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.     

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 - …     

Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables $t$, $q_s $ and $\dot {q}_s $. An example is given to illustrate the application of the results.     

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.     

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

Ｉｎ１９７９,Ｒ．ＢｅｎｇｔｓｓｏｎａｎｄＳ．Ｆｒａｕｅｎｄｏｒｆａｃｃｕｒａｔｌｙｍｅａｓｕｒｅｄｔｈｅｍａｘｉｍｕｍｖａｌｕｅｓｏｆｔｈｅｓｐｉｎｖｅｌｏｃｉｔｙｏｆ１４ｋｉｎｄｓｏｆｎｕｃｌｅｏｎｓ,ａｎｄｒｅｓｕｌｔｓｓｈｏｗｅｄｔｈｅｍａｘｉｍｕｍｖａｌｕｅｏｆｔｈｅｓｐｉｎｖｅｌｏｃｉｔｙｏｆｅａｃｈｎｕｃｌｅｏｎｗａｓｄｉｆｆｅｒｅｎｔｔｏａｎｏｔｈｅｒｓ［１］．Ｗｉｔｈｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｓｃｉｅｎｃｅａｎｄｔｅｃｈｎｏｌｏｇｙ,ｍｏｒｅａｎｄｍｏｒｅｅｘｐｅｒｉｍｅ…     

转动相对论系统动力学的积分理论

建立转动相对论系统动力学方程的积分理论.给出系统运动的第一积分,分别利用系统的循环积分和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,建立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.给出系统的Poincaré-Cartan型积分变量关系和积分不变量. 关键词： 转动相对论 运动方程 积分方法     

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…     

二阶自治Birkhoff系统的平衡点分岔

研究二阶自治Birkhoff系统的奇点、闭轨和极限环,以及与其相关的稳定性问题。给出奇点判据和闭轨判据。应用这些判据讨论了二阶自治Birkhoff系统的平衡点分岔。