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     

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.     

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     

单面Chetaev型非完整系统的共形不变性、Noether对称性和Lie对称性

研究单面Chetaev型非完整系统在无限小变换下的共形不变性及其与Noether对称性和Lie对称性的关系. 首先,给出了单面Chetaev型非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;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.最后分别举例说明了结果的应用.     

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     

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     

事件空间中完整系统的Hojman守恒量

研究事件空间中完整力学系统由特殊Lie对称性、Noether对称性和形式不变性导致的Hojman守恒量.列出系统的运动微分方程.给出Lie对称性、Noether对称性和形式不变性的判据，以及三种对称性之间的关系.将Hojman定理推广并应用于事件空间完整系统，得到非Noether守恒量.举例说明结果的应用. 关键词： 分析力学 完整系统 事件空间 对称性 Hojman守恒量     

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.     

广义线性非完整力学系统的Hojman守恒量

研究广义线性非完整力学系统的Lie对称性导致的Hojman守恒量,在时间不变的特殊Lie对称变换下,给出系统的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守恒量以及广义线性非完整力学系统的弱Hojman守恒量和强Hojman守恒量,并举一算例说明结果的应用.     

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     

Special Lie Symmetry and Hojman Conserved Quantity of Appell Equations for a Holonomic System

Special Lie symmetry and Hojman conserved quantity of Appell equations for a holonomic system are studied. Appell equations and differential equations of motion for holonomic mechanic systems are established. Under special Lie infinitesimal transformations in which the time is invariable, the determining equation of the special Lie symmetry and the expressions of Hojman conserved quantity for Appell equations of holonomic systems are presented. Finally, 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.     

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 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.     

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 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 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.     

Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion

Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.     

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.