Unified Symmetry of Nonholonomic Mechanical Systems with Non-Chetaev＇s Type Constraints

Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev＇s type constraints is studied. The definition and criterion of the unified symmetry of nonholonomic mechanical systems with non-Ohetaev＇s type constraints are given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. Two examples are given to illustrate the application of the results.     

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.     

Lie-form invariance of nonholonomic mechanical systems

The Lie-form invariance of a nonholonomic mechanical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechanical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. 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     

Unified Symmetry of Nonholonomic System of Non-Chetaev＇s Type with Variable Mass in Event Space

The unified symmetry of a nonholonomic system of non-Chetaev＇s type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced from the unified symmetry of the nonholonomic system of non-Chetaev＇s type with variable mass in event space at one time. An example is given to illustrate the application of the results.     

Unified Symmetry of Nonholonomic System of Non-Chetaev's Type in Event Space

The unified symmetry of a nonholonomic system of non-Chetaev's type in event space under infinitesimal transformations of group is studied.Firstly,the differential equations of motion of the system are given.Secondly,the definition and the criterion of the unified symmetry for the system are obtained.Thirdly,a new conserved quantity,besides the Noether conserved quantity and the Hojman conserved quantity,is deduced from the unified symmetry of a nonholonomic system of non-Chetaev's type.Finally,an example is given to illustrate the application of the result.     

Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.     

Unified Symmetry of Nonholonomic Mechanical Systems of Non-Chetaev＇s Type with Unilateral Constraints

The definition and the criterion for a unified symmetry of nonholonomic mechanical systems of non- Chetaev＇s type with unilateral constraints are presented based on the total time derivative along the trajectory of the system. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced froth the unified symmetry, is obtained. An example is given to illustrate the application of the results.     

非Chetaev型非完整可控力学系统的Noether-形式不变性

基于函数对时间的全导数采用沿系统的运动轨线方式, 研究非Chetaev型非完整可控力学系统的Noether-形式不变性. 给出非Chetaev型非完整可控力学系统的Noether-形式不变性的定义和判据. 由Noether-形式不变性同时得到了Noether守恒量和新型守恒量. 并举例说明结果的应用. 关键词： 非Chetaev型非完整系统 可控力学系统 Noether-形式不变性 守恒量     

具有非Chetaev型非完整约束的机电系统的统一对称性

研究具有非Chetaev型非完整约束的机电系统的统一对称性. 由系统的Lagrange-Maxwell方程, 给出系统的统一对称性的定义和判据, 得到了系统的统一对称性导出的Noether守恒量、Hojman守恒量和Mei守恒量. 举例说明结果的应用. 关键词： 非Chetaev型约束系统 机电系统 统一对称性 守恒量     

非Chetaev型非完整系统的Lagrange对称性与守恒量

研究非Chetaev型非完整非保守力学系统的Lagrange对称性.给出了系统的Lagrange对称性的定义和判据,得到了非Chetaev型非完整非保守力学系统的Lagrange对称性导致守恒量（第一积分)的条件及其形式.举例说明结果的应用. 关键词： 非Chetaev型非完整约束 Lagrange对称性 守恒量     

A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.     

Unified symmetry of the nonholonomic system of non-Chetaev type with unilateral constraints in event space

This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equations of motion of the system. Secondly, it obtains the definition and the criterion of the unified symmetry for the system. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints. Finally, 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     

变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量

研究了变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性和守恒量.在群的无限小变换下,定义了变质量Chetaev型非完整系统Appell方程Mei对称性和共形不变性,给出了该系统Mei对称性的共形不变性确定方程,并推导出系统相应的守恒量表达式.最后,给出了应用算例.     

非完整力学系统的非Noether守恒量——Hojman守恒量

研究非完整力学系统的非Noether守恒量——Hojman守恒量. 在时间不变的特殊Lie对称变换下，给出非完整力学系统的Lie对称性确定方程、约束限制方程和附加限制方程，得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出一个例子说明本文结果的应用. 关键词： 分析力学 非完整系统 Lie对称性 非Noether守恒量     

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained. An example is given to illustrate the application of the results.     

Mei Symmetry and Hojman Conserved Quantity of Nonholonomic Controllable Mechanical System

A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical system, is presented. Under general infinitesimal transformations, the determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the corresponding holonomic mechanical system, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomic controllable mechanical system are obtained. An example is given to illustrate the application of the results.     

Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system

A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.     

非完整系统的Noether对称性与Hojman守恒量

研究非完整力学系统的Noether对称性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下，给出系统的特殊Noether对称性与守恒量，并给出特殊Noether对称性导致特殊Lie对称性的条件. 由系统的特殊Noether对称性，得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出一个例子说明本结果的应用 关键词： 分析力学 非完整系统 Noether对称性 非Noether守恒量 Hojman守恒量