Complete Solution Manual for Classical Dynamics of Particles and Systems (5th Edition) by Thornton & Marion | All 14 Chapters Covered

All 14 Chapters Covered
k k k




SOLUTION MANUAL
k

, Contents




Preface v
ProblemskSolvedkinkStudentkSolutionskManual vii

1 Matrices,kVectors,kandkVectorkCalculus 1

2 NewtoniankMechanics—SinglekParticle 29

3 Oscillations 79

4 NonlinearkOscillationskandkChaos 127

5 Gravitation 149

6 SomekMethodskinkThekCalculuskofkVariations 165

7 Hamilton’skPrinciple—LagrangiankandkHamiltoniankDynamics 181

8 Central-ForcekMotion 233

9 DynamicskofkakSystemkofkParticles 277

10 MotionkinkakNoninertialkReferencekFrame 333

11 DynamicskofkRigidkBodies 353

12 CoupledkOscillations 397

13 ContinuouskSystems;kWaves 435

14 SpecialkTheorykofkRelativity 461



iii

,iv CONTENTS




Preface




ThiskInstructor’skManualkcontainsktheksolutionsktokallkthekend-of-
chapterkproblemsk(butknotkthekappendices)kfromkClassicalkDynamicskofkParticleskandkSystems,kFifthk
Edition,kbykStephenkT.kThorntonkandkJerrykB.kMarion.kItkiskintendedkforkusekonlykbykinstructorsku
singkClassicalkDynamicskaskaktextbook,kandkitkisknotkavailablektokstudentskinkanykform.kAkStudentkS
olutionskManualkcontainingksolutionsktokaboutk25%kofkthekend-of-
chapterkproblemskiskavailablekforksalektokstudents.kThekproblemknumberskofkthoseksolutionskinkth
ekStudentkSolutionskManualkareklistedkonktheknextkpage.
Askakresultkofksurveyskreceivedkfromkusers,kIkcontinuektokaddkmorekworkedkoutkexampleskink
thektextkandkaddkadditionalkproblems.kTherekareknowk509kproblems,kaksignificantknumberkoverkth
ek4thkedition.
Thekinstructorkwillkfindkaklargekarraykofkproblemskrangingkinkdifficultykfromktheksimplek“plu
gkandkchug”ktokthektypekworthykofkthekPh.D.kqualifyingkexaminationskinkclassicalkmechanics.kAkfe
wkofkthekproblemskarekquitekchallenging.kManykofkthemkrequireknumericalkmethods.kHavingkthisk
solutionskmanualkshouldkprovidekakgreaterkappreciationkofkwhatkthekauthorskintendedktokaccomp
lishkbykthekstatementkofkthekproblemkinkthosekcaseskwherekthekproblemkstatementkisknotkcomplete
lykclear.kPleasekinformkmekwhenkeitherkthekproblemkstatementkorksolutionskcankbekimproved.kSpe
cifickhelpkiskencouraged.kThekinstructorkwillkalsokbekablektokpickkandkchoosekdifferentklevelskofkdif
ficultykwhenkassigningkhomeworkkproblems.kAndksincekstudentskmaykoccasionallykneedkhintskto
kworkksomekproblems,kthiskmanualkwillkallowkthekinstructorktoktakekakquickkpeekktokseekhowkthek

studentskcankbekhelped.
Itkiskabsolutelykforbiddenkforkthekstudentsktokhavekaccessktokthiskmanual.kPleasekdoknotkgi
vekstudentsksolutionskfromkthiskmanual.kPostingktheseksolutionskonkthekInternetkwillkresultkinkwid
espreadkdistributionkofktheksolutionskandkwillkultimatelykresultkinkthekdecreasekofkthekusefulnessk
ofkthektext.
ThekauthorkwouldklikektokacknowledgekthekassistancekofkTrankngockKhanhk(5thkedition),kWa
rrenkGriffithk(4thkedition),kandkBriankGiambattistak(3rdkedition),kwhokcheckedktheksolutionskofkpr
eviouskversions,kwentkoverkuserkcomments,kandkworkedkoutksolutionskforknewkproblems.
Withoutktheirkhelp,kthiskmanualkwouldknotkbekpossible.kThekauthorkwouldkappreciatekreceivingkr
eportskofksuggestedkimprovementskandksuspectedkerrors.kCommentskcankbeksentkbykemailktokstt@
virginia.edu,kthekmorekdetailedkthekbetter.
StephenkT.kThornton
Charlottesville,kVirginia


v

, CHAPTER k 1
Matrices, Vectors,
k k




and Vector Calculus
k k




1-1.

x1

45˚
x1

45˚
x3
x3k

Axesk x1k andk x3k liekinkthek x1x3k plane.kTh
ektransformationkequationskare:
x1kkx1kcosk45kkx3kcosk45
x2kkx2
x3kkx3kcosk45kkx1kcosk45
1k 1k
xk k xk k x
1 1 3
2 2
x2kkx2
1k 1k
xk k xk k x
3 1 3
2 2
Sokthektransformationkmatrixkis:

k 1 1k 
 0 
2 2k

k 0 1 0k k 
k 1 1 
 0 
 2 2k 


1