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     

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic system of Chetaev’s type with variable mass

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev's type with variable mass are studied. The differential equations of motion of the Nielsen equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.     

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     

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.     

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied.Under the infinitesimal transformation of the groups,from the definition and the criterion of Mei symmetry,a type of structural equation and conserved quantity for the system by proposition 2 are obtained,and the inferences in two special cases are given.Finally,an example is given to illustrate the application of the results.     

事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性与Mei守恒量

研究事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性和Mei守恒量.建立系统的运动微分方程,给出系统Mei对称性、弱Mei对称性、强Mei对称性的定义和判据,得到由Mei对称性直接导致的Mei守恒量的存在条件以及Mei守恒量的表达式.举例说明结果的应用. 关键词： 事件空间 Nielsen方程 单面非Chetaev型非完整系统 Mei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.     

Mei Symmetry and Mei Conserved Quantity for a Non-holonomic Systemof Non-Chetaev's Type with Unilateral Constraints in Nielsen Style

Mei symmetry and Mei conserved quantity for a non-holonomic system of non-Chetaev's type with unilateral constraints in the Nielsen style are studied. The differential equations of motion for the system above are established. The definition and the criteria of Mei symmetry, conditions, and expressions of Mei conserved quantity deduced directly from the Mei symmetry are given. An example is given to illustrate the application of the results.     

完整系统Appell方程Mei对称性的共形不变性与守恒量

研究完整系统Appell方程Mei对称性的共形不变性与守恒量. 引入无限小单参数变换群及其生成元向量, 定义完整系统动力学方程的Mei对称性和共形不变性, 给出该系统Mei对称性共形不变性的确定方程. 利用规范函数满足的结构方程导出系统相应的Mei守恒量. 举例说明结果的应用. 关键词： Appell方程 Mei对称性 共形不变性 Mei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.     

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     

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.     

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.     

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investigated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.     

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     

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.     

A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints

<正>A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated.Nielsen equations and differential equations of motion for the holonomic mechanical system with unilateral constraints are established.The definition and the criterion of Mei symmetry for Nielsen equations in the holonomic systems with unilateral constraints under the infinitesimal transformations of Lie group are also given.The expressions of the structural equation and a type of new conserved quantity of Mei symmetry for Nielsen equations in the holonomic system with unilateral constraints are obtained.An example is given to illustrate the application of the results.     

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. 关键词： 弱非完整系统 Mei对称性 新型结构方程 新型守恒量     

Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints

The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.     

变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量

研究变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量.建立变质量Chetaev型非完整系统的Appell方程和系统的运动微分方程; 给出函数沿系统运动轨道曲线对时间t全导数的表示式,并在群的无限小变换下,给出变质量Chetaev型非完整系统Appell方程Mei对称性的定义和判据;得到用Appell函数表示的Mei对称性的结构方程和Mei守恒量的表达式,并举例说明结果的应用. 关键词： 变质量 非完整系统 Appell方程 Mei守恒量