THE LIE SYMMETRIES AND CONSERVED QUANTITIES OF VARIABLE-MASS NONHOLONOMIC SYSTEM OF NON-CHETAEV''''S TYPE IN PHASE SPACE

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Perturbation of symmetries for super-long elastic slender rods

This paper analyses perturbations of Noether symmetry, Lie symmetry, and form invariance for super-long elastic slender rod systems. Criterion and structure equations of the symmetries after disturbance are proposed. Considering perturbation of all infinitesimal generators, three types of adiabatic invariants induced by perturbation of symmetries for the system are obtained.     

A new type of conserved quantity of Lie symmetry for the Lagrange system

This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an example is given to illustrate the application of the result.     

Symmetry of Lagrangians of holonomic nonconservative system in event space

This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result in the end.     

Study of the Lie symmetries of a relativistic variable mass system

The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result.     

变质量非Четаев型非完整系统在相空间的Lie对称性与守恒量

在相空间引入无限小群变换,研究变质量非Четаев型非完整系统的Lie对称和守恒量.利用系统运动微分方程在无限小群变换下的不变性建立Lie对称的确定方程和限制方程,得到Lie对称的结构方程和守恒量,并举例说明结果的应用.     

事件空间中二阶非Четаев型非完整系统的守恒律

研究事件空间中二阶非чeTaeB型非完整系统的守恒律。提出事件空间中的Jourdain原理，引入事件空间中的Jorudain生成元，给出无限小变换下的Jourdain原理的不变性条件。在一定条件下得到事件空间中系统的守恒律。并举例说明结果的应用。     

THE CONSERVATION LAW OF NONHOLONOMIC SYSTEM OF SECOND-ORDER NON-CHETAVE''''S TYPE IN EVENT SPACE

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｎｏｔｏｎｌｙｈａｓｉｍｐｏｒｔａｎｃｅｉｎｍａｔｈｅｍａｔｉｃｓｂｕｔａｌｓｏｒｅｖｅａｌｓｐｒｏｆｏｕｎｄｐｈｙｓｉｃａｌｌａｗ .Ｉｎ 1 91 8,ｂａｓｅｄｏｎｉｎｖａｒｉａｎｃｅｏｆＨａｍｉｌｔｏｎ’ｓｐｒｉｎｃｉｐｌｅｕｎｄｅｒｉｎｆｉｎｉｔｅｓｉｍａｌｔｒａｎｓｆｏｒｍａｔｉｏｎ ,ｔｈｅｃｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃｓｓｙｓｔｅｍｗａｓｓｔｕｄｉｅｄｂｙＧｅｒｍａｎｓｃｉｅｎｔｉｓ…     

非保守力学系统Nielsen方程的形式不变性

研究非保守力学系统Nielsen方程的形式不变性.给出非保守力学系统Nielsen方程的形式不变性的定义和判据,研究形式不变性和Noether对称性的关系,并举例说明结果的应用 关键词： 非保守力学系统 Nielsen方程 形式不变性 Noether对称性     

Mei Adiabatic Invariants Induced by Perturbation of Mei Symmetry for Nonholonomic Controllable Mechanical Systems

Two types of Mei adiabatic invariants induced by perturbation of Mei symmetry for nonholonomic controllable mechanical systems are reported. Criterion and restriction equations determining Mei symmetry after being disturbed of the system are established. Form and existence condition of Mei adiabatic invariants are obtained.