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1、ClassicalMechanicsAlexeiDeriglazovClassicalMechanicsHamiltonianandLagrangianFormalism123AlexeiDeriglazovDepto.deMatemáticaUniversidadeFederaldeJuizdeFora36036-330JuizdeForaMG,Brazilalexei.deriglazov@ufjf.edu.brISBN978-3-642-14036-5e-ISBN978-3-642-14037-2DOI10.1007/978-3-642-14037-2Sp
2、ringerHeidelbergDordrechtLondonNewYorkLibraryofCongressControlNumber:2010932503cSpringer-VerlagBerlinHeidelberg2010Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recita
3、tion,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliabl
4、etoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:eStudio
5、CalamarS.L.,HeidelbergPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)PrefaceFormalismofclassicalmechanicsunderliesanumberofpowerfulmathematicalmethods,widelyusedintheoreticalandmathematicalphysics[111].Intheselec-tureswepresentsomeselectedtopics
6、ofclassicalmechanics,whichmaybeusefulforgraduatelevelstudentsintendingtoworkinoneofthebranchesofavastfieldoftheoreticalphysics.Exceptforthelastchapter,whichisdevotedtothediscussionofsingulartheoriesandtheirlocalsymmetries,thetopicsselectedcorrespondtothestandardcourseofclassicalmechan
7、ics.Fortheconvenienceofthereader,wehavetriedtomakethematerialofdifferentchaptersasindependentaspossible.So,thereaderwhoisfamiliarwithLagrangianmechanicscanproceedtoanyoneofChaps.3,4,5,6,7,8afterreadingthesecondchapter.Inourpresentationofthematerialwehavetried,wherepossible,toreplacei
8、ntu-itivemot
