简介：Hamiltonianstructureofarigidbodyinacircularorbitisestablishedinthispaper.Withthereductiontechnique,theHamiltonianstructureofarigidbodyinacircularorbitisderivedfromLie-Poissonstructureofsemidirectproduct,andHamiltonianisderivedfromJacobi’sintegral.TheabovemethodcanbegeneralizedtoestablishtheHamiltonianstructureofarigidbodywithaflexibleattachmentinacircularor-bit.Atlast,anexampleofstabilityanalysisisgiven.

简介：ThispaperstudiestheexistenceofperiodicsolutionsfornonautonomousasymptoticallylinearHamiltoniansystems.ByusingtheZ_pindextheorysomemultiplicityresultsfornonautonomoussystemsaregiven,whichgeneralizesomeresultsforautonomoussystemsduetoAmmanandZenhder.

简介：§I.IntroductionInthispaperwearelookingforsolutionsofthefollowingHamiltoniansystemofsecondorder:wherex=（x1,x2）andVsatisfies（V.1）V:R×R2→RisaC1-function,1-periodicInt,（V.2）Visperiodicinx1withtheperiodT>0,（V.3）V→O,Vx→Oas|x2|→∞,uniformlyin（t,x1）.

简介：ThispaperinvestigatestheasymptoticalstabilizationofHamiltoniancontrolsystemswithtimedelay.First,Hamiltoniancontrolsystemswithtimedelayareproposed.Second,atwo-to-one（TTO）principleisintroducedthattwodifferentHamiltonianfunctionsaresimultaneouslyenergy-shapingbyonedesiredenergyfunction.Third,anovelmatchingequationisbuiltviatheTTOprinciplefortheHamiltoniancontrolsystemswithtimedelay,whichgeneratesaneffectivecontrollawfortheHamiltoniancontrolsystemswithtimedelay.Finally,anumericalexampleshowstheeffectivenessofproposedmethod.

简介：InthispaperanapproximateequationisderivedtodescribesmoothpartsofthestabilityboundaryforlinearHamiltoniansystems,dependingonarbitrarynumberofparameters.Withthisequation,wecanobtainparameterscorrespondingtothestabilityboundary,aswellastothestabilityandinstabilitydomains,pro-videdthatonepointonthestabilityboundaryisknown.Thendifferentialequationsdescribingtheevolutionofeigenvaluesandeigenvectorsalongacurveonthesta-bilityboundarysurfacearederived.Theseequationsalsoallowustoobtaincurvesbelongingtothestabilityboundary.Applicationstolineargyroscopicsystemsareconsideredandstudiedwithexamples.

简介：Abstract.LetSnbethesymmetricgroup

简介：SameexistenceandmultiplicityofhomoclinicorbitforsecondorderHamiltoniansystem¨↑x-a（t)x+Wx(t,x)=0aregivenbymeansofvariationalmethods,wherethepotentialV(t,x)=-1/2a（t)|s|^2+W(t,s)isquadraticinsatinfinityandsubquadraticinsatzero,andthefunctiona（t)satisfiesthegrowthconditionlimt→∞∫t…t+la（t)dt=+∞，A↓ι∈R^1.

简介：SymplecticintegrationofseparableHamiltonianordinaryandpartialdifferentialequationsisdiscussed.AvonNeumannanalysisisperformedtoachievegenerallinearstabilitycriteriaforsymplecticmethodsappliedtoarestrictedclassofHamiltonianPDEs.Inthistreatment,thesymplecticstepisperformedpriortothespatialstep,asopposedtothestandardapproachofspatiallydiscretisingthePDEtoformasystemofHamiltonianODEstowhichasymplecticintegratorcanbeapplied.InthiswaystabilitycriteriaareachievedbyconsideringthespectraoflinearisedHamiltonianPDEsratherthanspatialstepsize.

简介：MeasuresynchronizationisanewphenomenonfoundincoupledHamiltoniansystemsrecentlyanditisinterestingtounderstanditspropertiescomprehensively.Wediscussthemeasuresynchronizationofacoupledpairofstandardmapsinhighperiodquasi-periodorbits,andthemeasuresynchronizationtransitionisassociatedwiththetransitionofcoupledsystemsfromquasi-periodicitytochaos.ThisbehaviourisverydifferentfromthatfoundbyHamptonandZanette[Phys.Rev.Lett.83(1999)2179].

简介：ForarelativisticHamiltoniansystem,twonewtypesoftheLiesymmetriesandconservationlawsaregivenunderinfinitesimaltransformaitonsofgroups.OnthebasisofthetheoryofinvarianceoftherelativisticHamiltonianequationsunderinfinitesimaltransformationsandintroducinginfinitesimaltransformationsfortimet,generalizedcoordinatesqsandgeneralizedmonentaps,weobtainthedetermingingequations,thestructureequationsandtheconservedquantitiesoftheLiesymmetries.Introducinginfinitesimaltransformationforgeneralizedcoordinatesqsandgeneralizedmomentaps,weconstructtheLiesymmetricaltransformationsofthesystem,whichonlydependonthecanonicalvariables.AsetofconservedquantitiesaredirectlyobtainedfromtheLiesymmetriesofthesyste.Anexampleisgiventoillustrantetheapplicationoftheresults.

简介：Anewdiscreteisospectralproblemisintroduced,fromwhichthecoupleddiscreteKdVhierarchyisdeducedandiswritteninitsHamiltonianformbymeansofthetraceidentity.ItisshownthateachequationintheresultinghierarchyisLiouvilleintegrable.Furthermore,aninfinitenumberofconservationlawsareshownexplicitlybydirectcomputation.

简介：AsubalgebraofloopalgebraA2isestablished.Therefore,anewisospectralproblemisdesigned.BymakinguseofTu''sscheme,anewintegrablesystemisobtained,whichpossessesbi-Hamiltonianstructure.Asitsreductions,aformalismsimilartothewell-knownAblowitz-Kaup-Newell-Segur(AKNS)hierarchyandageneralizedstandardformoftheSchrodingerequationarepresented.Inaddition,inorderforakindofexpandingintegrablesystemtobeobtained,aproperalgebraictransformationissuppliedtochangeloopalgebraA2intoloopalgebraA1.Furthermore,ahigh-dimensionalloopalgebraisconstructed,whichisdifferentfromanypreviousone.Anintegrablecouplingofthesystemobtainedisgiven.Finally,theHamiltonianformofabinarysymmetricconstrainedflowofthesystemobtainedispresented.

简介：Inthispaperwestudytheexistenceofinfinitelymanyperiodicsolutionsforsecond-orderHamiltoniansystems{ü(t)+A(t)u(t)+▽F(t,u(t))=0,u(0)-u(T)=(0)-(T)=0,whereF(t,u)iseveninu,and▽(t,u)isofsublineargrowthatinfinityandsatisfiestheAhmad-Lazer-Paulcondition.

简介：在由域的一个简短分类以后，为无限维的Hamiltonian操作符的一些不同的类的invertibility和光谱的结果被给。由上述结果，有简单的支持的矩形的板的联系无限维的Hamiltonian操作员被证明可颠倒。由某个紧密，而且，我们发现这个操作符的光谱与有限几何复合仅仅由孤立的特征值组成，它将在为把方程弄弯的板的一个类基于Hamiltonian系统发现分析、数字的解决方案起一个重要作用。

简介：ConsideringfullperturbationtoinfinitesimalgeneratorsintheMeistructureequation,anewtypeofMeiadiabaticinvariantinducedbyperturbationtoMeisymmetryforHamiltoniansystemwasreported.

简介：WepresentanewdiscreteintegrablecouplingsystembyusingthematrixLaxpairU,V∈sl(4).AnovelspectralproblemofmodifiedTodalatticesolitonhierarchyisconsidered.Then,anewdiscreteintegrablecouplingequationhierarchyisobtainedthroughthemethodoftheenlargedLaxpair.Finally,weobtaintheHamiltonianstructureoftheintegrablecouplingsystemofthesolitonequationhierarchyusingthematrix-formtraceidentity.ThisdiscreteintegrablecouplingsystemincludesakindofamodifiedTodalatticehierarchy.

简介：InthispaperwedevelopakindofdissipativediscreteschemeforthecomputationofhomoclinicorbitsnearTB-pointinHamiltoniansystems.Itisprovedbyusingcontinuationmethodthatwhenthedissipativetermanditscoefficientaresuitablychosen,thisschemepossessesdiscretehomoclinicorbits,whichapproximatethecontinuoushomoclinicorbitswithsecondorderaccuracyw.r.totime-stepsize.

简介：

简介：Inthispaper,thestresssingularityanalysisatthecracktiponelasticbi-materialinter-facesisconsidered.ThegoverningequationsofplaneelasticityinsectorialdomainarederivedtobeinHamiltonianformviavariablesubstitutionandvariationalprinciple.Themethodsofseparationofvariablesandconjugatesymplecticeigen-functionexpansionaredevelopedtosolvetheequationsinsectorialdomain.Thegeneralformulaeforthesolutionofstresssingularitiesatthecracktiponbi-ma-terialinterfacesareputforward,andanewsolutiontechniqueforfractureproblemsispresented.

简介：为有致动器浸透的部分可见的非线性的伪Hamiltonian系统的最佳的颤动控制策略被建议。首先，一控制了部分可见的非线性的系统由于Charalambous和Elliott基于定理被变换成有限尺寸的一个完全可见的线性控制系统。然后部分平均它随机的微分方程和动态编程方程与完全可见的线性系统联系了的^o被分别地使用随机的平均方法和随机的动态编程原则导出。最佳的控制法律从解决最后的动态编程方程被获得。结果证明建议控制策略有高控制有效性和控制效率。