All 14 Chapters Covered
ss ss ss
SOLUTION MANUAL
ss
, Contents
Preface v
Problems ssSolved ssin ssStudent ssSolutions ssManual vii
1 Matrices, ssVectors, ssand ssVector ssCalculus 1
2 Newtonian ssMechanics—Single ssParticle 29
3 Oscillations 79
4 Nonlinear ssOscillations ssand ssChaos 127
5 Gravitation 149
6 Some ssMethods ssin ssThe ssCalculus ssof ssVariations 165
7 Hamilton’s ssPrinciple—Lagrangian ssand ssHamiltonian ssDynamics 181
8 Central-Force ssMotion 233
9 Dynamics ssof ssa ssSystem ssof ssParticles 277
10 Motion ssin ssa ssNoninertial ssReference ssFrame 333
11 Dynamics ssof ssRigid ssBodies 353
12 Coupled ssOscillations 397
13 Continuous ssSystems; ssWaves 435
14 Special ssTheory ssof ssRelativity 461
iii
,iv CONTENTS
, Preface
This ssInstructor’s ssManual sscontains ssthe sssolutions ssto ssall ssthe ssend-of-chapter ssproblems ss(but
ssnot ssthe ssappendices) ssfrom ssClassical ssDynamics ssof ssParticles ssand ssSystems, ssFifth ssEdition, ssby
ssStephen ssT. ssThornton ssand ssJerry ssB. ssMarion. ssIt ssis ssintended ssfor ssuse ssonly ssby ssinstructors
ssusing ssClassical ssDynamics ssas ssa sstextbook, ssand ssit ssis ssnot ssavailable ssto ssstudents ssin ssany
ssform. ssA ssStudent ssSolutions ssManual sscontaining sssolutions ssto ssabout ss25% ssof ssthe ssend-of-
chapter ssproblems ssis ssavailable ssfor sssale ssto ssstudents. ssThe ssproblem ssnumbers ssof ssthose
sssolutions ssin ssthe ssStudent ssSolutions ssManual ssare sslisted sson ssthe ssnext sspage.
As ssa ssresult ssof sssurveys ssreceived ssfrom ssusers, ssI sscontinue ssto ssadd ssmore ssworked ssout
ssexamples ssin ssthe sstext ssand ssadd ssadditional ssproblems. ssThere ssare ssnow ss509 ssproblems, ssa
sssignificant ssnumber ssover ssthe ss4th ssedition.
The ssinstructor sswill ssfind ssa sslarge ssarray ssof ssproblems ssranging ssin ssdifficulty ssfrom ssthe
sssimple ss“plug ssand sschug” ssto ssthe sstype ssworthy ssof ssthe ssPh.D. ssqualifying ssexaminations ssin
ssclassical ssmechanics. ssA ssfew ssof ssthe ssproblems ssare ssquite sschallenging. ssMany ssof ssthem
ssrequire ssnumerical ssmethods. ssHaving ssthis sssolutions ssmanual ssshould ssprovide ssa ssgreater
ssappreciation ssof sswhat ssthe ssauthors ssintended ssto ssaccomplish ssby ssthe ssstatement ssof ssthe
ssproblem ssin ssthose sscases sswhere ssthe ssproblem ssstatement ssis ssnot sscompletely ssclear. ssPlease
ssinform ssme sswhen sseither ssthe ssproblem ssstatement ssor sssolutions sscan ssbe ssimproved. ssSpecific
sshelp ssis ssencouraged. ssThe ssinstructor sswill ssalso ssbe ssable ssto sspick ssand sschoose ssdifferent
sslevels ssof ssdifficulty sswhen ssassigning sshomework ssproblems. ssAnd sssince ssstudents ssmay
ssoccasionally ssneed sshints ssto sswork sssome ssproblems, ssthis ssmanual sswill ssallow ssthe ssinstructor
ssto sstake ssa ssquick sspeek ssto sssee sshow ssthe ssstudents sscan ssbe sshelped.
It ssis ssabsolutely ssforbidden ssfor ssthe ssstudents ssto sshave ssaccess ssto ssthis ssmanual.
ssPlease ssdo ssnot ssgive ssstudents sssolutions ssfrom ssthis ssmanual. ssPosting ssthese sssolutions sson ssthe
ssInternet sswill ssresult ssin sswidespread ssdistribution ssof ssthe sssolutions ssand sswill ssultimately
ssresult ssin ssthe ssdecrease ssof ssthe ssusefulness ssof ssthe sstext.
The ssauthor sswould sslike ssto ssacknowledge ssthe ssassistance ssof ssTran ssngoc ssKhanh ss(5th
ssedition), ssWarren ssGriffith ss(4th ssedition), ssand ssBrian ssGiambattista ss(3rd ssedition), sswho
sschecked ssthe sssolutions ssof ssprevious ssversions, sswent ssover ssuser sscomments, ssand ssworked
ssout sssolutions ssfor ssnew ssproblems.
Without sstheir sshelp, ssthis ssmanual sswould ssnot ssbe sspossible. ssThe ssauthor sswould ssappreciate
ssreceiving ssreports ssof sssuggested ssimprovements ssand sssuspected sserrors. ssComments sscan ssbe
sssent ssby ssemail ssto , ssthe ssmore ssdetailed ssthe ssbetter.
Stephen ssT. ssThornton
Charlottesville, ssVirginia
ss ss ss
SOLUTION MANUAL
ss
, Contents
Preface v
Problems ssSolved ssin ssStudent ssSolutions ssManual vii
1 Matrices, ssVectors, ssand ssVector ssCalculus 1
2 Newtonian ssMechanics—Single ssParticle 29
3 Oscillations 79
4 Nonlinear ssOscillations ssand ssChaos 127
5 Gravitation 149
6 Some ssMethods ssin ssThe ssCalculus ssof ssVariations 165
7 Hamilton’s ssPrinciple—Lagrangian ssand ssHamiltonian ssDynamics 181
8 Central-Force ssMotion 233
9 Dynamics ssof ssa ssSystem ssof ssParticles 277
10 Motion ssin ssa ssNoninertial ssReference ssFrame 333
11 Dynamics ssof ssRigid ssBodies 353
12 Coupled ssOscillations 397
13 Continuous ssSystems; ssWaves 435
14 Special ssTheory ssof ssRelativity 461
iii
,iv CONTENTS
, Preface
This ssInstructor’s ssManual sscontains ssthe sssolutions ssto ssall ssthe ssend-of-chapter ssproblems ss(but
ssnot ssthe ssappendices) ssfrom ssClassical ssDynamics ssof ssParticles ssand ssSystems, ssFifth ssEdition, ssby
ssStephen ssT. ssThornton ssand ssJerry ssB. ssMarion. ssIt ssis ssintended ssfor ssuse ssonly ssby ssinstructors
ssusing ssClassical ssDynamics ssas ssa sstextbook, ssand ssit ssis ssnot ssavailable ssto ssstudents ssin ssany
ssform. ssA ssStudent ssSolutions ssManual sscontaining sssolutions ssto ssabout ss25% ssof ssthe ssend-of-
chapter ssproblems ssis ssavailable ssfor sssale ssto ssstudents. ssThe ssproblem ssnumbers ssof ssthose
sssolutions ssin ssthe ssStudent ssSolutions ssManual ssare sslisted sson ssthe ssnext sspage.
As ssa ssresult ssof sssurveys ssreceived ssfrom ssusers, ssI sscontinue ssto ssadd ssmore ssworked ssout
ssexamples ssin ssthe sstext ssand ssadd ssadditional ssproblems. ssThere ssare ssnow ss509 ssproblems, ssa
sssignificant ssnumber ssover ssthe ss4th ssedition.
The ssinstructor sswill ssfind ssa sslarge ssarray ssof ssproblems ssranging ssin ssdifficulty ssfrom ssthe
sssimple ss“plug ssand sschug” ssto ssthe sstype ssworthy ssof ssthe ssPh.D. ssqualifying ssexaminations ssin
ssclassical ssmechanics. ssA ssfew ssof ssthe ssproblems ssare ssquite sschallenging. ssMany ssof ssthem
ssrequire ssnumerical ssmethods. ssHaving ssthis sssolutions ssmanual ssshould ssprovide ssa ssgreater
ssappreciation ssof sswhat ssthe ssauthors ssintended ssto ssaccomplish ssby ssthe ssstatement ssof ssthe
ssproblem ssin ssthose sscases sswhere ssthe ssproblem ssstatement ssis ssnot sscompletely ssclear. ssPlease
ssinform ssme sswhen sseither ssthe ssproblem ssstatement ssor sssolutions sscan ssbe ssimproved. ssSpecific
sshelp ssis ssencouraged. ssThe ssinstructor sswill ssalso ssbe ssable ssto sspick ssand sschoose ssdifferent
sslevels ssof ssdifficulty sswhen ssassigning sshomework ssproblems. ssAnd sssince ssstudents ssmay
ssoccasionally ssneed sshints ssto sswork sssome ssproblems, ssthis ssmanual sswill ssallow ssthe ssinstructor
ssto sstake ssa ssquick sspeek ssto sssee sshow ssthe ssstudents sscan ssbe sshelped.
It ssis ssabsolutely ssforbidden ssfor ssthe ssstudents ssto sshave ssaccess ssto ssthis ssmanual.
ssPlease ssdo ssnot ssgive ssstudents sssolutions ssfrom ssthis ssmanual. ssPosting ssthese sssolutions sson ssthe
ssInternet sswill ssresult ssin sswidespread ssdistribution ssof ssthe sssolutions ssand sswill ssultimately
ssresult ssin ssthe ssdecrease ssof ssthe ssusefulness ssof ssthe sstext.
The ssauthor sswould sslike ssto ssacknowledge ssthe ssassistance ssof ssTran ssngoc ssKhanh ss(5th
ssedition), ssWarren ssGriffith ss(4th ssedition), ssand ssBrian ssGiambattista ss(3rd ssedition), sswho
sschecked ssthe sssolutions ssof ssprevious ssversions, sswent ssover ssuser sscomments, ssand ssworked
ssout sssolutions ssfor ssnew ssproblems.
Without sstheir sshelp, ssthis ssmanual sswould ssnot ssbe sspossible. ssThe ssauthor sswould ssappreciate
ssreceiving ssreports ssof sssuggested ssimprovements ssand sssuspected sserrors. ssComments sscan ssbe
sssent ssby ssemail ssto , ssthe ssmore ssdetailed ssthe ssbetter.
Stephen ssT. ssThornton
Charlottesville, ssVirginia
