Classical Dynamics of Particles and Systems 5th Edition Solution Manual (2025) - Thornton & Marion

All 14 Chapters Covered
l l l




SOLUTION MANUAL
l

, Contents




Preface v
ProblemslSolvedlinlStudentlSolutionslManual vii

1 Matrices,lVectors,landlVectorlCalculus 1

2 NewtonianlMechanics—SinglelParticle 29

3 Oscillations 79

4 NonlinearlOscillationslandlChaos 127

5 Gravitation 149

6 SomelMethodslinlThelCalculusloflVariations 165

7 Hamilton’slPrinciple—LagrangianlandlHamiltonianlDynamics 181

8 Central-ForcelMotion 233

9 DynamicsloflalSystemloflParticles 277

10 MotionlinlalNoninertiallReferencelFrame 333

11 DynamicsloflRigidlBodies 353

12 CoupledlOscillations 397

13 ContinuouslSystems;lWaves 435

14 SpeciallTheoryloflRelativity 461



iii

,iv CONTENTS




Preface




ThislInstructor’slManuallcontainslthelsolutionsltolalllthelend-of-
chapterlproblemsl(butlnotlthelappendices)lfromlClassicallDynamicsloflParticleslandlSystems,lFifthlE
dition,lbylStephenlT.lThorntonlandlJerrylB.lMarion.lItlislintendedlforluselonlylbylinstructorslusin
glClassicallDynamicslaslaltextbook,landlitlislnotlavailableltolstudentslinlanylform.lAlStudentlSoluti
onslManuallcontaininglsolutionsltolaboutl25%loflthelend-of-
chapterlproblemslislavailablelforlsaleltolstudents.lThelproblemlnumbersloflthoselsolutionslinlthel
StudentlSolutionslManuallarellistedlonlthelnextlpage.
Aslalresultloflsurveyslreceivedlfromlusers,lIlcontinueltoladdlmorelworkedloutlexampleslinlth
eltextlandladdladditionallproblems.lTherelarelnowl509lproblems,lalsignificantlnumberloverlthel4t
hledition.
Thelinstructorlwilllfindlallargelarrayloflproblemslranginglinldifficultylfromlthelsimplel“plug
landlchug”ltoltheltypelworthyloflthelPh.D.lqualifyinglexaminationslinlclassicallmechanics.lAlfewl
oflthelproblemslarelquitelchallenging.lManyloflthemlrequirelnumericallmethods.lHavinglthislsol
utionslmanuallshouldlprovidelalgreaterlappreciationloflwhatlthelauthorslintendedltolaccomplishl
bylthelstatementloflthelproblemlinlthoselcaseslwherelthelproblemlstatementlislnotlcompletelylcle
ar.lPleaselinformlmelwhenleitherlthelproblemlstatementlorlsolutionslcanlbelimproved.lSpecificlh
elplislencouraged.lThelinstructorlwilllalsolbelableltolpicklandlchooseldifferentllevelslofldifficultyl
whenlassigninglhomeworklproblems.lAndlsincelstudentslmayloccasionallylneedlhintsltolworklso
melproblems,lthislmanuallwilllallowlthelinstructorltoltakelalquicklpeekltolseelhowlthelstudentslc
anlbelhelped.
Itlislabsolutelylforbiddenlforlthelstudentsltolhavelaccessltolthislmanual.lPleaseldolnotlgiv
elstudentslsolutionslfromlthislmanual.lPostingltheselsolutionslonlthelInternetlwilllresultlinlwides
preadldistributionloflthelsolutionslandlwilllultimatelylresultlinltheldecreaseloflthelusefulnessloflt
heltext.
ThelauthorlwouldllikeltolacknowledgelthelassistanceloflTranlngoclKhanhl(5thledition),lWar
renlGriffithl(4thledition),landlBrianlGiambattistal(3rdledition),lwholcheckedlthelsolutionsloflprevi
ouslversions,lwentloverluserlcomments,landlworkedloutlsolutionslforlnewlproblems.
Withoutltheirlhelp,lthislmanuallwouldlnotlbelpossible.lThelauthorlwouldlappreciatelreceivinglre
portsloflsuggestedlimprovementslandlsuspectedlerrors.lCommentslcanlbelsentlbylemailltolstt@vi
rginia.edu,lthelmoreldetailedlthelbetter.
StephenlT.lThornton
Charlottesville,lVirginia


v

, CHAPTERl 1
Matrices, Vectors,
l l


and Vector Calculus
l l




1-1.

x1

45˚
x1

45˚
x3
xl
3


Axesl x1l andl x3l lielinlthel x1x3l plane.lTh
eltransformationlequationslare:
x1l=lx1lcosl45l−lx3lcosl45
x2l=lx2
x3l=lx3l cosl45l+lx1lcosl45
1l 1l
xl =l xl −l x
1 1 3
2 2
x2l=lx2
1l 1l
xl =l xl −l x
3 1 3
2 2
Soltheltransformationlmatrixlis:

l 1 1l 
 0 −
2 2l

l 0 1 0l l 
l 1 1 
 0 
 2 2l 


1