运动方程

Based on the sliding response theory of the free-standing equipment, the differential equation of motion of the free-standing equipment under seismic excitations is presented. The equation is solved by Runge-Kutta algorithm, therefore the absolute acceleration, relative velocity and relative displacement of the equipment can be obtained. The sequential coulomb friction model is applied to the analysis.

以前人研究建立的浮放设备滑移反应分析理论为基础，给出了浮放设备在水平和竖向地震输入下滑移反应运动微分方程，选取连续型的库仑摩擦力模型，采用Runge-Kutta法求解浮放设备地震滑移反应运动微分方程，可以得到浮放设备在地震作用下的绝对加速度、相对速度和相对位移反应时程。

Taking HPAM solutions as an example, the unsteady flow of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially is calculated; the distribution of velocity, flow rate and stability parameter is obtained; taking HEC solutions as another example, the flow of second order fluid in eccentric annuli with the inner cylinder moving axially is calculated too; the distribution of velocity and stress is obtained; the effect of eccentricity and axial movement on stress distribution on the outwall of the inner cylinder is analysed.

在理论上，分别用二阶流体和幂律流体模型描述聚合物驱油井产出液的非Newton流变性；分别建立了双极坐标系下二阶流体和幂律流体在内管做轴向往复运动的偏心环空中非定常流的控制方程及边界条件和初始条件方程；建立了幂律流体在内管做轴向往复运动的偏心环空中流动的稳定性参数和流体在内管壁上的压力分布计算公式；建立了二阶流体在内管做轴向运动的偏心环空中流动的流体在内管壁上的压力分布计算公式。

For intramolecular electron transfer reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.

对于扩散控制的溶液中的电子转移反应，分子内振动模的运动比溶剂运动快很多，Sumi-Marcus理论提出用反应扩散方程(reaction-diffusion equation)处理溶剂的扩散运动，而分子内的振动用sink函数来表示，我们基于此理论发展了用虚时间分裂算符的方法(imaginary-time Split operator approach)解反应扩散方程，并将其应用于嗪1(oxazine 1，OX1)和N，N-二甲基苯胺分子之间的电子转移反应，Sink函数采用几种不同的微扰表达式，通过计算得到给体几率衰减的两种平均速率和长时间极限下的速率常数，揭示了该体系电子转移过程中的一些动力学性质。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

To more briefly calculate the accurate solution of the hangingpoint motion parameters of the beampumping unit,the walking beam's swing equation according to the geometry relationship and movement characteristic of the four pitmen mechanism in the beampumping unit is found.

根据游梁式抽油机四连杆机构的几何关系和运动特点，建立了游梁的摆动方程，并由该方程得出了游梁摆角变化规律以及悬点运动的位移、速度和加速度的计算公式，从而给出了求游梁式抽油机悬点运动参数精确解的一种计算方法。

In order to reduce geometric errors between motion trajectory and work piece curve,this paper present a means of controlling trajectory motion law to replace traditional position control.

为了减小刀具运动轨迹与工件几何曲线的误差，提出将传统的位置控制改为物理运动规律控制，即建立数控机床的运动模型，分析被加工轮廓的曲线方程、加工工艺运动要求与刀具加工运动的合成或分解关系，推导出轨迹运动方程组。

In the second part of the paper, the sport techniques of the flight elements was analysised in-depth theoretically by the movement technical structure:①the giant swing was first analysised in mechanics by applying the Kane's method, the dynamic equation of 5-link multi-body model was established, and the computer simulation software of the giant swing on the high bar was developed.

其次，作为单杠上飞行动作系统性研究的另一主要方面，本论文对飞行动作一般技术结构中的各技术环节进行了深入的理论分析：①着重对飞行动作准备阶段的回环运动技术进行了动力学分析，主要采用了多体力学理论中的Kane方法，建立了5环节人体回环运动的动力学方程，并应用计算机数值仿真技术研制开发了用于回环运动动力学分析的数值仿真软件，进而以动作实例对回环运动进行了数值仿真与误差分析，其所得到的数值仿真结果能够满足对人体回环运动的动力学分析和仿真要求；②对于飞行动作的撒手技术环节，本论文从人体环节相对运动角度，来分析撒手时人体质心的运动以及撒手时角动量参数，并列举了几种飞行动作撒手技术的基本力学指标；③关于飞行动作的空中技术，论文在总结了空翻转体动力学机理的研究成果基础上，对人体空中运动定量化问题进行了一般性描述，并进一步应用刚体动力学理论，着重建立起了描述空翻与转体技术之间定量化的关系，讨论了空翻转体运动的稳定性及其运动模式的转换问题，它对于定量地评定空翻转体技术以及今后对空翻转体动作进行数值仿真都具有理论上和实践上的重要意义；④关于飞行动作再握技术环节，本论文避免了以再握瞬时性的力学参数指标来描述再握技术特征的简单化途径，提出以再握下摆与回环下摆相对比的方法来研究再握技术，并以飞行动作再握技术的具体实例进行了对比分析，表明再握下摆技术相比回环下摆技术有着相当的困难性和复杂性，运动员对再握下摆过程中各环节的相对运动实施有效的控制，是连接高难动作以及顺利流畅地完成成套动作的关键。

On the basis of propulsive model,a mathematical model which is used to describe the motion of pitching and heaving of dolphin's caudal fin by ways of coordinate transformation is deduced.Meanwhile,this model can show the relationship between the motion of caudal fin and parameters related,then the motion of caudal fin of dolphin is simulated by the software of Matlab which showed the swimming principle.

以海豚背腹式摆动推进方程为基础，应用坐标变换的方法，建立了描述海豚尾鳍俯仰－沉浮运动的数学模型，同时建立了描述豚尾各运动参数之间关系的方程，随后运用Matlab的仿真功能再现了海豚在游动过程中尾鳍的运动规律。

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