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     

广义Hojman定理

研究利用Lie对称的生成元τ(t,q,q·)和ξ_s(t,q,q·)来构造广义H ojman守恒 量，并讨论三种特殊情况，研究表明：Hojman守恒量是该广义守恒量的特例，且在Lie对称 的生成元的形式为τ(t,q)和ξ_s(t,q)时，该广义Hojman守恒量可以导出Lu tzky守恒 量，此外，还给出一个排除平凡守恒量的条件.最后，给出两个简单例子，作为所获得结果 的说明. 关键词： 动力学系统 广义Hojman定理 Lie对称 守恒量     

The discrete variational principle and the first integrals of Birkhoff systems＊

This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.     

Lie symmetries and conserved quantities of Birkhoff systems with unilateral constraints

In this paper we study the Lie symmetries of Birkhoff systems with unilateral constraints.We give the conditions for,and the form of,conserved quantities due to the Lie symmetries of the systems.and we also study the inverse problem of the Lie symmetries of the systems.Finally,an example is given to illustrate the application of the results.     

非惯性参照系中的伯努利方程

一般非惯性参照系可分解为加速平动参照系和转动参照系。给出这两种参照系中理想流失满足的动力学方程，可解决非惯性参照系中的流体动力学问题。     

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     

相对论Birkhoff系统的第一积分与积分不变量的构造

建立了相对论Birkhoff系统的变分方程,由此证明:由已知系统的一个第一积分,可以构造系统的一个积分不变量,并通过算例说明其结果的应用.     

Noether's theory of Lagrange systems in discrete case

In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations, such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.     

Hojman's theorem of the third-order ordinary differential equation

This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results.     

Birkhoff系统的一般Lie对称性和非Noether守恒量

研究Birkhoff系统的一般Lie对称性导致的非Noether守恒量。得到非Noether守恒量的存在定理,举例说明结果的应用。