All 14 Chapters Covered
m m m
SOLUTION MANUAL
m
, Contents
Preface v
ProblemsmSolvedminmStudentmSolutionsmManual vii
1 Matrices,mVectors,mandmVectormCalculus 1
2 NewtonianmMechanics—SinglemParticle 29
3 Oscillations 79
4 NonlinearmOscillationsmandmChaos 127
5 Gravitation 149
6 SomemMethodsminmThemCalculusmofmVariations 165
7 Hamilton’smPrinciple—LagrangianmandmHamiltonianmDynamics 181
8 Central-ForcemMotion 233
9 DynamicsmofmamSystemmofmParticles 277
10 MotionminmamNoninertialmReferencemFrame 333
11 DynamicsmofmRigidmBodies 353
12 CoupledmOscillations 397
13 ContinuousmSystems;mWaves 435
14 SpecialmTheorymofmRelativity 461
iii
,iv CONTENTS
Preface
ThismInstructor’smManualmcontainsmthemsolutionsmtomallmthemend-of-
chaptermproblemsm(butmnotmthemappendices)mfrommClassicalmDynamicsmofmParticlesmandmSystem
s,mFifthmEdition,mbymStephenmT.mThorntonmandmJerrymB.mMarion.mItmismintendedmformusemon
lymbyminstructorsmusingmClassicalmDynamicsmasmamtextbook,mandmitmismnotmavailablemtomstude
ntsminmanymform.mAmStudentmSolutionsmManualmcontainingmsolutionsmtomaboutm25%mofmthe
mend-of-
chaptermproblemsmismavailablemformsalemtomstudents.mThemproblemmnumbersmofmthosemsoluti
onsminmthemStudentmSolutionsmManualmaremlistedmonmthemnextmpage.
Asmamresultmofmsurveysmreceivedmfrommusers,mImcontinuemtomaddmmoremworkedmoutmex
amplesminmthemtextmandmaddmadditionalmproblems.mTheremaremnowm509mproblems,mamsignifi
cantmnumbermovermthem4thmedition.
Theminstructormwillmfindmamlargemarraymofmproblemsmrangingminmdifficultymfrommthemsi
mplem“plugmandmchug”mtomthemtypemworthymofmthemPh.D.mqualifyingmexaminationsminmclass
icalmmechanics.mAmfewmofmthemproblemsmaremquitemchallenging.mManymofmthemmrequiremnu
mericalmmethods.mHavingmthismsolutionsmmanualmshouldmprovidemamgreatermappreciationmof
mwhatmthemauthorsmintendedmtomaccomplishmbymthemstatementmofmthemproblemminmthosemca
sesmwheremthemproblemmstatementmismnotmcompletelymclear.mPleaseminformmmemwhenmeither
mthemproblemmstatementmormsolutionsmcanmbemimproved.mSpecificmhelpmismencouraged.mThe
minstructormwillmalsombemablemtompickmandmchoosemdifferentmlevelsmofmdifficultymwhenmassig
ningmhomeworkmproblems.mAndmsincemstudentsmmaymoccasionallymneedmhintsmtomworkmso
memproblems,mthismmanualmwillmallowmtheminstructormtomtakemamquickmpeekmtomseemhowmt
hemstudentsmcanmbemhelped.
Itmismabsolutelymforbiddenmformthemstudentsmtomhavemaccessmtomthismmanual.mPleasem
domnotmgivemstudentsmsolutionsmfrommthismmanual.mPostingmthesemsolutionsmonmthemInternet
mwillmresultminmwidespreadmdistributionmofmthemsolutionsmandmwillmultimatelymresultminmthe
mdecreasemofmthemusefulnessmofmthemtext.
ThemauthormwouldmlikemtomacknowledgemthemassistancemofmTranmngocmKhanhm(5thmedi
tion),mWarrenmGriffithm(4thmedition),mandmBrianmGiambattistam(3rdmedition),mwhomcheckedmt
hemsolutionsmofmpreviousmversions,mwentmovermusermcomments,mandmworkedmoutmsolutions
mformnewmproblems.
Withoutmtheirmhelp,mthismmanualmwouldmnotmbempossible.mThemauthormwouldmappreciatemre
ceivingmreportsmofmsuggestedmimprovementsmandmsuspectedmerrors.mCommentsmcanmbemsent
,mthemmoremdetailedmthembetter.
StephenmT.mThornton
Charlottesville,mVirginia
, v
m m m
SOLUTION MANUAL
m
, Contents
Preface v
ProblemsmSolvedminmStudentmSolutionsmManual vii
1 Matrices,mVectors,mandmVectormCalculus 1
2 NewtonianmMechanics—SinglemParticle 29
3 Oscillations 79
4 NonlinearmOscillationsmandmChaos 127
5 Gravitation 149
6 SomemMethodsminmThemCalculusmofmVariations 165
7 Hamilton’smPrinciple—LagrangianmandmHamiltonianmDynamics 181
8 Central-ForcemMotion 233
9 DynamicsmofmamSystemmofmParticles 277
10 MotionminmamNoninertialmReferencemFrame 333
11 DynamicsmofmRigidmBodies 353
12 CoupledmOscillations 397
13 ContinuousmSystems;mWaves 435
14 SpecialmTheorymofmRelativity 461
iii
,iv CONTENTS
Preface
ThismInstructor’smManualmcontainsmthemsolutionsmtomallmthemend-of-
chaptermproblemsm(butmnotmthemappendices)mfrommClassicalmDynamicsmofmParticlesmandmSystem
s,mFifthmEdition,mbymStephenmT.mThorntonmandmJerrymB.mMarion.mItmismintendedmformusemon
lymbyminstructorsmusingmClassicalmDynamicsmasmamtextbook,mandmitmismnotmavailablemtomstude
ntsminmanymform.mAmStudentmSolutionsmManualmcontainingmsolutionsmtomaboutm25%mofmthe
mend-of-
chaptermproblemsmismavailablemformsalemtomstudents.mThemproblemmnumbersmofmthosemsoluti
onsminmthemStudentmSolutionsmManualmaremlistedmonmthemnextmpage.
Asmamresultmofmsurveysmreceivedmfrommusers,mImcontinuemtomaddmmoremworkedmoutmex
amplesminmthemtextmandmaddmadditionalmproblems.mTheremaremnowm509mproblems,mamsignifi
cantmnumbermovermthem4thmedition.
Theminstructormwillmfindmamlargemarraymofmproblemsmrangingminmdifficultymfrommthemsi
mplem“plugmandmchug”mtomthemtypemworthymofmthemPh.D.mqualifyingmexaminationsminmclass
icalmmechanics.mAmfewmofmthemproblemsmaremquitemchallenging.mManymofmthemmrequiremnu
mericalmmethods.mHavingmthismsolutionsmmanualmshouldmprovidemamgreatermappreciationmof
mwhatmthemauthorsmintendedmtomaccomplishmbymthemstatementmofmthemproblemminmthosemca
sesmwheremthemproblemmstatementmismnotmcompletelymclear.mPleaseminformmmemwhenmeither
mthemproblemmstatementmormsolutionsmcanmbemimproved.mSpecificmhelpmismencouraged.mThe
minstructormwillmalsombemablemtompickmandmchoosemdifferentmlevelsmofmdifficultymwhenmassig
ningmhomeworkmproblems.mAndmsincemstudentsmmaymoccasionallymneedmhintsmtomworkmso
memproblems,mthismmanualmwillmallowmtheminstructormtomtakemamquickmpeekmtomseemhowmt
hemstudentsmcanmbemhelped.
Itmismabsolutelymforbiddenmformthemstudentsmtomhavemaccessmtomthismmanual.mPleasem
domnotmgivemstudentsmsolutionsmfrommthismmanual.mPostingmthesemsolutionsmonmthemInternet
mwillmresultminmwidespreadmdistributionmofmthemsolutionsmandmwillmultimatelymresultminmthe
mdecreasemofmthemusefulnessmofmthemtext.
ThemauthormwouldmlikemtomacknowledgemthemassistancemofmTranmngocmKhanhm(5thmedi
tion),mWarrenmGriffithm(4thmedition),mandmBrianmGiambattistam(3rdmedition),mwhomcheckedmt
hemsolutionsmofmpreviousmversions,mwentmovermusermcomments,mandmworkedmoutmsolutions
mformnewmproblems.
Withoutmtheirmhelp,mthismmanualmwouldmnotmbempossible.mThemauthormwouldmappreciatemre
ceivingmreportsmofmsuggestedmimprovementsmandmsuspectedmerrors.mCommentsmcanmbemsent
,mthemmoremdetailedmthembetter.
StephenmT.mThornton
Charlottesville,mVirginia
, v
