查询词典 equation of motion

The equation of relative motion of the liquid in a TLCGD can be derived using the extended non-stationary Bernoulli's equation and equivalently linearized.

由广义Bernoulli方程推导出液体在管道中的运动方程并等价线性化。

Because of the nonuniqueness in the positional solution, it's not easy to test the performance of the coordinated control system. So the model of NN was built to convert the vector of the length of 6 jars into the vector of the position of the motion deck. It's fast and accurate for the lengthwise direction. The state space system model of the six degree freedom motion simulator was built by the equations of electrodraulic servo mechanism and the multi-body dynamics equation of the six degree freedom motion simulator,the vector of the length of 6 jars was the control variable.

本文结合六自由度运动模拟器的多体动力学方程和电液伺服驱动机构的特性，经简化得出了具有实际意义的六自由度运动模拟器整体系统的状态空间方程式，通过分析该系统的稳定条件和能控性，采用状态反馈对系统的状态方程式进行合理配置，从而建立了以运动模拟器杆长向量为控制变量的运动模拟器整体控制系统，并将该控制系统输出的杆长向量转换为位置向量。

This method undertakes comparative getting the area between the spare parts to equation of geometry of the face in model of CAD of different spare parts above all - surface contact relation and type, use amount coming back theory general face - the face expresses to be helix; relative to instantaneous motion next, the helix that goes up to many surface contact undertakes making operation,; of helix of the motion when making the opposite very short time between the spare parts is final, according to the spare parts abut concern plan and abut spare parts move relatively helix, undertook an analysis to assembling instantaneous of whole of the spare parts in the model to concern with drive movably, give out not between the method of calculation of helix of opposite instantaneous motion between photograph adjacent spare parts and them but the judgement method of drive sex.

该方法首先对不同零件CAD模型中面几何方程进行比较得到零件之间的面-面接触关系和类型，并应用旋量理论将面-面相对瞬时运动表示为螺旋；然后，对多个面接触上的螺旋进行交运算，生成零件之间的相对瞬时运动螺旋；最后，根据零件邻接关系图和邻接零件相对运动螺旋，对装配模型中零件整体瞬时可动性和驱动关系进行了分析，给出不相邻零件之间的相对瞬时运动螺旋计算方法和它们之间可驱动性的判定方法。

This make it difficult to know the essence of fluidized beds. In order to viewthe motion behavior of a single particle in a fluidized bed in a reasonable cost, thegas-solid flow in a fluidized bed is modeled by a combined approach of discrete particlemethod and computational fluid dynamics, in which the motion ofindividual Particles is obtained by solving Newton\'s second law of motion and gas flowby the Navier-Stokes equation based on the concept of local average.

为了用数值模拟方法来弥补传统实验方法的不足，达到从单个颗粒的尺度上来研究流化床中颗粒的运动和气体流场的剧烈变化情况的目的，本论文建立了基于用Newton第二定律计算单个颗粒运动轨迹的离散颗粒法和基于区域平均值的计算流体动力学方法的数学模型的建立和求解过程；并依据Newton第三定律建立了DPM模型和CFD模型的耦合模型，编写和调试了DPM和CFD的耦合程序。

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。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too.

摘 要：通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设，介绍了天体运行轨道的具体方程形式及理论框架概要；进一步地通过讨论天体运行轨道 Binet 方程的一般形式及其行星近日点进动角的解，给出了连续轨道理论与 Newton 理论及 Einstein 广义相对论的联系与区别；通过讨论天体运行轨道的分维扩展方程，给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道方程及其预言数据。

By discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too.

在深入研究引力理論及廣義相對論的基礎上，通過討論天體運行背景介質理論的連續軌道及離散軌道這二個研究方向的基礎假設，介紹了天體運行軌道的具體方程形式及理論框架概要；進一步地通過討論天體運行軌道Binet方程的一般形式及其行星近日點進動角的解，給出了連續軌道理論與Newton理論及Einstein廣義相對論的聯繫與區別；通過討論天體運行軌道的分維擴展方程，給出了包括太陽系行星、天王星衛星、地球衛星、繞月航天器等在內的離散軌道方程及其預言資料。

In this paper the writer employs complex Riemannian Geometry and defines the absolute interval between two points as consisting of a real part and an imaginary part. Two postulates and are used: the first may be called law of gravitation and electro-magnetism; the second equation of motion.

在此文内，作者利用复变来曼几何以宇宙间两点之距离为一实数及一虚数部分相构而成，於此并用假说：一可称为吸力及电磁定律，一为物体行动定律，解释吸力及电磁力之各种现象。

Nonlinear partial differential dynamic equations of bending vibration of a tilting stepped drive shaft with two supports were built under non-inertia movement coordinate system by theorem of the motion of mass center and Heaviside function. According to the condition of equal displacement in an adjoining plane of the shaft, an equivalent shaft and its equation were obtained. A motion equation of the equivalent shaft was obtained by method of Galerkin. An approximate steady-state solution of the main resonance was obtained by method of multiple scales. The influence factors, motion stability, amplitude jump of main resonance of a stepped drive shaft and so on were analyzed.

用质心运动定理、Heaviside函数建立了非惯性系下倾料两端支承阶梯传动轴的非线性弯曲振动偏微分动力学方程，并根据相邻轴段的衔接面处位移相等的条件，得到阶梯轴的当量轴及其动力学方程；用Galerkin法得到当量轴的弯曲运动方程，用多尺度法求得稳态下当量轴的主共振的一次近似定常解，分析了影响阶梯传动轴主共振的因素、运动稳定性、振幅突变性等。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。