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1、AnalyticalClassicalDynamics:AnintermediatelevelcourseRichardFitzpatrickAssociateProfessorofPhysicsTheUniversityofTexasatAustin1INTRODUCTION1Introduction1.1IntendedaudienceTheselecturenotesoutlineasinglesemestercourseintendedforupperdivisionundergraduates.1.2MajorsourcesThetex
2、tbookswhichIhaveconsultedmostfrequentlywhilstdevelopingcoursematerialare:Analyticalmechanics,G.R.Fowles(Holt,Rinehart&Winston,NewYorkNY,1977).Classicaldynamicsofparticlesandsystems,5thEdition,S.T.Thornton,andJ.B.Marion(Brooks/Cole
3、ThomsonLearning,BelmontCA,2004).Analyticalmec
4、hanics,G.R.Fowles,andG.L.Cassiday,7thEdition(Brooks/Cole
5、ThomsonLearning,BelmontCA,2005).1.3ScopeofcourseThescopeofthiscourseisindicatedbyitstitle,AnalyticalClassicalDynamics".Takingtheelementsofthetitleinreverseorder,Dynamics"isthestudyofthemotionsofthevariousobjectsinthew
6、orldaroundus.Amathematicaltheoryofdynamicsisanaxiomaticsystem,ultimatelybasedonafewfundamentallaws,whichcanbeusedtobothunderstandandpredictthesemotions.ByClassical",weunderstandthatthetheoryofmotionwhichwearegoingtouseinourinvesti-gationofdynamicsisthat rstpublishedbyIsaacNe
7、wtonin1687.Wenowknowthatthistheoryisonlyapproximatelytrue.Thetheorybreaksdownwhenthevelocitiesoftheobjectsunderinvestigationapproachthespeedoflight,andmustbereplacedbyEinstein'sspecialtheoryofrelativity.Thetheoryalsobreaksdown21INTRODUCTION1.4Outlineofcourseontheatomicandsuba
8、tomicscales,andmustbereplacedbyquantummechanics.Inthiscourse,weshallneglectbothrelativisticandquantume ectsentirely.Itfollowsthatwemustrestrictourinvestigationtothemotionsoflarge(comparedtoanatom)slow(comparedtothespeedoflight)objects.Fortunately,however,mostofthemotionswhich
9、weobserveintheworldaroundusfallintothisclass.Finally,byAnalytical",weunderstandthatweshallonlyconsiderthosetypesofmotionwhosegoverningdi erentialequationscanbesolvedviastandardanalytictechniques.Inpractice,thismeansthatthegoverningequationsmustbelinearinnature,sinceourabilit
10、ytosolvenonlineardi erentialequationsanalyticallyisverylimited.Fortu
