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1、PrefaceThisisabookaboutcontinuummeChanics,electrodynamicsandthemechanicsofelectricallypolarizedmedia,andgravity.Itdiffersfromotherbooksonthesesubjectsinthatthetheoriesareformulatedbymeansoftheprincipleofleastaction.Thechiefadvantageofthisformulationisthatitissimpleandeasy,
2、sincethephysicalinputintothetheoryconsistsofchoosingonlyonescalarfunctionofthe,fieldsinvolved—theLagrangiandensity.Thusmychiefmotivationforwritingthisbookwastomakethephysicalcontentoftheclassicalsubjectsdiscussedavailabletostudentsofphysicsinacon-centrated,easytodigestform
3、.Mysecondgoalhasbeentoexplainthegeneralstructureoffieldtheoriesbasedontheleastactionformulation.Ihopethatthisdiscussionofgeneralprinciplesinapurelyclassicalsettingwillbeusefultostudentsofquantumfieldtheory,sincequantumfieldtheoryisalmostwithoutexceptionbasedontheprincipleo
4、fleastaction.Itisalsomyhopethatmycolleaguesinquantumfieldtheorywillenjoyseeingtheireverydaymethodsappliedtosuchsubjectsasthemotionoffluids.AlthoughIhavebornetheapplicationstoquantumfieldtheoryinmind,Ihavetriedtoremaintruetothesubjectofclassicalfieldtheory.Ihavethereforeavo
5、idedinteresting,diversionsthatdonotbearonrealclassicalphenomenaandhaveomittedsuchsubjectsasspin.1fields,non-Abeliangaugefields,andPoissonbrackets.PhysicistsoftenregardHamilton'sprincipleofleastactionasthestart-ingpointforparticlemechanics.However,modernworkersincontinuumme
6、chanicsalmostalwayspreferNewton'sformulationofmechanics,inwhichonewritestheequationsofmotiondirectlyinsteadofwritinganactionandderivingtheequationsofmotion.Theirpreferenceisnotwithoutgoodreason,fortheyseektodescribebothmechanicsandvilviiiPrefacethermodynamics—thatis,bothen
7、tropyconservingphenomena,whichgenerallycanbedescribedbyanactionprinciple,andentropyincreasingphenomena,whichgenerallycannot.Inthisbook,Ihavefollowedtheusualphysicists'inclinationtosweep"friction"undertheruganddiscussconservativeforcesonly'atleasttobeginwith.Inthefinalchapt
8、er,dissipationisresurrectedandaddedontosomesimpletheories.Whendissipationisincluded,theLa
