查询词典 derived equation

The ellipse curre equation of circular image is derived based on the theory of spatial analytic geometry and rotation matrix s representation with unit quaternion then a mathematical model of the distortion error is established which relates the distortion error to the foca length of the used CCD camera,the radius as well as the position and the attitude of the inspected circle directly.

研究三维视觉检测中圆的中心经针孔摄像机成像后存在畸变误差的问题，首先基于空间解析几何理论和旋转矩阵的四元数表示法推导出像平面上投影椭圆的参数方程；然后根据参数方程建立圆中心成像畸变误差的数学模型；最后对影响畸变误差的主要因素进行分析。

A set of mathematical expressions are derived including geometrical matrix,stress matrix,stiffness matrix of weak plane element,equation of equivalent nodol load caused by unit initial stress in element.

文中推导了弱面单位的几何矩阵~6，应力矩阵~6，刚度矩阵~6以及单元初应力引起的等效结点荷载{P}等计算公式。它们有别于一般文献所列算式。

Firstly, the integral-differential equation described the radiation field evolution is derived, and then the instability of its solution is also investigated analytically. By using the perturbation and iteration method, the threshold detuning and threshold linear growth rate of the unstable solution are analyzed and discussed in detail.

首先，建立了一个描述辐射场演化的积分一微分方程，解析分析了系统解的不稳定性，并采用线性方程解的微扰迭代方法进一步对系统不稳定解出现的失谐量阈值和线性增长率阈值等作了详细讨论。

A nonlinear evolution equation for the radiation field in magnetically insulated transmission line oscillator is derived and the threshold conditions of the nonlinear unstable solution are studied.

导出了磁绝缘传输线振荡器中辐射场的非线性演化方程，并讨论了在临界值点附近可能出现非线性不稳定解的条件。

The distribution of gear's contact stress, root stress, and contact engagement line in the engagement situation of gear pairs, were obtained on the base of explicit integration method. 3. Adopting the method of system matrix, the torsional vibration differential equation of general shafting was gained. The simple harmonic forms of excitation torque under the normal combustion or piston flameout of in-line engine and v-type engine were analysed. The decoupled algorithm of free vibration and forced vibration and the solution to the vibration damper's energy of resistance and the off-resonance calculation were studied. The sensitivity formulations of the natural frequency and vibration mode to physical parameters of system were derived by solving the eigenvalue problem. These sensitivity formulations provided the theoretical base for the dynamic modification of structure.

运用系统矩阵法建立了轴系的扭振微分方程，并对直列和V型发动机在正常发火和气缸熄火工况下的激振力矩进行了详细的简谐分析；基于精确方法推导了自由振动和强迫振动的解耦算法，给出了能量法计算中的减振器阻尼功求解和非共振计算方法；并研究了曲轴系扭振非线性分析中的变惯量问题，得到了单缸转动惯量的精确求解公式以及变惯量和固有频率的关系式；最后，从特征方程和振型正交性出发，推导了固有频率和振型对轴系转动惯量和刚度等物理参数的灵敏度，为扭振系统的结构动力学修改提供了理论基础。

The characteristics equation for the distance is derived by using the variational formulation for a generalized resonator.

应用谐振腔的变分公式，导出了确定短路面之间距离的特征方程。

Using the principles of transformation matrix and vector operation, the trajectory equation of cutting edge relative to workpiece is derived.

摘 要：运用图形矩阵变换原理和矢量运算法则，推导出了立铣刀周铣过程中刀具切削刃上任意点相对于工件运动的轨迹方程，在此基础上构造出一种基于工件网格划分的三维表面形貌仿真算法，并给出了相应的仿真算例。

Based on the discussion,a simple and clearly defined vector equation of kinematic error for robots,has been derived for practical use by means of space vector,characteristicsof space vecto...

据此，利用D-H 坐标变换与空间矢量的关系，以及空间矢量导数性质，推导了简洁实用、意义明确的机器人运动误差矢量方程，并就该方程在一般空间机构运动精度研究时的应用实例作了说明。

The thesis also gives the estimated upper bounds of error decision probability. When the compressor is confined to be a lattice vector quantizer, a explicit mathematic equation for the rate of the performance convergence to the optimum is derived. On the other hand, Distortion Ratio Aproachs to the design of testing system on the basis of vector quantization are put forward, and methods for building the variable length decision tree as well as the fixed length one presented.

在算法方面，提出了失真比矢量量化检验器的设计方法以及可变长和固定码长分类判决树的生成算法；为了解决以矢量量化器为核心的处理系统运算量大，不易实时实现的问题，论文中引入了熵减的概念，在此基础上提出一种快速最近邻搜索编码方法，理论分析及实验结果均证实了这种算法的有效性。

Based upon a vectorial identity, an integral equation system concerning electromagnetic field in inhomogeneous medium is derived.

计算三维不均匀介质中测井响应的最常用的方法是有限元素法和有限差分法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。