Application of vibrational control to linear-quadratic control problems

The application of the theory of vibrational control to linear-quadratic control problems is developed. The solution of the matrix Riccati differential equation (RDE) and the optimal trajectory are found approximately as power series of a small parameter. The minimizing effect of vibrations on the maximal solution of RDE and the cost functional is studied. The region of attraction of the maximal solution of RDE for the case of Hamiltonian matrix with imaginary axis eigenvalues is found. Special attention is paid to the application of vibrations to the linear-quadratic problem of stabilization with respect to a part of variables and transfer of the other variables to a given position. A problem of vibrational stabilization and optimal control of a carriage with an inverted pendulum is solved as an example.     

对CMOS门电路的物理参数基于理想化的分析

以CMOS门电路元件产品为例，提出了如何从理想化出发，对元件产品的物理参数进行设定与正确解读．讨论表明该分析方法可以澄清一些以往对参数的误解，并能有助于指导该型元件产品的正确应用。     

Calculation of curved open channel flow using physical curvilinear non‐orthogonal co‐ordinates

There are two main difficulties in numerical simulation calculations using FD/FV method for the flows in real rivers. Firstly, the boundaries are very complex and secondly, the generated grid is usually very non‐uniform locally. Some numerical models in this field solve the first difficulty by the use of physical curvilinear orthogonal co‐ordinates. However, it is very difficult to generate an orthogonal grid for real rivers and the orthogonal restriction often forces the grid to be over concentrated where high resolution is not required. Recently, more and more models solve the first difficulty by the use of generalized curvilinear co‐ordinates (ξ,η). The governing equations are expressed in a covariant or contra‐variant form in terms of generalized curvilinearco‐ordinates (ξ,η). However, some studies in real rivers indicate that this kind of method has some undesirable mesh sensitivities. Sharp differences in adjacent mesh size may easily lead to a calculation stability problem oreven a false simulation result. Both approaches used presently have their own disadvantages in solving the two difficulties that exist in real rivers. In this paper, the authors present a method for two‐dimensional shallow water flow calculations to solve both of the main difficulties, by formulating the governing equations in a physical form in terms of physical curvilinear non‐orthogonal co‐ordinates (s,n). Derivation of the governing equations is explained, and two numerical examples are employed to demonstrate that the presented method is applicable to non‐orthogonal and significantly non‐uniform grids. Copyright © 2004 John Wiley & Sons, Ltd.     

利用线化和校正法求非线性单摆运动的周期

应用线化和校正方法,研究了单摆的非线性振动,作出了周期比和相对误差随摆角的变化曲线.将所得近似解与精确解比较可知,该方法具有简单实用,精度高,相对误差低等优点,对于求解非线性振动问题具有一定的实用价值.     

带电导体球表面处的电场强度

通过带电导体球阐述了面电荷所在处的电场强度并且对分别采用的面和壳物理模型的结果进行了比较。     

物理实验微机数据处理系统

本文介绍了物理实验微机数据处理软件及编制的技术要点，并对微机应用于物理实验辅助教学的前景进行了探讨。     

物理实验教学内容高新化趋势的探索和尝试

适应高等教育教学改革大趋势，结合本院专业特点，对大学物理实验教学内容高新化进行了初步探索和尝试，收到了良好的效果。     

Bound Motion of Bodies and Paticles in the Rotating Systems

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton “feels” the Coriolis force caused by the rotation of the Earth.     

将"物理思想"融入物理实验教学改革的探索与实践

从当前物理实验教学改革、培养有创新能力工程技术人才的角度,论述了理解物理实验中的物理思想和认识它的重要性。     

物理实验选修课的教学方法研究

介绍了开放实验室开设物理实验选修课的方法。