广义Raitzin正则方程的Hojman守恒定理

利用时间不变的无限小变换下的Lie对称性，研究广义经典力学中Raitzin正则方程的Hojman 守恒定理。建立广义Raitzin正则方程。给出无限小变换下Lie对称性的确定方程。建立系统的Hojman守恒定理，并举例说明结果的应用。     

非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量

研究非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量.列出系统的Raitzin正则方程.提出在无限小变换下系统形式不变性的定义和判据.给出系统的形式不变性是Lie对称性的充要条件.建立Hojman守恒定理，并举例说明结果的应用. 关键词： 非保守系统 Raitzin正则方程 形式不变性 非Noether守恒量     

变质量完整力学系统的非Noether守恒量

利用时间不变的无限小变换下的Lie对称性,研究变质量完整力学系统的一类新的守恒量.给出系统的运动微分方程,研究时间不变的无限小变换下的Lie对称性确定方程,将Hojman定理推广并应用于这类系统 关键词： 变质量系统 完整约束 确定方程 非Noether守恒量     

准坐标下完整力学系统的非Noether守恒量——Hojman定理的推广

利用时间不变的无限小变换下的Lie对称性，研究准坐标下完整力学系统的一类新守恒量.建立系统的运动微分方程，给出无限小变换下的Lie对称性确定方程.将Hojman定理推广，并举例说明结果的应用. 关键词： 准坐标 完整力学系统 Lie对称性 非Noether守恒量 Hojman定理     

相空间中变质量力学系统的Hojman守恒量

研究一般的无限小变换下相空间中变质量力学系统Lie对称性的Hojman守恒量. 给出了相空 间中变质量力学系统Lie 对称性的确定方程和Hojman守恒量定理,并举例说明结果的应用. 关键词： 相空间 变质量系统 一般的无限小变换 Lie对称性 Hojman守恒量     

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     

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     

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     

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.     

Non-Noether Conserved Quantity of Nonholonomic System Having Variable Mass and Unilateral Constraints

Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman‘s conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.     

On Form Invariance, Lie Symmetry and Three Kinds of Conserved Quantities of Generalized Lagrange''''s Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

On Form Invariance,Lie Symmetry,and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

Generalized Conformal Symmetries and Its Application of Hamilton Systems

In this paper the generalized conformal symmetries and conserved quantities by Lie point transformations of Hamilton systems are studied. The necessary and sufficient conditions of conformal symmetry by the action of infinitesimal Lie point transformations which are simultaneous Lie symmetry are given. This kind type determining equations of conformal symmetry of mechanical systems are studied. The Hojman conserved quantities of the Hamilton systems under infinitesimal special transformations are obtained. The relations between conformal symmetries and the Lie symmetries are derived for Hamilton systems. Finally, as application of the conformal symmetries, an illustration example is introduced.     

Hojman Conservation Laws for Relativistic Birkhoffian System

For a relativistic Birkhoman system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhottian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results.     

Hojman Conservation Laws for Relativistic Birkhoffian System

For a relativistic Birkhoffian system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhoffian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. 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.