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

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanical system are studied. 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.     

相空间中变质量力学系统Lie-Mei对称性的两个守恒量

研究相空间中变质量力学系统Lie-Mei对称性导致的两个守恒量,给出系统Lie-Mei对称性的定义和判据,引入谐调函数,得到系统Lie-Mei对称性导致的两个守恒量的条件和形式,并给出应用算例. 由于谐调函数可根据寻找规范函数的需要适当选取,且选取具有多样性,因此能够找到系统Lie-Mei对称性更多的守恒量. 关键词： 相空间 变质量系统 Lie-Mei对称性 守恒量     

Two New Types of Conserved Quantities Deduced from Noether Symmetry for Nonholonomic Mechanical System

For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.     

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     

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.     

Noether-Mei Symmetry of Mechanical System in Phase Space

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the application of the results.     

Two Types of New Conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space

In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the results.     

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.     

Noether-Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.     

单面非Chetaev型非完整约束系统的非Noether守恒量

研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程；给出了系统的Lie对称性和Mei对称性的定义和判据；对于单面非Chetaev型非完整系统，证明了在一定条件下，由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量，由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量；研究了对称性和新守恒量之间的相互关系.文末，举例说明结果的应用. 关键词： 分析力学 单面约束 非完整系统 对称性 Hojman守恒量 Mei守恒量     

Chetaev型约束力学系统Appell方程的Lie对称性与守恒量

研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用. 关键词： Appell方程 Chetaev 型约束力学系统 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.     

相空间中单面完整约束力学系统的对称性与守恒量

在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程；给出了系统的Norther对称性，Lie对称性和Mei对称性的判据；研究了三种对称性之间的关系；得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量，研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用. 关键词： 分析力学 单面约束 对称性 守恒量 相空间     

Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems

In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.     

Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems

In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.     

非完整系统的共形不变性导致的新型守恒量

研究了非完整系统的共形不变性与新型守恒量.提出了该系统共形不变性的概念;得出了非完整系统的运动微分方程具有共形不变性并且是Lie对称性的充要条件.利用规范函数满足的新型结构方程,导出系统相应的新型守恒量.最后给出应用算例.     

离散差分变分Hamilton系统的Lie对称性与Noether守恒量

研究离散差分Hamilton系统的Lie对称性与Noether守恒量. 根据扩展的时间离散力学变分原理构建Hamilton系统的差分动力学方程.定义离散系统运动差分方程在无限小变换群下的不变性为Lie对称性, 导出由Lie对称性得到系统离散Noether守恒量的判据. 举例说明结果的应用. 关键词： 离散力学 差分Hamilton系统 Lie对称性 Noether守恒量     

Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space

Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetaev type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetaev type in the event space. An example is given to illustrate the application of the results.     

Conformal invariance and conserved quantities of a general holonomic system with variable mass

Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal one-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.     

相空间中力学系统的Lie-Mei对称性

研究了相空间中力学系统的一种新对称性——Lie-Mei对称性及其守恒量. 提出这种新对称性的定义, 给出了系统Lie-Mei对称性的判据, 得到了系统Lie-Mei对称性导致的广义Hojman守恒量和Mei守恒量. 举例说明了结果的应用. 关键词： 相空间 力学系统 Lie-Mei对称性 守恒量