变质量非完整系统Tzénoff方程的Lie 对称性与其导出的守恒量

航天器运行系统大都属于变质量力学系统, 变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律. 本文首先导出了变质量非完整力学系统的Tzénoff方程, 然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量, 给出了这种守恒量的函数表达式和导出这种守恒量的判据方程. 该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.     

A New Conserved Quantity Corresponding to Mei Symmetry of Tzenoff Equations for Nonholonomic Systems

A new conserved quantity is investigated by utilizing the definition and discriminant equation of Mei symmetry of Tzénoff equations for nonholonomic systems. In addition, the expression of this conserved quantity, and the determining condition induced new conserved quantity are also presented.     

Another Conserved Quantity by Mei Symmetry of Tzénoff Equation for Non-Holonomic Systems

As a direct result of Mei symmetry of the Ténoff equation for non-holonomic mechanical systems, another conserved quantity is studied. The expression and the determining equations of the above conserved quantity are also presented. Using this method, it is easier to find out conserved quantity than ever. In the last, an example is presented to illustrate applications of the new results.     

非完整系统Tzénoff方程的Mei对称性和守恒量

研究了在群的无限小变换下非完整系统Tzénoff方程的Mei对称性，给出了非完整系统Tzénoff方程Mei对称性的定义和判据方程.给出了这种Mei对称性导致Lie对称性的充要条件，通过特殊Mei对称性条件下的Lie对称性，找到了非完整系统Tzénoff方程的Hojman守恒量.     

Structure equation and Mei conserved quantity for Mei symmetry of Appell equation

This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results.     

事件空间中非Chetaev型非完整约束系统的Hojman守恒量

研究了事件空间中非Chetaev型非完整约束系统由特殊的Lie对称性、Noether对称性和Mei对称性导致的Hojman守恒量.建立了系统的运动微分方程.给出了Lie对称性、Noether对称性和Mei对称性的判据,研究了三种对称性间的关系.将Hojman定理推广并应用于事件空间中的非Chetaev型非完整约束系统,得到Hojman守恒量.并举出一例说明结论的应用. 关键词： 事件空间 非Chetaev型非完整约束系统 对称性 Hojman守恒量     

事件空间中非Chetaev型非完整系统的Mei对称性与Mei守恒量

研究了事件空间中非Chetaev型非完整系统的Mei对称性和Mei守恒量.给出了事件空间中非Chetaev型非完整系统的运动微分方程、Mei对称性的定义和判据、Mei对称性直接导致的Mei守恒量的条件以及Mei守恒量的形式.并举例说明了结论的应用.     

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.     

Mei Symmetry and New Conserved Quantity of Tzenoff Equations for Holonomic Systems

A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example.     

完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量

研究了完整力学系统Tzénoff方程Mei对称性直接导致的另一种守恒量,给出了这种守恒量的函数表达式和导致这种守恒量的确定方程.利用该方法比以往更易找到守恒量.最后举例说明了新结果的应用.