相空间中单面完整约束力学系统的对称性与守恒量

在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程；给出了系统的Norther对称性，Lie对称性和Mei对称性的判据；研究了三种对称性之间的关系；得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量，研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用. 关键词： 分析力学 单面约束 对称性 守恒量 相空间     

广义经典力学系统的对称性与Mei守恒量

研究广义经典力学系统的对称性和一类新型守恒量——Mei守恒量.在高维增广相空间中建立 了系统的运动微分方程；给出了系统的Mei对称性、Noether对称性和Lie对称性的判据；得 到了分别由三种对称性导致Mei守恒量的条件和Mei守恒量的形式.举例说明结果的应用. 关键词： 广义经典力学 Mei对称性 Noether对称性 Lie对称性 守恒量     

相对论性转动变质量非完整可控力学系统的非Noether守恒量

研究相对论性转动变质量非完整可控力学系统的非Noether守恒量——Hojman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Mei对称性(形式不变性) 和Lie对称性的定义和判据, 以及系统的Mei对称性是Lie对称性的充分必要条件. 得到了系统Mei对称性导致非Noether守恒量的条件和具体形式. 举例说明结果的应用. 关键词： 相对论性转动 可控力学系统 变质量 非Noether守恒量     

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.     

Symmetries and Mei Conserved Quantities of Nonholonomic Controllable Mechanical Systems

This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.     

Symmetries and Mei Conserved Quantities of Nonholonomic Controllable Mechanical Systems

This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.     

Symmetries and Mei Conserved Quantities for Nonholonomic Systems with Servoconstraints

This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantities for Nonholonomic Systems with Servoconstraints. The criterions of the Mei symmetry, the Noether symmetry, and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the appfication of the results.     

单面非Chetaev型非完整约束系统的非Noether守恒量

研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程；给出了系统的Lie对称性和Mei对称性的定义和判据；对于单面非Chetaev型非完整系统，证明了在一定条件下，由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量，由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量；研究了对称性和新守恒量之间的相互关系.文末，举例说明结果的应用. 关键词： 分析力学 单面约束 非完整系统 对称性 Hojman守恒量 Mei守恒量     

Mei Symmetry and Conserved Quantity of Tzenoff Equations for Nonholonomic Systems of Non-Chetaev＇s Type

Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.     

Lieben Mei symmetry and conserved quantities of the Rosenberg problem

The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.     

Mei symmetry and generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints

This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.     

Symmetries and Two Types of Non-Noether Conservation Laws of Birkhoffian System with Unilateral Constraints

The symmetries and non-Noether conservation laws of Birkhoffian system with unilateral constraints are studied. The differential equations of motion of the system are established, and the criterions of Noether symmetry, Lie symmetry and Mei symmetry of the system are given. Two types of new conservation laws, called the Hojman conservation law and the Mei conservation law respectively, are obtained, and the intrinsic relations among the symmetries and the new conservation laws are researched. At the end of the paper, an example is given to illustrate the application of the results.     

带有附加项的广义Hamilton系统的Mei对称性

研究带附加项的广义Hamilton系统的Mei对称性的定义和判据，给出系统Mei对称性为Lie对称性的充分必要条件. 通过Lie对称性间接导出具有Mei对称性且带有附加项的广义Hamilton系统运动微分方程的Hojman守恒量. 举例说明结果的应用. 关键词： 附加项 广义Hamilton系统 Mei对称性 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     

Symmetry and Hojman Conserved Quantity of Tzénoff Equations for Unilateral Holonomic System

Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformations of groups is investigated. Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoff equations are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetry in the condition of special Mei symmetry respectively is obtained.     

Lagrange系统在施加陀螺力后的对称性

研究Lagrange系统在施加陀螺力后的Noether对称性与Lie对称性.给出系统在施加陀螺力后 ，可保持其Noether对称性与Noether守恒量的条件.给出系统在施加陀螺力后，可保持其Lie 对称性与Hojman守恒量的条件.最后，举例说明结果的应用. 关键词： Lagrange系统 陀螺力 对称性 守恒量     

Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space

In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.     

Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space

In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.     

Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system

In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given.Meanwhile,an example is discussed to illustrate the application of the results.The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.     

规范变换对Birkhoff系统对称性的影响

研究Birkhoff系统规范变换对其Noether对称性、Lie对称性和Mei对称性的影响.在一定条件下,Noether对称性和守恒量不改变.Lie对称性和Hojaman守恒量仍保持不变.Mei对称性和新型守恒量可能变化,得到了Mei对称性和新型守恒量保持不变的条件.举例说明结果的应用. 关键词： Birkhoff系统 规范变换 对称性 守恒量