机电系统Mei对称性导致的另一种守恒量

研究机电系统Mei对称性导致的另一种守恒量.在群的无限小变换下,给出机电系统的Mei对称性的定义和判据,得到机电系统Mei对称性导致的另一种守恒量.举例说明结果的应用. 关键词： 机电系统 Mei对称性 守恒量     

Lagrange系统Mei对称性的Ⅲ型结构方程和Ⅲ型Mei守恒量

研究Lagrange系统Mei对称性的Ⅲ型结构方程和Ⅲ型Mei守恒量.在群的无限小变换下,由Lagrange系统Mei对称性的定义和判据,得到Lagrange系统Mei对称性的Ⅲ型结构方程和Ⅲ型Mei守恒量.举例说明结果的应用.     

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. 关键词： Hamilton系统 Mei对称性 新守恒量     

关于Lagrange系统和Hamilton系统的Mei对称性

对Lagrange 系统和Hamilton系统Mei对称性的研究表明，Mei对称性的两种表述对Lagrange系统是等价的，给出一类Mei对称性，而对Hamilton系统不等价，给出两类Mei对称性. 关键词： Lagrange系统 Hamilton系统 Mei对称性 守恒量     

Appell方程Mei对称性导致的一种新型守恒量

研究完整系统Appell方程Mei对称性导致的一种新型守恒量.首先,给出完整系统Appell方程Mei对称性的定义和判据.其次,得到用Appell函数表示的完整系统Appell方程Mei对称性导致的一种新型守恒量.最后,举例说明由所得结果可找到新的守恒量.     

相对运动动力学系统Appell方程Mei对称性导致的Mei守恒量

研究相对运动动力学系统Appell方程的Mei对称性及其直接导致的Mei守恒量.在群的无限小变换下,给出相对运动动力学系统Appell方程Mei对称性的定义和判据;得到相对运动动力学系统Appell方程Mei对称性的结构方程以及Mei对称性直接导致的Mei守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Appell方程 Mei对称性 Mei守恒量     

非完整系统Nielsen方程的Mei对称性与Mei守恒量

研究了Chetaev型非完整非保守系统带乘子的Nielsen方程的Mei对称性和Mei守恒量-对Chetaev型非完整非保守系统带乘子的Nielsen方程的运动微分方程、Mei对称性的定义和判据、Mei对称性直接导致的Mei守恒量的条件以及守恒量的形式进行了具体的研究-举例说明结果的应用- 关键词： 非完整系统 Nielsen方程 Mei对称性 Mei守恒量     

Nielsen方程Mei对称性导致的一种新型守恒量

研究完整系统Nielsen方程Mei对称性导致的一种新型守恒量.在群的无限小变换下,由Nielsen方程Mei对称性的定义和判据,得到完整系统Nielsen方程Mei对称性导致的新型结构方程和新型守恒量.举例说明结果的应用. 关键词： Nielsen方程 Mei对称性 新型结构方程 新型守恒量     

一般完整力学系统Mei对称性的一种守恒量

研究一般完整力学系统的Mei对称性直接导致的一种守恒量,给出系统的Mei对称性的定义和判据方程,得到系统Mei对称性直接导致的一种守恒量的条件和形式,并举例说明结果的应用.     

一类完整系统的Mei对称性与守恒量

对一类完整系统的方程给出其Mei对称性的定义和判据.如果Mei对称性是Noether对称性,则可找到Noether守恒量.如果Mei对称性是Lie对称性,则可找到Hojman型守恒量.举例说明结果的应用. 关键词： 分析力学 完整系统 Mei对称性 守恒量     

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.     

A generalized Mei conserved quantity and Mei symmetry of Birkhoff system

This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system. The conditions under which the Mei symmetry can directly lead to generalized Mei conserved quantity and the form of generalized Mei conserved quantity are given. An example is given to illustrate the application of the results.     

广义Hamilton系统的Mei对称性导致的Mei守恒量

研究广义Hamilton系统的Mei对称性导致的守恒量. 首先,在群的一般无限小变换下给出广义Hamilton系统的Mei对称性的定义、判据和确定方程;其次,研究系统的Mei守恒量存在的条件和形式,得到Mei对称性直接导致的Mei守恒量; 而后,进一步给出带附加项的广义Hamilton系统Mei守恒量的存在定理; 最后,研究一类新的三维广义Hamilton系统,并研究三体问题中3个涡旋的平面运动. 关键词： 广义Hamilton系统 Mei对称性 Mei守恒量 三体问题     

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.     

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.