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.MItMisMintendedMforMuseMonly
MbyMinstructorsMusingMClassicalMDynamicsMasMaMtextbook,MandMitMisMnotMavailableMtoMstudents
MinManyMform.MAMStudentMSolutionsMManualMcontainingMsolutionsMtoMaboutM25%MofMtheMend
-of-
chapterMproblemsMisMavailableMforMsaleMtoMstudents.MTheMproblemMnumbersMofMthoseMsolutio
nsMinMtheMStudentMSolutionsMManualMareMlistedMonMtheMnextMpage.
AsMaMresultMofMsurveysMreceivedMfromMusers,MIMcontinueMtoMaddMmoreMworkedMoutMexa
mplesMinMtheMtextMandMaddMadditionalMproblems.MThereMareMnowM509Mproblems,MaMsignifica
ntMnumberMoverMtheM4thMedition.
TheMinstructorMwillMfindMaMlargeMarrayMofMproblemsMrangingMinMdifficultyMfromMtheMsi
mpleM“plugMandMchug”MtoMtheMtypeMworthyMofMtheMPh.D.MqualifyingMexaminationsMinMclassi
calMmechanics.MAMfewMofMtheMproblemsMareMquiteMchallenging.MManyMofMthemMrequireMnum
ericalMmethods.MHavingMthisMsolutionsMmanualMshouldMprovideMaMgreaterMappreciationMofMw
hatMtheMauthorsMintendedMtoMaccomplishMbyMtheMstatementMofMtheMproblemMinMthoseMcasesM
whereMtheMproblemMstatementMisMnotMcompletelyMclear.MPleaseMinformMmeMwhenMeitherMtheM
problemMstatementMorMsolutionsMcanMbeMimproved.MSpecificMhelpMisMencouraged.MTheMinstru
ctorMwillMalsoMbeMableMtoMpickMandMchooseMdifferentMlevelsMofMdifficultyMwhenMassigningMho
meworkMproblems.MAndMsinceMstudentsMmayMoccasionallyMneedMhintsMtoMworkMsomeMproble
ms,MthisMmanualMwillMallowMtheMinstructorMtoMtakeMaMquickMpeekMtoMseeMhowMtheMstudentsM
canMbeMhelped.
ItMisMabsolutelyMforbiddenMforMtheMstudentsMtoMhaveMaccessMtoMthisMmanual.MPleaseM
doMnotMgiveMstudentsMsolutionsMfromMthisMmanual.MPostingMtheseMsolutionsMonMtheMInternetM
willMresultMinMwidespreadMdistributionMofMtheMsolutionsMandMwillMultimatelyMresultMinMtheMd
ecreaseMofMtheMusefulnessMofMtheMtext.
TheMauthorMwouldMlikeMtoMacknowledgeMtheMassistanceMofMTranMngocMKhanhM(5thMediti
on),MWarrenMGriffithM(4thMedition),MandMBrianMGiambattistaM(3rdMedition),MwhoMcheckedMthe
MsolutionsMofMpreviousMversions,MwentMoverMuserMcomments,MandMworkedMoutMsolutionsMfor
MnewMproblems.
WithoutMtheirMhelp,MthisMmanualMwouldMnotMbeMpossible.MTheMauthorMwouldMappreciateMrec
eivingMreportsMofMsuggestedMimprovementsMandMsuspectedMerrors.MCommentsMcanMbeMsentM
,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.MItMisMintendedMforMuseMonly
MbyMinstructorsMusingMClassicalMDynamicsMasMaMtextbook,MandMitMisMnotMavailableMtoMstudents
MinManyMform.MAMStudentMSolutionsMManualMcontainingMsolutionsMtoMaboutM25%MofMtheMend
-of-
chapterMproblemsMisMavailableMforMsaleMtoMstudents.MTheMproblemMnumbersMofMthoseMsolutio
nsMinMtheMStudentMSolutionsMManualMareMlistedMonMtheMnextMpage.
AsMaMresultMofMsurveysMreceivedMfromMusers,MIMcontinueMtoMaddMmoreMworkedMoutMexa
mplesMinMtheMtextMandMaddMadditionalMproblems.MThereMareMnowM509Mproblems,MaMsignifica
ntMnumberMoverMtheM4thMedition.
TheMinstructorMwillMfindMaMlargeMarrayMofMproblemsMrangingMinMdifficultyMfromMtheMsi
mpleM“plugMandMchug”MtoMtheMtypeMworthyMofMtheMPh.D.MqualifyingMexaminationsMinMclassi
calMmechanics.MAMfewMofMtheMproblemsMareMquiteMchallenging.MManyMofMthemMrequireMnum
ericalMmethods.MHavingMthisMsolutionsMmanualMshouldMprovideMaMgreaterMappreciationMofMw
hatMtheMauthorsMintendedMtoMaccomplishMbyMtheMstatementMofMtheMproblemMinMthoseMcasesM
whereMtheMproblemMstatementMisMnotMcompletelyMclear.MPleaseMinformMmeMwhenMeitherMtheM
problemMstatementMorMsolutionsMcanMbeMimproved.MSpecificMhelpMisMencouraged.MTheMinstru
ctorMwillMalsoMbeMableMtoMpickMandMchooseMdifferentMlevelsMofMdifficultyMwhenMassigningMho
meworkMproblems.MAndMsinceMstudentsMmayMoccasionallyMneedMhintsMtoMworkMsomeMproble
ms,MthisMmanualMwillMallowMtheMinstructorMtoMtakeMaMquickMpeekMtoMseeMhowMtheMstudentsM
canMbeMhelped.
ItMisMabsolutelyMforbiddenMforMtheMstudentsMtoMhaveMaccessMtoMthisMmanual.MPleaseM
doMnotMgiveMstudentsMsolutionsMfromMthisMmanual.MPostingMtheseMsolutionsMonMtheMInternetM
willMresultMinMwidespreadMdistributionMofMtheMsolutionsMandMwillMultimatelyMresultMinMtheMd
ecreaseMofMtheMusefulnessMofMtheMtext.
TheMauthorMwouldMlikeMtoMacknowledgeMtheMassistanceMofMTranMngocMKhanhM(5thMediti
on),MWarrenMGriffithM(4thMedition),MandMBrianMGiambattistaM(3rdMedition),MwhoMcheckedMthe
MsolutionsMofMpreviousMversions,MwentMoverMuserMcomments,MandMworkedMoutMsolutionsMfor
MnewMproblems.
WithoutMtheirMhelp,MthisMmanualMwouldMnotMbeMpossible.MTheMauthorMwouldMappreciateMrec
eivingMreportsMofMsuggestedMimprovementsMandMsuspectedMerrors.MCommentsMcanMbeMsentM
,MtheMmoreMdetailedMtheMbetter.
StephenMT.MThornton
Charlottesville,MVirginia
, v
