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.     

相对运动变质量完整系统的共形不变性与守恒量

研究了相对运动变质量完整系统的共形不变性与守恒量,提出了该系统共形不变性的概念,推导出了相对运动变质量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,借助规范函数满足的结构方程导出系统相应的守恒量,并给出应用算例. 关键词： 变质量 相对运动 共形不变性 守恒量     

变质量完整系统的共形不变性和Noether对称性及Lie对称性

研究变质量完整系统在无限小变换下的共形不变性与Noether对称性和Lie对称性.首先,给出了变质量完整系统的共形不变性的定义;其次,研究了系统的共形不变性与Noether对称性之间的关系,得到了共形不变性导致的Noether守恒量;最后,研究了系统的共形不变性与Lie对称性之间的关系,得到了共形不变性同时是Lie对称性导致的Hojman守恒量.最后举例说明了结果的应用.     

变质量完整动力学系统的共形不变性与守恒量

研究变质量完整力学系统在无限小变换下微分方程的共形不变性.提出了该系统共形不变性的概念,推导出变质量完整力学系统运动微分方程具有共形不变性,同时又是Lie对称性的充分必要条件.得到由共形不变性导致的Noether守恒量. 关键词： 变质量系统 无限小变换 共形不变 守恒量     

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.     

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 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

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.     

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 Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are 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.     

Lagrange系统Lie点变换下的共形不变性与守恒量

研究Lagrange系统Lie点变换下的共形不变性与守恒量,给出Lagrange系统的共形不变性定义和确定方程,讨论系统共形不变性与Lie对称性的关系,得到在无限小单参数点变换群作用下系统共形不变性同时是Lie对称性的充要条件,导出系统相应的守恒量,并给出应用算例. 关键词： Lagrange系统 Lie点变换 共形不变性 守恒量     

一般完整系统Mei对称性的共形不变性与守恒量

研究一般完整系统Mei对称性的共邢不变性与守恒量.引入无限小单参数变换群及其生成元向量,定义一般完整系统动力学方程的Mei对称性共形不变性,借助Euler算子导出Mei对称性共形不变性的相关条件,给出其确定方程.讨论共形不变性与Noether对称性、Lie对称性以及Mei对称性之间的关系.利用规范函数满足的结构方程得到系统相应的守恒量.举例说明结果的应用. 关键词： 一般完整系统 Mei对称性 共形不变性 守恒量     

Conformal invariance and conserved quantity of Hamilton systems

This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.     

Conformal Invariance and Noether Symmetry,Lie Symmetry of Birkhoffian Systems in Event Space

This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

相空间中相对运动完整力学系统的共形不变性与守恒量

研究了相空间中相对运动完整力学系统的共形不变性与守恒量.给出了该系统共形不变性的定义,并推导出相空间中相对运动完整力学系统的运动微分方程具有共形不变性并且是Lie对称性的充分必要条件.利用规范函数满足的结构方程导出该系统相应的守恒量,并给出应用算例.     

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.     

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.     

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.     

相对运动变质量力学系统Appell方程的广义Lie对称性导致的广义Hojman守恒量

研究相对运动变质量完整系统Appell方程的广义Lie对称性及其直接导致的广义Hojman守恒量.在群的无限小变换下,给出相对运动变质量完整系统Appell方程广义Lie对称性的确定方程;得到相对运动变质量完整系统Appell方程广义Lie对称性直接导致的广义Hojman守恒量的表达式.最后,利用本文结果研究相对运动变质量完整约束的三自由度力学系统问题.