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1、TensorAnalysiswithApplicationsinMechanicsThispageintentionallyleftblankTensorAnalysiswithApplicationsinMechanicsLeonidP.LebedevNationalUniversityofColombiaSouthernFederalUniversity,RussiaMichaelJ.CloudLawrenceTechnologicalUniversity,USAVictorA.EremeyevMartin-Luther-University
2、Halle-Wittenberg,GermanySouthernScientificCenterofRussianAcademyofScienceSouthernFederalUniversity,RussiaWorldScientificNEWJERSEY•LONDON•SINGAPORE•BEIJING•SHANGHAI•HONGKONG•TAIPEI•CHENNAIPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27Wa
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4、ingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmate
5、rialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.DeskEditor:TjanKwangWeiISBN-13978-981-4313-12-4ISBN-10981-4313-12-2PrintedinSingapore.ForewordEverysc
6、ienceelaboratestoolsforthedescriptionofitsobjectsofstudy.Inclassicalmechanicswemakeextensiveuseofvectorialquantities:forces,moments,positions,velocities,momenta.Confiningourselvestoasinglecoordinateframe,wecanregardavectorasafixedcolumnmatrix.Thedefinitivetraitofavectorquantity,
7、however,isitsobjectivity;avectordoesnotdependonourchoiceofcoordinateframe.Thismeansthatassoonasthecomponentsofaforcearespecifiedinoneframe,thecomponentsofthatforcerelativetoanyotherframecanbefoundthroughtheuseofappropriatetransformationrules.Butvectorquantitiesalonedonotsufficef
8、orthedescriptionofcon-tinuummedia.Thestressandstrainatapointinsideab
