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1、ThisispageiPrinter:OpaquethisIntroductiontoMechanicsandSymmetryABasicExpositionofClassicalMechanicalSystemsSecondEditionJerroldE.MarsdenandTudorS.RatiuLastmodi¯edon15July1998vToBarbaraandLilianfortheirloveandsupport...........................15July1998
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4、18h02...........................ThisispageixPrinter:OpaquethisPrefaceSymmetryandmechanicshavebeenclosepartnerssincethetimeofthefoundingmasters:Newton,Euler,Lagrange,Laplace,Poisso
5、n,Jacobi,Ha-milton,Kelvin,Routh,Riemann,Noether,Poincar¶e,Einstein,SchrÄodinger,Cartan,Dirac,andtothisday,symmetryhascontinuedtoplayastrongrole,especiallywiththemodernworkofKolmogorov,Arnold,Moser,Kir-illov,Kostant,Smale,Souriau,Guillemin,Sternberg,and
6、manyothers.Thisbookisaboutthesedevelopments,withanemphasisonconcreteapplica-tionsthatwehopewillmakeitaccessibletoawidevarietyofreaders,especiallyseniorundergraduateandgraduatestudentsinscienceanden-gineering.Thegeometricpointofviewinmechanicscombinedwi
7、thsolidanaly-sishasbeenaphenomenalsuccessinlinkingvariousdiverseareas,bothwithinandacrossstandarddisciplinarylines.Ithasprovidedbothinsightintofundamentalissuesinmechanics(suchasvariationalandHamiltonianstructuresincontinuummechanics,°uidmechanics,andp
8、lasmaphysics)andprovidedusefultoolsinspeci¯cmodelssuchasnewstabilityandbifur-cationcriteriausingtheenergy-Casimirandenergy-momentummethods,newnumericalcodesbasedongeometricallyexactupdateproceduresandvariationalintegrators,andnewreorientationtechniques
9、incontroltheoryandrobotics.Symmetrywasalreadywidelyusedinmechanicsbythefoundersofthesubject,andhasbeendevelopedconsiderablyinrecenttimesinsuchdi-versephenomenaasreduction,stability,bifurcationandsolutionsymmetrybreakingrelativetoagivensystemsymmetrygro
10、up,methodsof¯ndingexplicitsolutionsforintegrablesystems,andadeeperunderstandingofspe-xPrefacecialsystems,suchastheKowalewskitop.Wehopethisbookwillprovideareasonableavenueto,andfoundationfor,theseexcitingdevelopments.Becauseoftheextensiv
