Lie-Mei symmetry and conserved quantities of the Rosenberg problem

The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems.The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied.For the Rosenberg problem,the Lie and the Mei symmetries for the equation are obtained,the conserved quantities are deduced from them and then the definition and the criterion for the Lie-Mei symmetry of the Rosenberg problem are derived.Finally,the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie-Mei symmetry.     

Rosenberg问题的Noether-Lie对称性与守恒量

研究Rosenberg问题的对称性与守恒量.给出Rosenberg问题的Noether-Lie对称性的定义和判据,以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量. 关键词： 非完整系统 Noether-Lie对称性 守恒量     

完整系统Appell方程的Lie-Mei对称性与守恒量

研究了完整系统Appell方程的Lie-Mei对称性与守恒量.在完整系统Appell方程的基础上,给出了Appell方程的Lie-Mei对称性的定义和判据,得到了Appell方程的Lie-Mei对称性导致的Hojman守恒量和Mei守恒量.举例说明结果的应用.     

事件空间中单面约束系统的Noether定理

首先提出了事件空间中单面约束系统的D‘Alembert-Lagrange原理；其次基于微分变分原理在群的无限小变换下的不变性，研究并给出事件空间中单面约束系统的Noether定理及逆定理；最后举例说明结果的应用。     

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained. An example is given to illustrate the application of the results.     

变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量

研究变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量.首先通过一般无限小变换下的Lie对称性得到广义Hojman型的守恒量；然后基于力学系统高阶绝热不变量的定义，研究小扰动作用下系统Lie对称性的摄动，得到系统广义Hojman型绝热不变量；最后举例说明结果的应用. 关键词： 变质量 单面完整约束 对称性 摄动 绝热不变量     

Unified symmetry of mechano-electrical systems with nonholonomic constraints

The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results.     

二阶Birkhoff系统的Hamilton化

研究Birkhoff系统的Hamilton化问题。得到二阶Birkhoff系统可以Hamilton化的充分条件，给出Hamilton函数的构成方法。最后研究高阶Birkhoff系统的Hamilton化。     

奇异 Chetaev型非完整系统Nielsen方程的Lie-Mei对称性与守恒量

研究奇异Chetaev型非完整系统Nielsen方程的Lie-Mei对称性, 建立系统Nielsen方程的Lie-Mei对称性方程, 给出系统Nielsen方程强Lie-Mei对称性和弱Lie-Mei对称性的定义, 得到对称性导致的Hojman守恒量和Mei守恒量, 最后给出说明性算例. 关键词： 奇异非完整系统 Nielsen方程 Lie-Mei对称性 守恒量     

完整系统Nielsen方程的统一对称性与守恒量

研究完整系统Nielsen方程的统一对称性与守恒量.在完整系统Nielsen方程的基础上,首先给出了Nielsen方程的Noether对称性、Lie对称性和Mei对称性与守恒量,其次给出了Nielsen方程的统一对称性的定义和判据,得到Nielsen方程的统一对称性导致的Noether守恒量、Hojman守恒量和Mei守恒量.举例说明结果的应用.