束力学系统的变分原理。本部分有5章，阐述微分变分原理、积分变分原理以及Pfaff-Birkhoff原理；第三部分：约束力学系统的运动微分方程。本部分共11章，系统介绍完整系统、非完整系统的各类运动方程；第四部分：约束力学系统的专门问题。本部分有8章，讨论运动稳定性和微扰理论、刚体定点转动、相对运动动力学、可控力学系统动力学、打击运动动力学、变质量系统动力学、机电系统动力学、事件空间动力学等内容；第五部分：约束力学系统的积分方法。本部分有6章，介绍降阶方法、动力学代数与Poisson方法、正则变换、Hamilton-Jacobi方法、场方法、积分不变量；第六部分：约束力学系统的对称性与守恒量。本部分共10章，讨论Noether对称性、Lie对称性、形式不变性，以及由它们导致的各种守恒量。《约束力学系统动力学（英文版）》的出版必将引起国内外同行的关注，对该领域的发展将起到重要的推动作用。

【作者简介】

MeiFengxiang（1938-）,anativeofShenyang,China,andagraduateoftheDepartmentofMathematicsandMechanicsofPekingUniversity（in1963）andEcoleNationalleSuperieredeM6canique（DocteurdEtat,1982）,hasbeenteachingtheoreticalmechanics,analyticalmechanics,dynamicsofnonholonomicsystems,stabilityofmotion,andapplicationsofLiegroupsandLiealgebrastoconstrainedmechanicalsystemsatBeijingInstituteofTechnology.Hisresearchinterestsareintheareasofdynamicsofconstrainedsystemsandmathematicalmethodsinmechanics.Hecurrentlydirects12doctoralcandidates.HewasavisitingprofessoratENSM（1981-1982）andUniversitLAVAL（1994）.Meihasauthoredover300researchpapersandistheauthorofthefollowing10books（inChinese）：FoundationsofMechanicsofNonholonomicSystems（1985）;ResearchesonNonholonomicDynamics（1987）;FoundationsofAnalyticalMechanics（1987）;SpecialProblemsinAnalyticalMechanics（1988）;MechanicsofVariableMassSystems（1989）;AdvancedAnalyticalMechanics（1991）;DynamicsofBirkhoffianSystem（1996）;StabilityofMotionofConstrainedMechanicalSystems（1997）;SymmetriesandInvariantsofMechanicalSystems（1999）;andApplicationsofLieGroupsandLieAlgebrastoConstrainedMechanicalSystems（1999）.

【目录】

ⅠFundamentalConceptsinConstrainedMechanicalSystems
1ConstraintsandTheirClassification
1.1Constraints
1.2EquationsofConstraint
1.3ClassificationofConstraints
1.3.1HolonomicConstraintsandNonholonomicConstraints
1.3.2StationaryConstraintsandNon-stationaryConstraints
1.3.3UnilateralConstraintsandBilateralConstraints
1.3.4PassiveConstraintsandActiveConstraints
1.4IntegrabilityTheoremofDifferentialConstraints
1.5GeneralizationoftheConceptofConstraints
1.5.1FirstIntegralasNonholonomicConstraints
1.5.2ControllableSystemasHolonomicorNonholonomicSystem
1.5.3NonholonomicConstraintsofHigherOrder
1.5.4RestrictiononChangeofDynamicalPropertiesasConstraint
1.6Remarks
2GeneralizedCoordinates
2.1GeneralizedCoordinates
2.2GeneralizedVelocities
2.3GeneralizedAccelerations
2.4ExpressionofEquationsofNonholonomicConstraintsinTermsofGeneralizedCoordinatesandGeneralizedVelocities
2.5Remarks
3Quasi-VelocitiesandQuasi-Coordinates
3.1Quasi-Velocities
3.2Quasi-Coordinates
3.3Quasi-Accelerations
3.4Remarks
4VirtualDisplacements
4.1VirtualDisplacements
4.1.1ConceptofVirtualDisplacements
4.1.2ConditionofConstraintsExertedonVirtualDisplacements
4.1.3DegreeofFreedom
4.2NecessaryandSufficientConditionUnderWhichActualDisplacementIsOneofVirtualDisplacements
4.3GeneralizationoftheConceptofVirtualDisplacement
4.4Remarks
5IdealConstraints
5.1ConstraintReactions
5.2ExamplesofIdealConstraints
5.3ImportanceandPossibilityofHypothesisofIdealConstraints
5.4Remarks
6TranspositionalRelationsofDifferentialandVariationalOperations
6.1TranspositionalRelationsforFirstOrderNonholonomicSystems
6.1.1TranspositionalRelationsinTermsofGeneralizedCoordinates
6.1.2TranspositionalRelationsinTermsofQuasi-Coordinates
6.2TranspositionalRelationsofHigherOrderNonholonomicSystems
6.2.1TranspositionalRelationsinTermsofGeneralizedCoordinates
6.2.2TranspositionalRelationsinTermsofQuasi-Coordinates
6.3VujanovicTranspositionalRelations
6.3.1TranspositionalRelationsforHolonomicNonconservativeSystems
6.3.2TranspositionalRelationsforNonholonomicSystems
6.4Remarks

ⅡVariationalPrinciplesinConstrainedMechanicalSystems
7DifferentialVariationalPrinciples
7.1DAlembert-LagrangePrinciple
7.1.1DAlembertPrinciple
7.1.2PrincipleofVirtualDisplacements
7.1.3DAlembert-LagrangePrinciple
7.1.4DAlembert-LagrangePrinciplein
TermsofGeneralizedCoordinates
7.2JourdainPrinciple
7.2.1JourdainPrinciple
7.2.2JourdainPrincipleinTermsofGeneralizedCoordinates
7.3GaussPrinciple
7.3.1GaussPrinciple
7.3.2GaussPrincipleinTermsofGeneralizedCoordinates
7.4UniversalDAlerabertPrinciple
7.4.1UniversalDAlembertPrinciple
7.4.2UniversalDAlembertPrinciplein
TermsofGeneralizedCoordinates
7.5ApplicationsofGaussPrinciple
7.5.1SimpleApplications
7.5.2ApplicationofGaussPrincipleinRobotDynamics
7.5.3ApplicationofGaussPrincipleinStudyApproximateSolutionofEquationsofNonlinearVibration
7.6Remarks

8IntegralVariationalPrinciplesinTermsofGeneralizedCoordinatesforHolonomicSystems
8.1HamiltonsPrinciple
8.1.1HamiltonsPrinciple
8.1.2DeductionofLagrangeEquations
byMeansofHamiltonsPrinciple
8.1.3CharacterofExtremeofHamiltonsPrinciple
8.1.4ApplicationsinFindingApproximateSolution
8.1.5HamiltonsPrincipleforGeneralHolonomicSystems
8.2LagrangesPrinciple
8.2.1Non-contemporaneousVariation
8.2.2LagrangesPrinciple
8.2.3OtherFormsofLagrangesPrinciple
8.2.4DeductionofLagrangcsEquationsbyMeansofLagrangesPrinciple
8.2.5GeneralizationofLagrangesPrincipletoNon-conservativeSystemsandItsApplication
8.3Remarks

9IntegralVariationalPrinciplesinTermsofQuasi-CoordinatesforHolonomicSystems
9.1HamiltonsPrincipleinTermsofQuasi-Coordinates
9.1.1HamiltonsPrinciple
9.1.2TranspositionalRelations
9.1.3DeductionofEquationsofMotioninTermsofQuasi-CoordinatesbyMeansofHamiltonsPrinciple
9.1.4HamiltonsPrincipleforGeneralHolonomicSystems
9.2LagrangesPrincipleinTermsofQuasi-Coordinates
9.2.1LagrangesPrinciple
9.2.2DeductionofEquationsofMotioninTermsofQuasi-CoordinatesbyMeansofLagrangesPrinciple
9.3Remarks

l0IntegralVariationalPrinciplesforNonholonomicSystems
10.1DefinitionsofVariation
10.1.1NecessityofDefinitionofVariationofGeneralizedVelocitiesforNonholonomicSystems
10.1.2SuslovsDefinition
10.1.3HSldersDefinition
10.2IntegralVariationalPrinciplesinTermsofGeneralizedCoordinatesforNonholonomicSystems
10.2.1HamiltonsPrincipleforNonholonomicSystems
10.2.2NecessaryandSufficientConditionUnderWhichHamiltonsPrincipleforNonholonomicSystemsIsPrincipleofStationaryAction
10.2.3DeductionofEquationsofMotionforNonholonomieSystemsbyMeansofHamiltonsPrinciple
10.2.4GeneralFormofHamiltonsPrincipleforNonhononomicSystems
10.2.5LagrangesPrincipleinTermsofGeneralizedCoordinatesforNonholonomicSystems
10.3IntegralVariationalPrincipleinTermsofQuasiCoordinatesforNonholonomicSystems
10.3.1HamiltonsPrincipleinTermsofQuasi-Coordinates
10.3.2LagrangesPrincipleinTermsofQuasi-Coordinates
10.4Remarks

11Pfaff-BirkhoffPrinciple
11.1StatementofPfaff-BirkhoffPrinciple
11.2HamiltonsPrincipleasaParticularCaseofPfaff-BirkhoffPrinciple
11.3BirkhoffsEquations
11.4Pfaff-Birkhoff-dAlembertPrinciple
11.5Remarks

IIIDifferentialEquationsofMotionofConstrainedMechanical
Systems

12LagrangeEquationsofHolonomicSystems
12.1LagrangeEquationsofSecondKind
12.2LagrangeEquationsofSystemswithRedundantCoordinates
12.3LagrangeEquationsinTermsofQuasi-Coordinates
12.4LagrangeEquationswithDissipativeFunction
12.5Remarks

13LagrangeEquationswithMultiplierforNonholonomicSystems
13.1DeductionofLagrangeEquationswithMultiplier
13.2DeterminationofNonholonomicConstraintForces
13.3Remarks

14MacMillanEquationsforNonholonomieSystems
14.1DeductionofMacMillanEquations
14.2ApplicationofMacMiUanEquations
14.3Remarks

15VolterraEquationsforNonholonomicSystems
15.1DeductionofGeneralizedVolterraEquations
15.2VolterraEquationsandTheirEquivalentForms
15.2.1VolterraEquationsofFirstForm
15.2.2VolterraEquationsofSecondForm
15.2.3VolterraEquationsofThirdForm
15.2.4VolterraEquationsofFourthForm
15.3ApplicationofVolterraEquations
15.4Remarks

16ChaplyginEquationsforNonholonomicSystems
16.1GeneralizedChaplyginEquations
16.2VoronetzEquations
16.3ChaplyginEquations
16.4ChaplyginEquationsinTermsofQuasi-Coordinates
16.5ApplicationofChaplyginEquations
16.6Remarks
……

ⅣSpecialProblemsinConstrainedMechanicalSystems
ⅤIntegrationMethodsinConstrainedMechanicalSystems
ⅥSymmetriesandConservedQuantitiesinConstrainedMechanicalSystems