classical mechanics

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1、LosAlamosElectronicArchives:physics/9909035CLASSICALMECHANICSHARETC.ROSUrosu@ifug3.ugto.mxaadp(r)pdtVgraduatecoursephysics/990903519Sep1999Copyrightc1999H.C.RosuLeon,Guanajuato,Mexicov1:September1999.1CONTENTS1.THEMINIMUM"PRINCIPLES...3.2.MOTIONINCENTRALFORCES...19.3.RIGIDBODY.

2、..32.4.SMALLOSCILLATIONS...52.5.CANONICALTRANSFORMATIONS...70.6.POISSONPARENTHESES...79.7.HAMILTON-JACOBIEQUATIONS...82.8.ACTION-ANGLEVARIABLES...90.9.PERTURBATIONTHEORY...96.10.ADIABATICINVARIANTS...111.11.MECHANICSOFCONTINUOUSSYSTEMS...116.21.THEMINIMUM"PRINCIPLESForward:Thehi

3、storyofminimum"principlesinphysicsislongandinter-esting.Thestudyofsuchprinciplesisbasedontheideathatthenatureactsalwaysinsuchawaythattheimportantphysicalquantitiesareminimizedwheneverarealphysicalprocesstakesplace.Themathematicalbackgroundfortheseprinciplesisthevariationalcalcul

4、us.CONTENTS1.Introduction2.Theprincipleofminimumaction3.TheprincipleofD'Alembert4.Phasespace5.Thespaceofcongurations6.Constraints7.Hamilton'sequationsofmotion8.Conservationlaws9.Applicationsoftheactionprinciple31.IntroductionTheempiricalevidencehasshownthatthemotionofaparticlein

5、aninertialsystemiscorrectlydescribedbyNewton'ssecondlawF~=d~p=dt,wheneverpossibletoneglecttherelativisticeects.Whentheparticlehappensnottobeforcedtoacomplicatedmotion,theCartesiancoordinatesaresucienttodescribethemovement.Ifnoneoftheseconditionsarefullled,rathercomplicatedequa

6、tionsofmotionaretobeexpected.Inaddition,whentheparticlemovesonagivensurface,certainforcescalledconstraintforcesmustexisttomaintaintheparticleincontactwiththesurface.Suchforcesarenotsoobviousfromthephenomenologicalpointofview;theyrequireaseparatepostulateinNewtonianmechanics,theon

7、eofactionandreaction.Moreover,otherformalismsthatmaylookmoregeneralhavebeendeveloped.TheseformalismsareequivalenttoNewton'slawswhenappliedtosimplepracticalproblems,buttheyprovideageneralapproachformorecomplicatedproblems.TheHamiltonprincipleisoneofthesemethodsanditscorrespondinge

8、quationsofmotionarecalledtheEuler-Lagran