Introduction to classical mechanics, with problems and solutions

739 Pages·2008·3.47 MB·English

by  David Morin

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Introduction to Classical Mechanics
Thistextbookcoversallthestandardintroductorytopicsinclassicalmechanics,
includingNewton’slaws,oscillations,energy,momentum,angularmomentum,
planetarymotion,andspecialrelativity.Italsoexploresmoreadvancedtopics,
suchasnormalmodes,theLagrangianmethod,gyroscopicmotion,fictitious
forces,4-vectors,andgeneralrelativity.
Itcontainsmorethan250problemswithdetailedsolutionssostudentscan
easilychecktheirunderstandingofthetopic.Therearealsoover350unworked
exercises,whichareidealforhomeworkassignments.Password-protected
solutionsareavailabletoinstructorsatwww.cambridge.org/9780521876223.
Thevastnumberofproblemsalonemakesitanidealsupplementarybookfor
alllevelsofundergraduatephysicscoursesinclassicalmechanics.Thetextalso
includesmanyadditionalremarkswhichdiscussissuesthatareoftenglossed
overinothertextbooks,anditisthoroughlyillustratedwithmorethan600
figurestohelpdemonstratekeyconcepts.
DavidMorinisaLecturerinthePhysicsDepartmentatHarvardUniversity.He
receivedhisPh.D.intheoreticalparticlephysicsfromHarvardin1996.Whennot
writingphysicslimericksorthinkingofnewproblemswhoseanswersinvolvee
orthegoldenratio,hecanbefoundrunningalongtheCharlesRiverorhikingin
theWhiteMountainsofNewHampshire.

Introduction to Classical
Mechanics
With Problems and Solutions
David Morin
Harvard University
CAMBRIDGEUNIVERSITY 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/9780521876223
© D. Morin 2007
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-13 978-0-511-37723-5 eBook (EBL)
ISBN-13 978-0-521-87622-3 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.
ToAllenGerryandNeilTame,
whotookthetime
togiveagroupofkids
somereallycoolproblems
Thereoncewasaclassicaltheory,
Ofwhichquantumdiscipleswereleery.
Theysaid,“Whyspendsolong
Onatheorythat’swrong?”
Well,itworksforyoureverydayquery!
Contents
Preface pagexiii
1 Strategiesforsolvingproblems 1
1.1 Generalstrategies 1
1.2 Units,dimensionalanalysis 4
1.3 Approximations,limitingcases 7
1.4 Solvingdifferentialequationsnumerically 11
1.5 Problems 14
1.6 Exercises 15
1.7 Solutions 18
2 Statics 22
2.1 Balancingforces 22
2.2 Balancingtorques 27
2.3 Problems 30
2.4 Exercises 35
2.5 Solutions 39
3 UsingF=ma 51
3.1 Newton’slaws 51
3.2 Free-bodydiagrams 55
3.3 Solvingdifferentialequations 60
3.4 Projectilemotion 65
3.5 Motioninaplane,polarcoordinates 68
3.6 Problems 70
3.7 Exercises 75
3.8 Solutions 84
4 Oscillations 101
4.1 Lineardifferentialequations 101
4.2 Simpleharmonicmotion 105
vii
viii Contents
4.3 Dampedharmonicmotion 107
4.4 Driven(anddamped)harmonicmotion 109
4.5 Coupledoscillators 115
4.6 Problems 120
4.7 Exercises 122
4.8 Solutions 127
5 Conservationofenergyandmomentum 138
5.1 Conservationofenergyinonedimension 138
5.2 Smalloscillations 147
5.3 Conservationofenergyinthreedimensions 148
5.4 Gravity 152
5.5 Momentum 156
5.6 Thecenterofmassframe 161
5.7 Collisions 164
5.8 Inherentlyinelasticprocesses 167
5.9 Problems 173
5.10 Exercises 180
5.11 Solutions 194
6 TheLagrangianmethod 218
6.1 TheEuler–Lagrangeequations 218
6.2 Theprincipleofstationaryaction 221
6.3 Forcesofconstraint 227
6.4 Changeofcoordinates 229
6.5 Conservationlaws 232
6.6 Noether’stheorem 236
6.7 Smalloscillations 239
6.8 Otherapplications 242
6.9 Problems 246
6.10 Exercises 251
6.11 Solutions 255
7 Centralforces 281
7.1 Conservationofangularmomentum 281
7.2 Theeffectivepotential 283
7.3 Solvingtheequationsofmotion 285
7.4 Gravity,Kepler’slaws 287
7.5 Problems 296
7.6 Exercises 298
7.7 Solutions 300