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1、UnderconsiderationforpublicationinEuro.JnlofAppliedMathematics1Dynamiccouplingbetweenshallow-watersloshingandhorizontalvehiclemotionHAMIDALEMIARDAKANIandTHOMASJ.BRIDGESDepartmentofMathematics,UniversityofSurrey,GuildfordGU27XH,UKemail:H.Alemiardakani@surrey.ac
2、.uk&T.Bridges@surrey.ac.uk(Received21May2010)Thecoupledmotionbetweenshallowwatersloshinginamovingvehicleandthevehicledynamicsisconsidered,withthevehicledynamicsrestrictedtohorizontalmotion.ThepaperismotivatedbyCooker’sexperimentsandtheoryforwaterwavesinasuspen
3、dedcontainer.AnewderivationofthecoupledproblemintheEulerianfluidrepresentationisgiven.However,itisfoundthattransformationtoaLagrangianrepresentationleadstoaformulationwhichhasnicepropertiesfornumericalsimulation.IntheLagrangianrepresentation,asimpleandfastnumer
4、icalalgorithmwithexcellentenergyconservationoverlongtimes,basedontheSt¨ormer-Verletmethod,isimplemented.Numericalsimulationsofthecoupleddynamicsinboththelinearandnonlinearcasearepresented.1IntroductionTheeffectofliquidsloshingonthedynamicsandcontrolofliquidtran
5、sport,e.g.theterrestrialtransportofliquids,oilandliquidnaturalgasinships,andfuelinaviationandastrodynamics,hasmotivatedawiderangeofresearch.AnindicationofthebreadthofresearchinthisareaisthebookofIbrahim[14]whichcitesover2000references.Theinterestinthispaperisi
6、nthedynamiccouplingbetweenshallow-waterfluidsloshingandthemotionofthetransportvehicle.Examplesofwheredynamiccouplingisofinterestisthesloshingofwateronthethedeckoffishingvessels[6],transportofliquidbyrobots[26,27],motionplanningforindustrialcontrol[10,11,12,24],s
7、loshinginautomobilefueltanks[29],andmotionofwaterwavesinasuspendedcontainer[8].Itisthelatterpaperthatmotivatesthepresentstudy.Inthispaper,attentionwillberestrictedtothecaseofhorizontalmotiononly(fortranslationandrotationofthevesselcoupledtoshallow-watersloshin
8、gsee[3]).EquationsforthiscoupledproblemhavebeenderivedbyCooker[8].Letq(t)bethehorizontalpositionofthevessel,thenthegoverningequationsareht+uhx+hux=0,(1.1)ut+uux+ghx=−q,¨ontheinterv
