Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.     

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

Conformal invariance and Hojman conservedquantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations

This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.     

广义Hamilton系统的共形不变性与Hojman守恒量

研究了广义Hamilton系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,找到在无限小变换下的共形不变性并且是Lie对称性的共形因子,最后导出广义Hamilton系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例. 关键词： 广义Hamilton系统 共形不变性 Hojman守恒量 确定方程     

Lagrange系统的共形不变性与Hojman守恒量

研究了一般完整Lagrange系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,并且找到在特殊无限小变换下的共形不变性并且是Lie对称性的共形因子,接下来导出Lagrange系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例. 关键词： Lagrange系统 共形不变性 Hojman守恒量 确定方程     

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system

Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transfor-mations are studied.The definition and the determining equation of conformal invariance of the system are presented.The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry un-der infinitesimal transformations is derived.Then,the condition of existence and a kind of Hojman conserved quantity are obtained.Finally,an example is given to illustrate the application of the results.     

广义Hamilton系统的共形不变性与Mei守恒量

研究广义Hamilton系统在无限小变换下的共形不变性与Mei对称性,给出系统共形不变性同时是Mei对称性的充分必要条件,得到广义Hamilton系统共形不变性导致的Mei守恒量,举例说明结果的应用.     

Conformal Invariance and a New Type of Conserved Quantities of MechanicalSystems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided.Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.     

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invariance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.     

完整系统Appell方程Lie对称性的共形不变性与Hojman守恒量

研究完整系统Appell方程Lie对称性的共形不变性与Hojman守恒量.在时间不变的特殊无限小变换下,定义完整系统动力学方程的Lie对称性和共形不变性,给出该系统Lie对称性共形不变性的确定方程及系统的Hojman守恒量,并举例说明结果的应用.     

Conformal Invariance and Conserved Quantity for?the?Nonholonomic System of Chetaev’s Type

In this paper the definition of conformal invariance and determining equation for the holonomic system which correspond to a nonholonomic system of Chetaev’s type are provided. Conformal factor expression is deduced through relationship between a system’s conformal invariance and Lie symmetry. The necessary and sufficient condition that the system’s conformal invariance would be Lie symmetry under transformations by the infinitesimal one-parameter transformation group is obtained. The conformal invariance of weak and strong Lie symmetry for the nonholonomic system of Chetaev’s type is given using restriction equations and additional restriction equations. And the system’s corresponding conserved quantity is derived with the aid of a structure equation that gauge function satisfied. Lastly, an example is taken to illustrate the application of the result.     

Conformal Invariance and Conserved Quantities of General Holonomic Systems

Conformed invariance and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described. The definition of conformal invariance and determining equation for the system are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and suttlcient condition, that conformal invariance of the system would be Lie symmetry, is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation. Lastly, an example is given to demonstrate the application of the result.     

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     

Conformal Invariance and Noether Conserved Quantities of First-Order Lagrange Systems

In this paper the conformal invariance by infinitesimal transformations of first-order Lagrange systems is discussed in detail. The necessary and sumeient conditions of conformal invariance by the action of infinitesimal transformations being Lie symmetry simultaneously are given. Then we get the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems

This paper studies conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems. The definition and the determining equation of conformal invariance for mechanico-electrical systems are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry under the infinitesimal single-parameter transformation group. The generalized Hojman conserved quantities from the conformal invariance of the system are given. An example is given to illustrate the application of the result.     

相对运动完整系统Appell方程Mei对称性的共形不变性与守恒量

研究相对运动完整系统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, 给出相对运动完整系统Appell方程的Mei对称性和共形不变性的定义, 导出系统Mei对称性的共形不变性确定方程, 重点讨论系统共形不变性和Mei对称性的关系, 然后借助规范函数满足的结构方程导出系统Mei对称性导致的Mei守恒量表达式, 最后举例说明结果的应用.     

Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry

In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system’s conformal invariance and Mei symmetry are discussed. And Appell system’s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.     

Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates

We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.     

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space 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 that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.