A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.

Two New Types of Conserved Quantities of Mei Symmetry for Holonomic Mechanical System

保存数量的二种新类型直接由 holonomic 的 Mei 对称推断机械系统被学习。为 holonomic 系统的 Mei 对称的定义和标准被给。协作功能被介绍， Mei 对称能直接在下面导致保存数量的二种类型和保存数量的二种类型的形式的条件被获得。一个解说性的例子被给。结果显示协作功能能根据计量器功能的需求适当地被选择，从而，计量器功能能更容易被发现。而且，后来，协作功能的选择有多形，为 holonomic 的 Mei 对称的更多保存数量机械系统能被获得。

A New Type of Conserved Quantity Deduced from Mei Symmetry for Relativistic Mechanical System in Phase Space

在这篇论文，间接地在阶段空格为相对论的机械系统从 Mei 对称推出的保存数量的一种新类型被学习。定义和为系统的 Mei 对称的标准被给。为存在和新保存数量的形式的条件被获得。最后，一个例子被给说明结果的申请。

A New Type of Conserved Quantity of Mei Symmetry for Relativistic Variable Mass Mechanical System in Phase Space

在这篇论文，保存数量的一种新类型直接为相对论的可变质量从 Mei 对称推断在阶段空格的系统被学习。定义和为系统的 Mei 对称的标准被给。为存在和新保存数量的形式的条件被获得。最后，一个例子被给说明结果的应用程序。

A new type of conserved quantity of Mei symmetry for Lagrange system

This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.

New conserved quantities of Noether-Mei symmetry of mechanical system in phase space

This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.

Mei symmetry and new conserved quantities of Tzénoff equations for higher-order nonholonomic system

In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantities and criterion equation which deduces these conserved quantities are presented.This result establishes the theory basis for further researches on conservation laws of Tzénoff equations of the higher-order nonholonomic constraint system.

New Conserved Quantities of Noether-Mei Symmetry for Nonholonomic Mechanical System

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanicalsystem are studied.The definition and criterion of Noether-Mei symmetry for the system are given.A coordinationfunction is introduced,and the conditions under which the Noether-Mei symmetry leads to the two types of conservedquantities and the forms of the two types of conserved quantities are obtained.An illustrative example is given.Thecoordination function can be selected according to the demand for finding the gauge function,and the choice of thecoordination function has multiformity,so more conserved quantities deduced from Noether-Mei symmetry of mechanicalsystem can be obtained.

相对运动动力学系统Nielsen方程Mei对称性导致的一种新型守恒量

研究相对运动动力学系统Nielsen方程的Mei对称性导致的一种新型守恒量.在群的无限小变换下,给出相对运动动力学系统Nielsen方程Mei对称性的定义和判据;得到相对运动动力学系统Nielsen方程Mei对称性导致的新型结构方程和新型守恒量的表达式.

Nielsen系统Mei对称性的新型守恒量

研究Nielsen系统Mei对称性的新型守恒量.在群的无限小变换下,由Nielsen系统Mei对称性的定义和判据,得到Nielsen系统Mei对称性的一种新结构方程和一种新型守恒量.

完整系统Tzénoff方程的Mei对称性对应的新守恒量

研究了完整力学系统Tzénoff方程Mei对称性所对应的一种新守恒量.给出了这种守恒量的函数表达式并导出了产生这种守恒量的判据方程.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.

非完整系统的Mei对称性直接导致的另一种守恒量

研究了非完整系统的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条件方程.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.

高阶非完整系统广义Tzénoff方程的Mei对称性导出的新守恒量

研究了高阶非完整系统广义Tzénoff方程的Mei对称性及其所导出的新守恒量,给出了这种新守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果具有一般性,为探究任意阶非完整系统广义Tzénoff方程的守恒规律奠定了理论基础.

弱非完整系统Mei对称性导致的新型精确和近似守恒量

研究弱非完整系统Lagrange方程的Mei对称性导致的一种结构方程和新型精确以及近似守恒量.首先建立系统的Lagrange方程.其次在群的无限小变换下,给出了弱非完整系统及其一次近似系统Mei对称性的定义和判据,然后得到了Mei对称性导致的新型结构方程、新型精确和近似守恒量的表达式.最后,举例研究系统的精确新型守恒量和近似新型守恒量问题.

Hamilton系统Mei对称性的一种新守恒量

研究Hamilton系统的Mei对称性直接导致的一种新守恒量.给出Hamilton系统的Mei对称性的定义和判据方程,引入谐调函数,得到系统Mei对称性直接导致新守恒量的条件和形式,并给出应用算例.结果表明,谐调函数可根据寻找规范函数的需要适当选取,从而使规范函数的寻求变得比较容易,而且由于谐调函数的选取具有多样性,因此能够找到系统Mei对称性的更多的守恒量.

非完整系统Tzénoff方程的Mei对称性所对应的一种新守恒量

研究了非完整力学系统Tzénoff方程Mei对称性所对应的一种新守恒量,给出了这种守恒量的函数表达式和导致这种守恒量的判据方程.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.

约束系统广义Tzénoff方程的Mei对称性及其对应的守恒量

以往关于约束动力学系统Tzénoff方程对称性和守恒量的研究,针对的都是一般Tzénoff方程,为了研究广义Tzénoff方程的Mei对称性和守恒量,首先建立了完整约束和非完整约束2种力学状态下的广义Tzénoff方程,给出了在群的无限小变换下Mei对称性的定义和判据,研究了Mei对称性产生守恒量的必要条件,给出了这种新守恒量的函数表达式和导出这种守恒量的条件方程,只要能找到规范函数满足条件方程,那么该系统就一定存在这种新守恒量.