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.     

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     

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     

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     

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 symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results.     

离散差分序列变质量力学系统的Mei对称性

研究离散差分序列变质量力学系统的Mei对称性与守恒量.定义离散系统的差分序列方程在无限小变换群下的形式不变性为Mei对称性. 给出由Mei对称性得到守恒量的判据. 举例说明结果的应用. 关键词： 离散力学 变质量系统 Mei对称性 离散守恒量     

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.     

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     

相空间中力学系统的两类Mei对称性及守恒量

研究相空间中力学系统的两类Mei对称性及守恒量，给出相空间中力学系统的两类Mei对称性的定义，得到其确定方程及守恒量，并举例说明结果的应用. 关键词： 相空间 力学系统 Mei对称性 守恒量     

Emden方程的Mei对称性、Lie对称性和Noether对称性

研究Emden动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Emden方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一个例子说明结果的应用. 关键词： Emden动力学方程 Mei对称性 Noether对称性 Lie对称性     

Symmetry and conserved quantities of discrete generalized Birkhoffian system

The Noether symmetry,the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper.Using the difference discrete variational approach,the difference discrete variational principle of discrete generalized Birkhoffian system is derived.The discrete equations of motion of the system are established.The criterion of Noether symmetry and Mei symmetry of the system is given.The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained.Finally,an example is given to show the applications of the results.     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie对称性 守恒量     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.     

Two Types of New Conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space

In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the results.     

Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System

The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the reoativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

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.     

Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性

研究Vacco动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Vacco动力学方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一 个例子说明结果的应用. 关键词： Vacco动力学方程 Mei对称性 Noether对称性 Lie对称性 守恒量