相空间中力学系统的Lie-Mei对称性

研究了相空间中力学系统的一种新对称性——Lie-Mei对称性及其守恒量. 提出这种新对称性的定义, 给出了系统Lie-Mei对称性的判据, 得到了系统Lie-Mei对称性导致的广义Hojman守恒量和Mei守恒量. 举例说明了结果的应用. 关键词： 相空间 力学系统 Lie-Mei对称性 守恒量     

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     

相对论性力学系统的Mei对称性导致的新守恒律

研究相对论性力学系统的Mei对称性和守恒律．基于动力学函数在无限小变换下的不变性，建立了相对论性力学系统的Mei对称性的定义和判据；直接由相对论性力学系统的Mei对称性导出了一类新守恒律，给出了Mei对称性导致新守恒律的条件和新守恒律的形式，并举例说明结果的应用． 关键词： 相对论 力学系统 Mei对称性 守恒律     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 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     

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     

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     

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     

关于Lagrange系统和Hamilton系统的Mei对称性

对Lagrange 系统和Hamilton系统Mei对称性的研究表明，Mei对称性的两种表述对Lagrange系统是等价的，给出一类Mei对称性，而对Hamilton系统不等价，给出两类Mei对称性. 关键词： Lagrange系统 Hamilton系统 Mei对称性 守恒量     

Chetaev型非完整约束相对运动动力学系统Nielsen方程的Mei对称性和Mei守恒量

研究Chetaev型非完整约束相对运动动力学系统Nielsen方程的Mei对称性和Mei守恒量.对Chetaev型非完整约束相对运动力学系统Nielsen方程的运动微分方程、Mei对称性定义和判据进行具体的研究,得到了Mei对称性直接导致的Mei守恒量的表达式.最后举例说明结果的应用.     

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 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.     

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.