运动方程

The key components in laser gyro is He-Ne ring laser, and the reciprocal action theory between light and medium is the base in studying the ring laser, use the Lamb half classical theory, and on the base of density matrix theory, the optical Brounch equation was established, which described the movement of amplifying medium atom in the ring syntonic cavity, and according to the medium polarize theory the self consistent equations was deduced, which describe the light intensity and phasic of the counter-propagating wave. On the basis of this equations, adopted the simulation software MATLAB and virtual instrument programming language LabWindows/CVI, we can do some simulated experiments in study the phenomenas such as amplify and dispersive characteristic of medium, mode pushing effection, burned hole effection and pattern competition, lock-in of frequency and the characteristic of light intensity and phasic of the counter-propagating wave in laser gyro.

激光陀螺的核心部件为He-Ne环形激光器，而掌握光与介质的相互作用理论是研究激光器的关键，采用拉姆半经典理论为主，在密度矩阵理论的基础上，推导环形谐振腔中描述He-Ne气体增益介质原子运动的光学布洛赫方程，运用介质极化理论得出描述激光陀螺反向行波的光强、位相所满足的自洽场方程组，在此基础上，运用MATLAB仿真软件和虚拟仪器编程语言LabWindows/CVI，对激光陀螺中的介质增益色散特性、频率牵引效应、烧孔效应及模竞争、闭锁效应及环激光的光强和相位特性进行仿真试验研究，并且运用全量子理论，对激光工作原理进行分析，得出二能级系统单模辐射场的光子数密度分布，得出激光场的光子统计分布，仿真激光场的动态建立过程。

A numerical simulation to the whole motion differential equation is finished, and a continuous angular displacement curve of micro reflectmirror is obtained.

通过对该模型的完整机电动力学微分方程数值求解所作的运动仿真，得到了微镜基板的连续角位移曲线，表明该装置具有良好的光束稳定特性

When effect of the lift force on the motion of particles near a plane wall is taken into account, a corresponding Fokker-Planck equation is developed.

考虑了近壁处升力对颗粒随机运动过程的影响后，建立了有升力影响时颗粒分布函数所满足的方程。

By the natural and harmonious relationship between differential forms and differential equations and between differential forms and vector analysis, we discuss the properties, which are covariant under the transformation of coordinates in the framework of differential forms, of particle motion in a central force field .

通过微分形式与微分方程和向量分析之间存在的自然而协调的关系，在微分形式框架下讨论了质点在有心力场中运动的特性并得出在坐标变换下其均是协变的

The coordinate system and the tooth trace function of the crown wheel is found by the analysis of the motion for the machine tool.

通过对机床各运动的分析构建坐标系和产形轮齿面方程。

According to the structure and motion characteristics of the spherical offset mono-cone bit, compound cylindrical coordinates were set up, and basic geometric equations and the conditions of teeth to penetrate rock for the bit were presented.

针对偏心单牙轮钻头的结构和运动特点，利用复合圆柱坐标系统的基本原理，建立了偏心单牙轮钻头几何学基本方程和牙齿对岩石的吃入条件。

The variable geometry truss mechanisms have been studied extensively and systematically by this project. The research plan has been completed all sidedly, and expected results have been obtained. Three new kinds of combination decahedrons and a new class of variable geometry truss mechanism, which is composed of an octahedron and three tetrahedrons connected in parallel form, are proposed. The position analyses for decahedrons, dodecahedrons, triple-octahedrons, combinations decahedron and a new type of structure of variable geometry truss mechanisms are presented by introducing additional extra linear displacement sensors and using resultant elimination and homotopy continuation algorithms. The method of kinematical analysis of variable geometry truss mechanisms is established.

课题组对变几何桁架机构进行了深入的研究，全面地完成了研究计划，取得了预期的成果；提出了三种新的十面体组合机构以及由一个八面体和三个四面体组成的新型变几何桁架机构的结构形式；应用结式消元、附加传感器和同伦方法等提出了十面体、十二面体、三重八面体、组合十面体和新型变几何桁架机构的位置分析方法；建立了变几何桁架机构运动分析的一般方法；建立了简洁的凯恩和拉格伦日动力学的模型；应用有限元和子结构方法，提出了变几何柞架机构弹性动力学模型，导出了逆动力学方程的显式形式；设计和研制了一台可折叠的八面体变几何杵架机构装置等。

In this paper,the diagonal Cartesian method simulating the complex boundary, together with thetreatment to wetting-drying dynamic variation of the boundary, is applied into thetwo-dimensional shallow-water flows and sediment transport mathematical modeling,and their governing equations are discretized and solved in diagonal Cartesiancoordinates.

本论文采用斜对角笛卡尔坐标方法对不规则的复杂边界进行模拟，重点处理好干湿动边界的变化，并在斜对角笛卡尔坐标系中进行二维浅水运动的水流泥沙基本控制方程的离散和数值计算求解。

Based on the flexible multibody dynamics model, that establish, a group of the algebra—differential hybrid equations which is made up of kinematics differential equation and spatial constraint algebra equations is listed by leading into the Lagrange multiplier to release the constraint of the system.

根据上述建立的多柔体动力学模型，通过引入Lagrange乘子释放系统的约束，列出了由系统的运动微分方程和空间约束代数方程组成的一组微分—代数混合方程组。

The solution can't already behalf the real movement of the constraint multibody system so the default of the constraint equation must be restrained; On the other hand is how to turn the differential — algebra hybrid equations into the pure differential equations effectively.

得到的解已经不能表示约束多体系统的真实运动，所以必须对约束方程的违约进行抑制；另一方面是怎样有效地将微分—代数混合方程组化为纯微分方程组，运用求解微分方程组的计算方法求解。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐