mit press - structure and interpretation of classical mechanics

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

2、nanyformorbyanyelectronicormechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthepublisher.ThisbookwassetbytheauthorsusingtheLATEXtypesettingsystemandwasprintedandboundintheUnitedStatesofAmerica.Thisbookisdedicated,inrespec

3、tandadmiration,toThePrincipleofLeastAction.Theauthorhassparedhimselfnopainsinhisendeavourtopresentthemainideasinthesimplestandmostintelligibleform,andonthewhole,inthesequenceandconnectioninwhichtheyactuallyoriginated.Intheinterestofclearness,itappearedtomeinevitablethatIshouldrepea

4、tmyselffrequently,withoutpay-ingtheslightestattentiontotheeleganceofthepresentation.IadheredscrupulouslytothepreceptofthatbrillianttheoreticalphysicistL.Boltzmann,accordingtowhommattersofeleganceoughtbelefttothetailorandtothecobbler."AlbertEinstein,inRelativity,theSpecialandGeneralT

5、heory,(1961),p.v.ContentsContentsviiPrefacexiiiAcknowledgmentsxvii1LagrangianMechanics11.1ThePrincipleofStationaryAction41.2Con¯gurationSpaces91.3GeneralizedCoordinates111.4ComputingActions161.5TheEuler-LagrangeEquations261.5.1DerivationoftheLagrangeEquations271.5.2ComputingLagrange

6、'sEquations341.6HowtoFindLagrangians371.6.1CoordinateTransformations441.6.2SystemswithRigidConstraints481.6.3ConstraintsasCoordinateTransformations601.6.4TheLagrangianisNotUnique621.7EvolutionofDynamicalState671.8ConservedQuantities761.8.1ConservedMomenta761.8.2EnergyConservation781

7、.8.3CentralForcesinThreeDimensions811.8.4Noether'sTheorem841.9AbstractionofPathFunctions881.10ConstrainedMotion931.10.1CoordinateConstraints95viiiContents1.10.2DerivativeConstraints1021.10.3Non-HolonomicSystems1061.11Summary1091.12Projects1102RigidBodies1132.1RotationalKineticEnergy

8、1142.2KinematicsofR