SYMMETRIES OF MECHANICAL SYSTEMS WITH NONLINEAR NONHOLONOMIC CONSTRAINTS

The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic constrained mechanical systems are analysed in two kinds of geometrical frameworks whose evolution equations are Routh's equations and generalized Chaplygin's equations, respectively. The Lagrangian inverse problem and the interrelation between Noether's symmetries and dynamical symmetries are briefly concerned with. Finally an illustrative example is analysed.     

CUMULANTS OF STOCHASTIC RESPONSE FOR A CLASS OF SPECIAL NONHOLONOMIC SYSTEMS

This paper studies the response cumulants for a kind of special nonholonomic systems under non-Gaussian, delta-correlated excitations. We present a new methodology for formulating the equations governing the evolution of the response cumulants of the stochastic dynamic systems. The response cumulant differential equations (CDEs) derived can be used to calculate the response cumulants for both linear and nonlinear systems. One example is given to illustrate how to use the CDEs for calculating response cumulants.     

THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS

We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.     

NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS

In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.     

正则变换与二粒子耦合体系哈密顿量的对角化技术

把耦合项为Ｃ（ａ＾１ａ２＾＋ａ２＾＋ａ１）＋Ｄ（ａ＾＋１ａ＋２＋ａ２ａ１）的Ｈａｍｉｌｔｏｎ量写成超矩阵相乘的形式，通过正则变换使其对角化。     

包含伺服约束的非完整系统的Lie对称性与守恒量

利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式. 关键词： 非完整系统 伺服约束 Lie对称性 守恒量     

EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS

After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain.     

正则方程在正则变换下形式不变的微分学证明

用单纯的微分方法证明正则方程在正则变换下形式保持不变     

一维强场模型研究中的非齐线性正则方程的辛算法

就一维强场模型,采用对称差商代替空间变量的2阶偏导数,将含有SchrÖdinger方程的初边值问题离散成"非齐线性正则方程",它的齐方程的通解和非齐方程特解都由"辛变换生成",分别采用辛格式计算.采用这种辛算法和R-K法计算了一个数值例子,并与精确解作了比较.结果表明,经长时间计算后,辛算法保持解的固有特征,而R-K法则面目全非.     

也谈正则动量算符之争

讨论了平直空间曲线坐标系中质点运动的两种不同的量子化假设，比较了它们在物理思想和实际操作上的区别和优劣。     

利用正则变换推导能量—时间不确定关系

利用Ｋｏｂｅ引入的正则变换以及Ｄｉｒａｃ的正则量子化程序，给出了推导能量－时间不确定关系的一种新方法。     

THERMODYNAMICS OF GLOBAL MONOPOLE ANTI-DE-SITTER BLACK HOLE IN GRAND CANONICAL ENSEMBLE

In this paper, we investigate the thermodynamics of the global monopole anti-de-Sitter black hole in the grand canonical ensemble following the York's formalism. The black hole is enclosed in a cavity with a finite radius where the temperature and potential are fixed. We have studied some thermodynamical properties, i.e. the reduced action, thermal energy and entropy. By investigating the stability of the solutions, we find stable solutions and instantons.     

硝棉有机膜的配方及工艺

论述红外二级串联变像管第二级屏工艺中硝棉有机膜的配方及工艺。对滴膜工艺进行改进,提高了滴膜合格率,基本上消除了荧光屏的绝化问题。     

仅含第二类约束的约束Hamilton系统的Lie对称性

研究仅含第二类约束的约束Hamilton系统的Lie对称性.建立Lie对称性的确定方程、限制方程和附加限制方程,给出由Lie对称性导致守恒量的条件及守恒量的形式 关键词： 奇异系统 正则变量 约束 Lie对称性 守恒量     

压电陶瓷材料的Hamilton体系与辛正交模型

建立了压电陶瓷材料电固耦合问题的Hamilton正则方程,并通过对全状态向量分离变量,给出了压电陶瓷材料的共轭辛正交解析解。     

BI-HAMILTONIAN REPRESENTATION,SYMMETRIES AND INTEGRALS OF MIXED HEAVENLY AND HUSAIN SYSTEMS

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain equation, formulated in a two-component form, we present recursion operators, Lax pairs of Olver–Ibragimov–Shabat type and discover their Lagrangians, symplectic and bi-Hamiltonian structure. We obtain all point and second-order symmetries, integrals and bi-Hamiltonian representations of these systems and their symmetry flows together with infinite hierarchies of nonlocal higher symmetries.     

单面约束Birkhoff系统的Noether理论

应用变换群G_r的无限小群变换的准对称性,给出了受单面约束的Brikhoff系统的Noether理论,并举例说明结果的应用. 关键词： 分析力学 单面约束Birkhoff系统 守恒量 对称性 Noether定理