Advanced dynamics

437 Pages·2006·1.822 MB·English

by  Donald T. Greenwood

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AdvancedDynamics
AdvancedDynamicsisabroadanddetaileddescriptionoftheanalyticaltoolsofdynamics
asusedinmechanicalandaerospaceengineering.Thestrengthsandweaknessesofvarious
approachesarediscussed,andparticularemphasisisplacedonlearningthroughproblem
solving.
The book begins with a thorough review of vectorial dynamics and goes on to cover
Lagrange’sandHamilton’sequationsaswellaslessfamiliartopicssuchasimpulseresponse,
anddifferentialformsandintegrability.Techniquesaredescribedthatprovideaconsiderable
improvementincomputationalefficiencyoverthestandardclassicalmethods,especially
whenappliedtocomplexdynamicalsystems.Thetreatmentofnumericalanalysisincludes
discussionsofnumericalstabilityandconstraintstabilization.Manyworkedexamplesand
homework problems are provided. The book is intended for use in graduate courses on
dynamics,andwillalsoappealtoresearchersinmechanicalandaerospaceengineering.
DonaldT.Greenwood receivedhisPh.D.fromtheCaliforniaInstituteofTechnology,andis
aProfessorEmeritusofaerospaceengineeringattheUniversityofMichigan,AnnArbor.
BeforejoiningthefacultyatMichiganheworkedfortheLockheedAircraftCorporation,
andhasalsoheldvisitingpositionsattheUniversityofArizona,theUniversityofCalifornia,
SanDiego,andETHZurich.Heistheauthoroftwopreviousbooksondynamics.

Advanced
Dynamics
Donald T. Greenwood
UniversityofMichigan
  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
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Published in the United States of America by Cambridge University Press, New York
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© Cambridge University Press 2003
This book 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 2003
- 
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- 
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- 
isbn-13 978-0-521-82612-9 hardback
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Contents
Preface pageix
1 Introductiontoparticledynamics
1.1 Particlemotion 1
1.2 Systemsofparticles 15
1.3 Constraintsandconfigurationspace 34
1.4 Work,energyandmomentum 40
1.5 Impulseresponse 53
1.6 Bibliography 65
1.7 Problems 65
2 Lagrange’sandHamilton’sequations
2.1 D’Alembert’sprincipleandLagrange’sequations 73
2.2 Hamilton’sequations 84
2.3 Integralsofthemotion 91
2.4 Dissipativeandgyroscopicforces 99
2.5 Configurationspaceandphasespace 110
2.6 Impulseresponse,analyticalmethods 117
2.7 Bibliography 130
2.8 Problems 130
3 Kinematicsanddynamicsofarigidbody
3.1 Kinematicalpreliminaries 140
3.2 Dyadicnotation 159
vi Contents
3.3 Basicrigidbodydynamics 162
3.4 Impulsivemotion 188
3.5 Bibliography 205
3.6 Problems 206
4 Equationsofmotion:differentialapproach
4.1 Quasi-coordinatesandquasi-velocities 217
4.2 Maggi’sequation 219
4.3 TheBoltzmann–Hamelequation 226
4.4 Thegeneraldynamicalequation 234
4.5 Afundamentalequation 246
4.6 TheGibbs–Appellequation 254
4.7 Constraintsandenergyrates 261
4.8 Summaryofdifferentialmethods 274
4.9 Bibliography 278
4.10 Problems 279
5 Equationsofmotion:integralapproach
5.1 Hamilton’sprinciple 289
5.2 Transpositionalrelations 296
5.3 TheBoltzmann–Hamelequation,transpositionalform 304
5.4 Thecentralequation 307
5.5 Suslov’sprinciple 315
5.6 Summaryofintegralmethods 322
5.7 Bibliography 323
5.8 Problems 324
6 Introductiontonumericalmethods
6.1 Interpolation 329
6.2 Numericalintegration 335
6.3 Numericalstability 349
6.4 Frequencyresponsemethods 356
6.5 Kinematicconstraints 364
6.6 Energyandmomentummethods 383
vii Contents
6.7 Bibliography 396
6.8 Problems 396
1 Appendix
A.1 Answerstoproblems 401
Index 421