Solution Manual for Classical Dynamics of Particles and Systems, 5th Edition by Thornton (Complete – All 14 Chapters)

All 14 Chapters Covered
h h h




SOLUTION MANUAL
h

, Contents




Preface v
ProblemshSolvedhinhStudenthSolutionshManual vii

1 Matrices,hVectors,handhVectorhCalculus 1

2 NewtonianhMechanics—SinglehParticle 29

3 Oscillations 79

4 NonlinearhOscillationshandhChaos 127

5 Gravitation 149

6 SomehMethodshinhThehCalculushofhVariations 165

7 Hamilton’shPrinciple—LagrangianhandhHamiltonianhDynamics 181

8 Central-ForcehMotion 233

9 DynamicshofhahSystemhofhParticles 277

10 MotionhinhahNoninertialhReferencehFrame 333

11 DynamicshofhRigidhBodies 353

12 CoupledhOscillations 397

13 ContinuoushSystems;hWaves 435

14 SpecialhTheoryhofhRelativity 461



iii

,iv CONTENTS




Preface




ThishInstructor’shManualhcontainshthehsolutionshtohallhthehend-of-
chapterhproblemsh(buthnoththehappendices)hfromhClassicalhDynamicshofhParticleshandhSystems,hFifthh
Edition,hbyhStephenhT.hThorntonhandhJerryhB.hMarion.hIthishintendedhforhusehonlyhbyhinstructorshu
singhClassicalhDynamicshashahtextbook,handhithishnothavailablehtohstudentshinhanyhform.hAhStudenthS
olutionshManualhcontaininghsolutionshtohabouth25%hofhthehend-of-
chapterhproblemshishavailablehforhsalehtohstudents.hThehproblemhnumbershofhthosehsolutionshinhth
ehStudenthSolutionshManualharehlistedhonhthehnexthpage.
Ashahresulthofhsurveyshreceivedhfromhusers,hIhcontinuehtohaddhmorehworkedhouthexampleshinh
thehtexthandhaddhadditionalhproblems.hThereharehnowh509hproblems,hahsignificanthnumberhoverht
heh4thhedition.
Thehinstructorhwillhfindhahlargeharrayhofhproblemshranginghinhdifficultyhfromhthehsimpleh“pl
ughandhchug”htohthehtypehworthyhofhthehPh.D.hqualifyinghexaminationshinhclassicalhmechanics.hAh
fewhofhthehproblemsharehquitehchallenging.hManyhofhthemhrequirehnumericalhmethods.hHavinght
hishsolutionshmanualhshouldhprovidehahgreaterhappreciationhofhwhaththehauthorshintendedhtohacc
omplishhbyhthehstatementhofhthehproblemhinhthosehcaseshwherehthehproblemhstatementhishnothcom
pletelyhclear.hPleasehinformhmehwhenheitherhthehproblemhstatementhorhsolutionshcanhbehimprove
d.hSpecifichhelphishencouraged.hThehinstructorhwillhalsohbehablehtohpickhandhchoosehdifferenthlevel
shofhdifficultyhwhenhassigninghhomeworkhproblems.hAndhsincehstudentshmayhoccasionallyhneedh
hintshtohworkhsomehproblems,hthishmanualhwillhallowhthehinstructorhtohtakehahquickhpeekhtohseehh
owhthehstudentshcanhbehhelped.
Ithishabsolutelyhforbiddenhforhthehstudentshtohhavehaccesshtohthishmanual.hPleasehdohnothgi
vehstudentshsolutionshfromhthishmanual.hPostinghthesehsolutionshonhthehInternethwillhresulthinhwid
espreadhdistributionhofhthehsolutionshandhwillhultimatelyhresulthinhthehdecreasehofhthehusefulnessh
ofhthehtext.
ThehauthorhwouldhlikehtohacknowledgehthehassistancehofhTranhngochKhanhh(5thhedition),hWa
rrenhGriffithh(4thhedition),handhBrianhGiambattistah(3rdhedition),hwhohcheckedhthehsolutionshofhpr
evioushversions,hwenthoverhuserhcomments,handhworkedhouthsolutionshforhnewhproblems.
Withouththeirhhelp,hthishmanualhwouldhnothbehpossible.hThehauthorhwouldhappreciatehreceivinghr
eportshofhsuggestedhimprovementshandhsuspectedherrors.hCommentshcanhbehsenthbyhemailhtohstt
@virginia.edu,hthehmorehdetailedhthehbetter.
StephenhT.hThornton
Charlottesville,hVirginia


v

, CHAPTER h 1
Matrices, Vectors,
h h




and Vector Calculus
h h




1-1.

x1

45˚
x1

45˚
x3
x3h

Axesh x1h andh x3h liehinhtheh x1x3h plane.hT
hehtransformationhequationshare:
x1hhx1hcosh45hhx3h cosh45
x2hhx2
x3h hx3hcosh45hhx1hcosh45
1h 1h
xh h xh h x
1 1 3
2 2
x2hhx2
1h 1h
xh h xh h x
3 1 3
2 2
Sohthehtransformationhmatrixhis:

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


1