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.     

相对论性转动变质量系统的Lie对称性与守恒量

给出相对论性转动变质量系统的d’Alembert原理和运动微分方程.利用运动微分方程在无限小变换下的不变性,建立相对论性转动变质量系统的Lie对称确定方程,得到结构方程和守恒量.并举例说明结果的应用 关键词： 相对论 转动 变质量 Lie对称     

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

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

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。     

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     

Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space

For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results.     

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.     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 守恒量     

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.