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ENGINEERING DYNAMICS
Engineering Dynamics is a new treatment of kinematics and classical and
analyticaldynamicsbasedonGinsberg’spopularAdvancedEngineeringDy-
namicsSecondEdition.Likeitspredecessor,thisbookconveysphysicaland
analytical understanding of the basic principles of dynamics, but it is more
comprehensiveandbetteraddressesreal-worldcomplexities.Everysection
hasbeenrewritten,andmanytopicshavebeenaddedorenhanced.Several
derivationsarenew,andothershavebeenreworkedtomakethemmoreac-
cessible,general,andelegant.Manynewexamplesareprovided,andthose
thatwereretainedhavebeenreworked.Theyalluseacarefulpedagogical
structure that mirrors the text presentation. Instructors will appreciate the
significantenhancementofthenumberandvarietyofhomeworkexercises.
Allofthetextillustrationshavebeenredrawntoenhancetheirclarity.
JerryGinsbergbeganhisacademiccareeratPurdueUniversityin1969,and
hewasaFulbright–HaysAdvancedResearchFellowin1975.Hemovedto
Georgia Tech in 1980, where he became the first holder of the Woodruff
Chair in Mechanical Systems in 1988. Professor Ginsberg has worked in a
broad range of areas in mechanical vibrations and acoustics, for which he
developed and applied specialized mathematical and computational solu-
tions that provide greater insight in comparison with standard numerical
techniques. Professor Ginsberg is the author of more than 150 technical
andarchivalpapersandthehighlyregardedtextbooks:AdvancedEngineer-
ing Dynamics, Mechanical and Structural Vibrations, Statics, and Dynam-
ics (the last two with Joseph Genin), as well as two chapters in Nonlinear
Acoustics. He is a Fellow of the Acoustical Society of America and of the
American Society of Mechanical Engineers, and he has served as an asso-
ciateeditoroftheJournaloftheAcousticalSocietyandoftheASMEJour-
nalofVibrationandAcoustics.HereceivedtheGeorgiaTechDistinguished
ProfessorAwardin1994,theArchieHigdonDistinguishedEducatorAward
fromASEEin1998,theTrent–CredeMedalfromASAin2005,andthePer
BruelGoldMedalfromASMEin2007.Hehasdeliveredanumberofdistin-
guishedlectures,includingthe2001ASMERayleighLectureandthe2003
SpecialLecturefortheNoiseControlandAcousticsDivisionofASME,as
wellaskeynotespeechesatseveralmeetings,includingtheSecondInterna-
tionalCongressonDynamics,Vibrations,andControlinBeijingin2006.
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CUFX195-Book CUFX195-Ginsberg 9780521883030 November13,2007 21:37
Engineering
Dynamics
JERRY GINSBERG
GeorgiaInstituteofTechnology
iii
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521883030
© Jerry Ginsberg 2008
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2008
ISBN-13 978-0-511-47872-7 eBook (EBL)
ISBN-13 978-0-521-88303-0 hardback
Cambridge University Press has no responsibility for the persistence or accuracy
of urls for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
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Contents
Preface . . . . . . . . . . . . . . page ix
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 BasicConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 VectorOperations 1
1.1.1 AlgebraandComputations 1
1.1.2 VectorCalculus—VelocityandAcceleration 9
1.2 NewtonianMechanics 13
1.2.1 Newton’sLaws 13
1.2.2 SystemsofUnits 15
1.2.3 EnergyandMomentum 17
1.3 BiographicalPerspective 21
2 ParticleKinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
2.1 PathVariables 30
2.1.1 TangentandNormalComponents 31
2.1.2 ParametricDescriptionofCurves 38
2.1.3 BinormalDirectionandTorsionofaCurve 43
2.2 RectangularCartesianCoordinates 45
2.3 CurvilinearCoordinates 50
2.3.1 CylindricalandPolarCoordinates 51
2.3.2 SphericalCoordinates 58
2.3.3 ArbitraryCurvilinearCoordinates 64
2.4 MixedKinematicalDescriptions 73
3 RelativeMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
3.1 CoordinateTransformations 91
3.1.1 RotationTransformations 92
3.1.2 RotationSequences 99
3.2 Displacement 112
3.3 TimeDerivatives 119
3.4 AngularVelocityandAcceleration 127
3.4.1 AnalyticalDescription 127
3.4.2 Procedure 128
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3.5 VelocityandAccelerationAnalysisUsingaMovingReference
Frame 134
3.6 ObservationsfromaMovingReferenceFrame 147
4 KinematicsofConstrainedRigidBodies . . . . . . . . . . . . . . . . . . . . . . 173
4.1 GeneralEquations 173
4.2 EulerianAngles 178
4.3 InterconnectionsandLinkages 183
4.4 Rolling 200
5 InertialEffectsforaRigidBody . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.1 LinearandAngularMomentum 228
5.1.1 SystemofParticles 229
5.1.2 RigidBody—BasicEquations 233
5.1.3 KineticEnergy 235
5.2 InertiaProperties 240
5.2.1 MomentsandProductsofInertia 241
5.2.2 Transformations 253
5.2.3 InertiaEllipsoid 263
5.2.4 PrincipalAxes 267
5.3 RateofChangeofAngularMomentum 275
6 Newton–EulerEquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . 296
6.1 FundamentalEquations 296
6.1.1 BasicConsiderations 296
6.1.2 ProceduralSteps 300
6.2 PlanarMotion 319
6.3 Newton–EulerEquationsforaSystem 331
6.4 MomentumandEnergyPrinciples 338
6.4.1 Impulse–MomentumPrinciples 338
6.4.2 Work–EnergyPrinciples 343
6.4.3 CollisionsofRigidBodies 359
7 IntroductiontoAnalyticalMechanics . . . . . . . . . . . . . . . . . . . . . . . 391
7.1 Background 391
7.1.1 PrincipleofVirtualWork 392
7.1.2 PrincipleofDynamicVirtualWork 394
7.2 GeneralizedCoordinatesandKinematicalConstraints 396
7.2.1 SelectionofGeneralizedCoordinates 397
7.2.2 ConstraintEquations 400
7.2.3 ConfigurationSpace 408
7.3 EvaluationofVirtualDisplacements 414
7.3.1 AnalyticalMethod 415
7.3.2 KinematicalMethod 419
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7.4 GeneralizedForces 426
7.4.1 DefinitionofGeneralizedForces 426
7.4.2 RelationBetweenConstraintForcesandConditions 431
7.4.3 ConservativeForces 444
7.5 Lagrange’sEquations 446
7.6 SolutionofEquationsforHolonomicSystems 466
8 ConstrainedGeneralizedCoordinates . . . . . . . . . . . . . . . . . . . . . . . 492
8.1 Lagrange’sEquations—ConstrainedCase 492
8.2 ComputationalMethods 508
8.2.1 Algorithms 510
8.2.2 NumericalErrorChecking 520
8.2.3 InitialConditions 521
8.2.4 AnalysisofCoulombFriction 536
9 AlternativeFormulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
9.1 Hamilton’sPrinciple 552
9.1.1 Derivation 553
9.1.2 CalculusofVariations 558
9.1.3 RitzSeriesMethod 565
9.2 GeneralizedMomentumPrinciples 571
9.2.1 Hamilton’sEquations 571
9.2.2 ConservationoftheHamiltonian 578
9.2.3 IgnorableCoordinatesandRouth’sMethod 582
9.3 FormulationswithQuasi-Coordinates 588
9.3.1 Quasi-VelocitiesandQuasi-Coordinates 589
9.3.2 Gibbs–AppellEquations 594
9.3.3 Kane’sEquations 616
9.3.4 RelationshipoftheFormulations 618
10 GyroscopicEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
10.1 FreeMotion 637
10.1.1 AxisymmetricBodies 637
10.1.2 ArbitraryBodies 643
10.1.3 Poinsot’sConstructionforArbitraryBodies 647
10.2 SpinningTop 656
10.3 GyroscopesforInertialGuidance 672
10.3.1 FreeGyroscope 672
10.3.2 Gyrocompass 677
10.3.3 Single-AxisGyroscope 685
Appendix page697
AnswerstoSelectedHomeworkProblems 703
Index 719
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