Form invariance and noether symmetrical conserved quantity of relativistic Birkhoffian systems

IntroductionIn 1 92 7,theAmericanmathematicianG .D .BirkhoffmadeprimaryresearchesonBirkhoffiandynamics[1].In 1 983,theAmericanphysicistR .M .SantillistudiedthetransformationtheoryofBirkhoffequationsandgeneralizationofGalileirelativity ,andsummarizedcomprehensivelytheoriginofBirkhoffequationsandthelaterstudiesonthem[2 ].Since 1 992 ,theChinesemechanicianMeiFeng_xianganditsco_workershaveconstructedthedynamicsofBirkhoffiansystemonthebasisofRefs.[1 ,2 ] ,andgavethebasictheoreticalframe[3 - …     

Birkhoff系统的Poincaré-Cartan积分不变量

基于现代微分几何学,分析了作为保守系统和非保守系统的推广——Birkhoff系统的辛结构.构造Birkhoff系统的Poincar-Cartan积分不变量.最后,将一维阻尼振动作为示例,求出其Poincar-Cartan积分不变量.     

A set of Lie symmetrical non－Noether conserved quantity for the relativistic Hamiltonian systems

For the relativistic Hamiltonian system, a new type of Lie symmetrical non-Noether conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing special infinitesimal transformations for q_s and p_s, we construct the determining equations of Lie symmetrical transformations of the system, which only depend on the canonical variables. A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.     

Algebraic structures and poisson integrals of relativistic dynamical equations for rotational systems

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The theory of relativistic analytical mechanics of the rotational systems

I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro…     

非线性非完整系统相对于非惯性系动力学的积分理论*

本文建立非线性非完整系统相对于非惯性系动力学的积分理论.首先,由这种相对运动的Routh方程给出系统的第一积分;其次,分别利用系统的循环积分、能量积分降阶运动方程,得到推广的Routh方程和推广的Whittaker方程;再次,建立这类系统运动的正则方程和变分方程,并由第一积分构造系统的积分不变量;然后,给出系统的Poincare-Cartan型积分变量关系和积分不变量.最后,给出一系列推论.     

RELATIVISTIC VARIATION PRINCIPLES AND EQUATION OF MOTION FOR VARIABLE MASS CONTROLLABLE MECHANICAL SYSTEM

ＲＥＬＡＴＩＶＩＳＴＩＣＶＡＲＩＡＴＩＯＮＰＲＩＮＣＩＰＬＥＳＡＮＤＥＱＵＡＴＩＯＮＯＦＭＯＴＩＯＮＦＯＲＶＡＲＩＡＢＬＥＭＡＳＳＣＯＮＴＲＯＬＬＡＢＬＥＭＥＣＨＡＮＩＣＡＬＳＹＳＴＥＭ￥(罗绍凯)ＬｕｏＳｈａｏｋａｉ（ＳｈａｎｇｑｉｕＴｅａｃｈｅｒｓ...     

事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性与Mei守恒量

研究事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性和Mei守恒量.建立系统的运动微分方程,给出系统Mei对称性、弱Mei对称性、强Mei对称性的定义和判据,得到由Mei对称性直接导致的Mei守恒量的存在条件以及Mei守恒量的表达式.举例说明结果的应用. 关键词： 事件空间 Nielsen方程 单面非Chetaev型非完整系统 Mei守恒量     

中国分析力学学科发展研讨会在杭召开

2007年7月21日至25日，来自全国各地的40余位专家、学者聚集在素有“人间天堂”之称的杭州西子湖畔，隆重举行“中国分析力学学科发展研讨会”——回顾研究工作的成就、寻找与国际水准的差距、探讨学科未来的发展，以此庆祝中国力学学会成立50周年!     

POINCAR-CARTAN INTEGRAL INVARIANTS OF BIRKHOFFIAN SYSTEMS

IntroductionThetheoryonPoincar啨＿Ｃａｒｔａｎｉｎｔｅｇｒａｌｉｎｖａｒｉａｎｔｈａｓｆｏｕｎｄｉｔｓｉｍｐｏｒｔａｎｔａｐｐｌｉｃａｔｉｏｎｓｉｎｐｈｙｓｉｃｓａｎｄｍｅｃｈａｎｉｃｓ.However,ithasbeenacceptedthatthetheoryisonlysuitableforHamiltoniansystemsandintegralinvariantsdonotexistfornon_HamiltoniansystemswhichadmitintegralvariantsofPoincar啨＿Ｃａｒｔａｎ’ｓｔｙｐｅｉｎｓｔｅａｄ[1- 3].SomeextensionsofPoincar啨＿Ｃａｒｔａｎｉｎｔｅｇｒａｌｉｎｖａｒｉａｎｔｓａｒｅｇｉｖｅｎｉｎ…