mit press - structure and interpretation of classical mechanics

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1、StructureandInterpretationofClassicalMechanicsStructureandInterpretationofClassicalMechanicsGeraldJaySussmanandJackWisdomwithMeinhardE.MayerTheMITPressCambridge,MassachusettsLondon,England°c2000byTheMassachusettsInstituteofTechnologyAllrightsreserved.Nopartofthisboo

2、kmaybereproducedinanyformorbyanyelectronicormechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthepublisher.ThisbookwassetbytheauthorsusingtheLATEXtypesettingsystemandwasprintedandboundintheUnitedStatesofAm

3、erica.Thisbookisdedicated,inrespectandadmiration,toThePrincipleofLeastAction.Theauthorhassparedhimselfnopainsinhisendeavourtopresentthemainideasinthesimplestandmostintelligibleform,andonthewhole,inthesequenceandconnectioninwhichtheyactuallyoriginated.Intheinteresto

4、fclearness,itappearedtomeinevitablethatIshouldrepeatmyselffrequently,withoutpay-ingtheslightestattentiontotheeleganceofthepresentation.IadheredscrupulouslytothepreceptofthatbrillianttheoreticalphysicistL.Boltzmann,accordingtowhommattersofeleganceoughtbelefttothetail

5、orandtothecobbler."AlbertEinstein,inRelativity,theSpecialandGeneralTheory,(1961),p.v.ContentsContentsviiPrefacexiiiAcknowledgmentsxvii1LagrangianMechanics11.1ThePrincipleofStationaryAction41.2Con¯gurationSpaces91.3GeneralizedCoordinates111.4ComputingActions161.5TheE

6、uler-LagrangeEquations261.5.1DerivationoftheLagrangeEquations271.5.2ComputingLagrange'sEquations341.6HowtoFindLagrangians371.6.1CoordinateTransformations441.6.2SystemswithRigidConstraints481.6.3ConstraintsasCoordinateTransformations601.6.4TheLagrangianisNotUnique621

7、.7EvolutionofDynamicalState671.8ConservedQuantities761.8.1ConservedMomenta761.8.2EnergyConservation781.8.3CentralForcesinThreeDimensions811.8.4Noether'sTheorem841.9AbstractionofPathFunctions881.10ConstrainedMotion931.10.1CoordinateConstraints95viiiContents1.10.2Deri

8、vativeConstraints1021.10.3Non-HolonomicSystems1061.11Summary1091.12Projects1102RigidBodies1132.1RotationalKineticEnergy1142.2KinematicsofR