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.     

Lagrange系统的Lie-形式不变性

本文研究Lagrange系统的Lie-形式不变性。给出系统Lie-形式不变性的定义和判据。导出由Lie-形式不变性导致的Hojman守恒量和一类新型守恒量。最后，举例说明结果的应用.     

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 non-holonomic systems with unilateral constraints

In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, an example is presented to illustrate the application of the results.     

完整力学系统的Lie-形式不变性

研究完整力学系统Lie-形式不变性的定义与判据，给出由Lie-形式不变性导出的Noether守恒量，Hojman守恒量和Lutzky守恒量. 举例说明结果的应用. 关键词： 完整系统 Lie-形式不变性 Noether守恒量 Hojman守恒量 Lutzky守恒量     

非完整系统的形式不变性与Hojman守恒量

研究非完整力学系统的形式不变性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下，给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程，提出并定义弱（强）形式不变性的概念. 研究特殊形式不变性导致特殊Lie对称性的条件，由系统的特殊形式不变性，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. 给出两个经典例子说明结果的应用. 关键词： 分析力学 非完整系统 形式不变性 非Noether守恒量 Hojman守恒量     

Lie-Form Invariance of a Type of Non-holonomic Singular Systems

In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity 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.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

非完整力学系统Raitzin正则方程的形式不变性

研究非完整力学系统Raitzin正则方程的形式不变性。建立系统的Raitzin正则方程。给出在无限小变换下系统形式不变性的定义和判据。得到系统的守恒量与形式不变性之间的关系并举例说明结果的应用。     

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     

非完整系统Hamilton正则方程的形式不变性

研究非完整系统Hamilton正则方程的形式不变性，给出形式不变性的定义和判据，建立形式不变性和系统守恒量之间的关系，并举例说明结果的应用. 关键词： 非完整系统 Hamilton正则方程 形式不变性 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.     

Non-Noether Conserved Quantity for Relativistic Nonholonomic System with Variable Mass

Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.     

相对论性变质量非完整可控力学系统的非Noether守恒量

在时间不变的特殊无限小变换下,研究相对论性变质量非完整可控力学系统的非Noether守恒量——Hojamn守恒量.建立了系统的运动微分方程, 给出了系统在特殊无限小变换下的形式不变性(Mei对称性)的定义和判据以及系统的形式不变性是Lie对称性的充分必要条件.得到了系统形式不变性导致非Noether守恒量的条件和具体形式.举例说明结果的应用. 关键词： 相对论 非完整可控力学系统 变质量 非Noether守恒量     

Chetaev型非完整系统Mei对称性的共形不变性与守恒量

研究Chetaev型非完整系统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,给出与Chetaev型非完整系统相应的完整系统的Mei对称性共形不变性定义和确定方程.讨论系统共形不变性与Mei对称性的关系.利用限制方程和附加限制方程得到非完整系统弱Mei对称性和强Mei对称性的共形不变性.借助规范函数满足的结构方程导出系统相应的守恒量,并举例说明结果的应用.     

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.     

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.     

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.