一维减幅-增幅谐振子的守恒量与对称性

从一维减幅-增幅谐振子的运动微分方程出发得到系统的运动积分常数,从而得到系统的Lagrange函数和Hamilton函数,再根据Hamilton函数的形式假定守恒量的形式,由Poisson括号的性质得到了系统的三个守恒量,并讨论与三个守恒量相应的无限小变换的Noether对称性与Lie对称性.还对守恒量与对称性的物理意义作了合理的解释. 关键词： 一维减幅-增幅谐振子 守恒量 Noether对称性 Lie对称性     

Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.     

Unified symmetry of non-holonomic singular systems

In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. 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.     

Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results.     

Mei Symmetry of General Discrete Holonomic System

The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in this paper. The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry. The criterion when a conserved quantity may be obtained from Mei symmetry is also deduced. An example is discussed for applications of the results.     

Symmetry of Lagrangians of a holonomic variable mass system

The symmetry of Lagrangians of a holonomic variable mass system is studied.Firstly,the differential equations of motion of the system are established.Secondly,the definition and the criterion of the symmetry of the system are presented.Thirdly,the conditions under which there exists a conserved quantity deduced by the symmetry are obtained.The form of the conserved quantity is the same as that of the constant mass Lagrange system.Finally,an example is shown to illustrate the application of the result.     

Lie-Form Invariance of a Type of Non-holonomic Singular Systems

In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

Form Invariance and Conserved Quantity for Non-holonomic Systems with Variable Mass and Unilateral Constraints

The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints.Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations,this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints.The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced.An example is given to illustrate the application of the results.     

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application 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     

准坐标下一般完整系统的统一对称性

研究准坐标下完整力学系统在时间不变的无限小变换下的统一对称性. 列出系统的运动微分方程, 给出系统的统一对称性的定义和判据, 由系统的统一对称性导出Noether守恒量、Hojman守恒量和一类新型守恒量. 举例说明结果的应用. 关键词： 准坐标 完整系统 统一对称性 守恒量     

事件空间中单面非Chetaev型非完整约束系统的Mei守恒量

研究事件空间中单面非Chetaev型非完整系统的Mei对称性和Mei守恒量.建立系统的运动微分方程,给出系统Mei对称性、弱Mei对称性、强Mei对称性的定义和判据,得到系统Mei守恒量的存在条件以及Mei守恒量的表达式.举例说明结论的应用.     

Generalized Lutzky Conserved Quantities of Holonomic Systems with Remainder Coordinates Subjected to Unilateral Constraints

This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given.The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and an example is given to illustrate the application of the results.     

相空间中相对运动完整力学系统的共形不变性与守恒量

研究了相空间中相对运动完整力学系统的共形不变性与守恒量.给出了该系统共形不变性的定义,并推导出相空间中相对运动完整力学系统的运动微分方程具有共形不变性并且是Lie对称性的充分必要条件.利用规范函数满足的结构方程导出该系统相应的守恒量,并给出应用算例.     

相对运动动力学系统的Lagrange对称性

研究相对运动动力学系统的Lagrange对称性.给出系统Lagrange对称性的定义和判据.找到这类对称性导致的守恒量的条件和形式.举例说明结果的应用. 关键词： 相对运动动力学 Lagrange对称性 守恒量     

相对运动变质量完整系统的共形不变性与守恒量

研究了相对运动变质量完整系统的共形不变性与守恒量,提出了该系统共形不变性的概念,推导出了相对运动变质量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,借助规范函数满足的结构方程导出系统相应的守恒量,并给出应用算例. 关键词： 变质量 相对运动 共形不变性 守恒量     

Unified symmetry of the nonholonomic system of non-Chetaev type with unilateral constraints in event space

This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equations of motion of the system. Secondly, it obtains the definition and the criterion of the unified symmetry for the system. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints. Finally, an example is given to illustrate the application of the results.