弱非完整系统的近似守恒量

建立弱非完整系统的运动微分方程,其中包含小参数.将无限小变换的生成元和规范函数按小参数的幂级数展开并代入系统的广义Noether等式,利用Noether定理求得系统的近似守恒量. 关键词： 弱非完整系统 Noether定理 近似守恒量     

Stability analysis of a simple rheonomic nonholonomic constrained system

It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems.     

Weak Noether symmetry for a nonholonomic controllable mechanical system

This paper discusses the weak Noether symmetry for a nonholonomic controllable mechanical system of Chetaev type, and presents expressions of three kinds of conserved quantities obtained by using weak Noether symmetry. Finally, the application of these new results is illustrated by an example.     

非完整约束奇异广义力学系统的Poincar-Cartan积分

对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系统 ,基于广义Apell_Четаев约束条件 ,并考虑到系统的内在约束 ,导出了该非完整约束奇异广义力学系统的广义Poincar _Cartan积分不变量 .并证明了该不变量与非完整约束奇异广义力学系统的广义正则方程等价     

非完整力学系统Raitzin正则方程的形式不变性

研究非完整力学系统Raitzin正则方程的形式不变性。建立系统的Raitzin正则方程。给出在无限小变换下系统形式不变性的定义和判据。得到系统的守恒量与形式不变性之间的关系并举例说明结果的应用。     

非完整约束奇异广义力学系统的Poincaré-Cartan积分

对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系 统，基于广义Apell-Четаев约束条件，并考虑到系统的内在约束，导出了该非完整 约 束奇异广义力学系统的广义Poincaré-Cartan积分不变量. 并证明了该不变量与非完整约束 奇异广义力学系统的广义正则方程等价.     

Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.     

非完整系统Nielsen方程的Mei对称性与Mei守恒量

研究了Chetaev型非完整非保守系统带乘子的Nielsen方程的Mei对称性和Mei守恒量-对Chetaev型非完整非保守系统带乘子的Nielsen方程的运动微分方程、Mei对称性的定义和判据、Mei对称性直接导致的Mei守恒量的条件以及守恒量的形式进行了具体的研究-举例说明结果的应用- 关键词： 非完整系统 Nielsen方程 Mei对称性 Mei守恒量     

Quantization of particle system with anomalous moments

A procedure is outlined for Hamiltonization of a particle system with anomalous magnetic moments and presumed electrical dipole moments, in the zero-plane formalism. Hamiltonization is undertaken in the covariant Lorentz gauge A = 0.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 78–81, September, 1987.     

非保守力与非完整约束对Lagrange系统Noether对称性的影响

研究非保守力和非完整约束对Lagrange系统的Noether对称性的影响. Lagrange系统受到非保守力或非完整约束作用时，系统的Noether对称性和守恒量都会发生变化. 原有的一些Noether对称性消失了，一些新的Noether对称性产生了，在一定条件下，一些Noether对称性仍保持不变. 分别给出系统的Noether对称性以及守恒量保持不变的条件，并举例说明结果的应用. 关键词： Lagrange系统 非保守力 非完整约束 Noether对称性     

一类特殊非完整力学系统的辛算法计算

对一类特殊的非完整力学系统的动力学性质进行数值研究,采用当前比较优越的保结构算法进行数值计算,并和传统的Runge-Kutta方法进行比较. 通过计算结果的比较而得出辛算法在这类特殊的非完整力学系统的数值计算中的优越性. 关键词： 非完整约束 辛算法 辛差分格式     

Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system

A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.     

非保守力和非完整约束对Hamilton系统Lie对称性的影响

研究非保守力和非完整约束对Hamilton系统的Lie对称性和守恒量的影响.分别研究了Hamilt on系统受到非保守力和非完整约束作用时，系统的Lie对称性保持不变的条件，同时给出了 系统的结构方程和守恒量保持不变的条件.以著名的Emden方程和Appell-Hamel模型为例进行 了分析讨论. 关键词： 分析力学 Hamilton系统 非保守力 非完整约束 对称性 守恒量     

The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system.By means of the Lagrange-Maxwell equation,the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained.The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity.Using the Noether theorem,we obtain an approximate conserved quantity.An example is provided to prove the existence of the approximate conserved quantity.     

奇异 Chetaev型非完整系统Nielsen方程的Lie-Mei对称性与守恒量

研究奇异Chetaev型非完整系统Nielsen方程的Lie-Mei对称性, 建立系统Nielsen方程的Lie-Mei对称性方程, 给出系统Nielsen方程强Lie-Mei对称性和弱Lie-Mei对称性的定义, 得到对称性导致的Hojman守恒量和Mei守恒量, 最后给出说明性算例. 关键词： 奇异非完整系统 Nielsen方程 Lie-Mei对称性 守恒量     

Quantization of a Hamiltonian system with an infinite number of degrees of freedom

We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schrödinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. Rigorous mathematical methods are used.     

Conservation laws of nonconservative nonholonomic system based on Herglotz variational problem

The generalized variational principle of Herglotz type provides a variational method for describing nonconservative or dissipative processes. The purpose of this letter is to extend this variational principle to a first order linear nonholonomic system and study the conservation laws of the nonconservative nonholonomic system based on Herglotz variational problem. A new differential variational principle of the nonconservative nonholonomic system is proposed, which is based on Herglotz variational problem. And the differential equations of motion of the system are also obtained. Then, according to the condition for the invariance of the differential variational principle, the conservation theorem based on Herglotz variational problem for the nonconservative nonholonomic system are obtained. The theorem contains the conservation theorem of the nonconservative holonomic system as its special case, which can be reduced to the first Noether's theorem based on Herglotz variational problem under proper conditions. The inverse theorem of the conservation theorem is also provided and proved. An example is given to illustrate the application at the end of this letter.     

变质量非完整系统的Lagrange对称性与守恒量

本文研究变质量非完整系统的Lagrange对称性, 给出变质量非完整系统Lagrange对称性的判据, 得到变质量非完整系统Lagrange对称性导致的守恒量及其存在的条件, 并举例说明结果的应用.     

二维方形量子点体系等离激元的量子化

量子点体系等离激元的研究是光电子学领域的热点.为进一步加深和完善对等离激元的量子效应的认识,本文利用紧束缚近似和线性响应理论研究了二维方形量子点体系对外场的集体响应.结果表明,当外场频率等于等离激元的频率时,量子点体系会有强烈的电荷振荡,并伴随着能量的极大吸收和近场的增强.在量子点中,等离子体存在分立的元激发.等离子体元激发的个数将随着量子点尺寸和电子个数的增加而增加.随量子点尺寸的增加,分立的等离激元将逐步呈现准连续的特性,即过渡为经典连续的等离激元,其频谱曲线演化为经典的色散曲线.结果还表明:随量子点尺寸的增加,等离激元的频率会红移,等离激元的激发强度会增大;随量子点中电子数的增加,等离激元的频率会蓝移,等离激元的激发强度会增大.