简化方程

The model was solved by the Ritz method, and the orthogonal polynomials generated by the Gram-Schmidt process were employed as admissible function for both disk and blades. With this approach, the matrix derived from kinetic energies becomes diagonal and numerical manipulation can become easy and stable.

采用Gram-Schmidt方法生成正交多项式作为李兹容许函数进行模型的离散化，简化了所得到的频率方程求解过程，有利於求解过程的数值稳定性，并可方便地通过对方程系数性质的分析了解结构振动模态的性质。

Therefore scientists have been engaged in research on approximate solutions of the partial differential equations,e.g.,the difference methods,the methods of characteristic curve and MWR method etc.,i.e., by using approx...

因此不少研究分布参数系统的科学工作者对这方程式近似方法进行了大量的研究，如差分法，特性曲线法和MWR法等；或者把分布参数系统近似成集中参数系统，或者把高价方程简化为低阶方程等。

In the predicted process, the forward simplification is used to get the interface equation, meanwhile taking the voltage of the concentrated grid as control vector to solve the control step length; in the correction process, by means of forward simplification and back substitution the Newton linearization incremental equations of both concentrated computational grid and contracted nodes are solved alternately.

进行计算时，通过前向简化形成预估环节的接口方程，同时以浓缩网络的电压为控制电压向量求出控制步长；校正环节通过双向迭代方法交替实现对浓缩网络和收缩节点的牛顿法线性增量方程的求解。

Tridiagonal block matrix elemination and sweep algorithm is successfully applied to solve the large matrix involved; central difference method is supplemented to Houbolt method to form a time integration method with estimation and correction, to solve the time integration of second order implicit non-linear equation; simplification of system equation by decoupling between the physical coordinates x and y further improves the calculation accuracy and speed.

其中：成功地引入块三对角矩阵追赶法求解上述问题构成的大型矩阵；提出中心差分法+Houbolt法的预估计—校正时间积分法，以解决二阶隐式非线性方程的时间积分问题；系统方程在物理坐标x和y上的"解耦"简化，使计算速度和计算精度得以进一步的提高。

A motion reference coordinate system of this quadruped robot and its simplified-structure of the multi-rigid body dynamics model are established. After kinematic and dynamic analysis, the kinematic equation, inverse kinematic equation and Jacobi matrix of the quadruped robot are presented, and the second kind of Lagrange dynamic equation group for simplified-structure of the quadruped robots multi-rigid body system is educed.

建立了该机器人的运动坐标体系，及其等效简化结构的多刚体动力学模型，对上述模型进行了运动学和动力学分析，给出了该机器人的运动学、逆运动学方程和雅可比矩阵，并导出了其简化结构多刚体系统的第二类Lagrange动力学方程组。

According to the complete geometric symmetry of the irons and windings, and the mirror symmetry during positive-negative operating-mode period, the expressions of current harmonics are derived, and the electromagnetic equitation are simplified. Based on this, the analytical calculation of flux density and the electromagnetic calculation of the reactor are performed.

根据两个铁心及绕组的结构完全对称以及它们工作状态在正负半周里呈镜像对称的特点，推导出电流谐波关系式，简化了本可控电抗器的电磁方程，并根据简化后的数学形式研究了其磁感应强度的解析计算，最终计算出了各项性能指标。

Aimed at the problems exists in the methods of former calculating of sequential transportation at the present,put forward the predigest ways of the confused oil former by using disorderly current speciality of fluid,enduce the essencial equation of confused oil's consistence by using the simplied ways and the Feck Law,present the method of calculating the consistence at the end of the pipeline which is called the Gauss-Lerang method.

针对现有顺序输送混油模型计算方法所存在的问题，利用流体紊流特性提出了混油模型的简化方式，利用简化模型及费克定律推导出了混油浓度的基本方程，给出了管道终端混油浓度的高斯-勒让德计算方法。

The results show that the equations have benefit to the deduction of the pantograph's mechanical differential equations.

研究结果表明：利用升角与升弓高之间的关系，可简化受电弓运动微分方程的推导；应用所建立的力学模型、实测数据以及简化公式可更准确地分析和计算弓网系统的力学行为。

The angular velocities in x-axis and z-axis directions can also give influences, but the influences are less.

并利用它的基本工作特点对该微分方程模型进行了简化，讨论了简化的合理性。

Finally, the wave equation of the electromagnetic field of this kind damper isderived from the Maxwells equation. The magnetic flux density at the boundary isassumed to be harmonic, so the analytical result of the wave equation is solved. When therotor rotates, eddy currents flowing inside the conducting material field are caused. Thetangential force acting on the rotor because of the action between eddy currents andmagnetic field is produced. The tangential force causes a retardation torque, which leadsto the increase of power and heating effects.

最后，应用Ahrens的电磁轴承简化模型，从Maxwell方程出发推导了应用于本文所述的被动式电磁阻尼器的波动方程，并用傅立叶级数把矩形磁场展开的谐变磁场作为磁场的边界条件，通过求解波动方程得到磁场的解析解，从而计算了阻尼器对转子的电磁力和由涡流引起的切向力产生的阻尼器附加功耗。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失