正交坐标

The simple algebraic procedure is used to form nearly orthogonal 2—D C—type and H—type bodyfitted grids for bodies of revolution, which is then used to generate 3—D C—O and H—O bodyfitted grids for fuselages.

五、用简单的代数方法生成了近于正交的旋成体子午面"C"型及"H"型贴体坐标网格，并以此为基础构造了三维任意截面机身的"C-O"型及"H-O"型贴体坐标网格。

In this paper, this method is extended into the orthotropic media. The parameterβ=μxμy is introduced to perform coordinate transformation. The basic equations of antiplane crack problem for orthotropic media can be transformed in terms of those of isotropic media.

本文将这一方法推广应用于正交各向异性材料，首先引入参数β=μxμy，利用坐标变换，将正交各向异性板反平面裂纹问题的基本问题转换为各向同性的形式进行求解，然后经过反变换求得问题的一般解。

Geometrically nonlinear strain-displacement relations, the total potential functions and equilibrium equations of the tires are derived with respect to the orthogonal curvilinear coordinates for details.

以轮胎的内轮廓曲面为参考面，用正交曲线坐标描述轮胎的几何变形，详细推导了正交曲线坐标系下轮胎的几何非线性的应变—位移公式和平衡微分方程。

Based on the Navier-Stokes equations in conservative form derived with respect to nonorthogonal curvilinear coordinates and nonorthogonal velocity components, the numerical method for solving 3D viscous flow has been discussed.

本文基于非正交曲线坐标与相应的非正交速度分量下导得的守恒型N—S方程，讨论了求解三维粘性流动的数值方法，计算中显式时间推进算法与Baldwin—Lomax湍流模型被采用，应用本工作发展的程序，作为算例计算了一个沿径向非等截面环形叶栅的三维粘性流场，得到了诸如三维压力分布，总压损失分布以及十分清晰的二次流动图景等丰富的流场信息。

The first kind is 0-equation model. It only includes mass and momentum conservation equations. Great progresses have been made in improving this model. It has successfully been applied to many natural rivers with complicated boundary geometry. The second kind is κ-ε model. The κ equation and ε equation are needed, besides mass and momentum conservation equations. Many researchers have studied the depth-averaged mathematical models of turbulence in recent years. However, the models were used mostly in regular artificial canals or natural water areas with simple boundaries.

对于宽浅型河流，采用深度平均法进行流场计算时，用得较多的有两类模型：一类是不增加任何脉动量的偏微分方程的模型，这类模型已在适体坐标下运用得较多且较成功；另一类是κ-ε二方程模型，它是近几十年来广泛应用的一类湍流模型，并发展了许多具体的形式，但大多数只对顺直河道进行了研究，对弯曲较大的河道研究不多，本文运用适体坐标，采用正交交错网格及非正交交错网格，把此模型运用到了弯曲较大的河段及具有汇流的河段，取得了较大的成功。

In this paper, draw the idea of beam unit, the bias along the vertical box is divided into a number of oblique beam. On the basis of analysis of the displacement, through positive and oblique coordinate transformation relations, and directly built on the oblique coordinate system to describe the methods of displacement unit space. With potential energy principle is derived in oblique beam element stiffness matrix and the establishment of the finite element formulation. The preparation process of the finite element analysis is used to verify the structure of bias.

本文吸取梁段单元的思想，将斜交箱梁沿纵向划分为若干斜梁段，在位移分析的基础上，通过正、斜交坐标转换关系，直接建立在斜交坐标系内描述单元空间位移的方法，用势能驻值原理推导斜梁单元刚度矩阵并建立其有限单元列式，利用编制的有限元程序进行斜交结构的分析。

Wavelet transform can be seen as translating an image into coordinate of orthogonal basis.

从函数正交分解的角度看，小波变换可以看作把图象的象素点转换成一系列正交小波基的坐标或者说是投影，每个坐标对应着这些基的能量大小。

In this paper, some decision theorems are suggested about the matrix orthogonal problem on the subspace of the finite dimensional Euclidan subspace. In addition, some concise results are obtained by matrix representation of the orthogonal complement and injection of vectors on the subspace.

利用向量组的Gram矩阵和向量的坐标矩阵对有限维欧氏空间中子空间的正交性给出了矩阵判定条件，对子空间的正交补及向量在子空间上的内射影给出了矩阵表示，获得了一些简捷有用的结果。

Through S-wave polarization scanning mode of ultrasonic impulse testing, rock samples with three different properties are measured to evaluate the variation of S-wave velocity in three perpendicular coordinates. By analyzing S-wave splitting of three directions and polarization of the maximum or minimum speed S-wave amplitudes, we think that the velocity orthotropy and fracture orientation observed in the grain sandstones and crack marble samples can be estimated in terms of the polarization and velocity of S-wave. Also, perpendicularity characteristics on the two types of rocks can attribute to the bedding and structure of rocks (directional grains or crystallize).

在实验室通过选择了三种不同岩性的岩石，采用超声脉冲测试方法中的横波偏振扫描方式，观测了岩石样品三个坐标方向上的横波速度变化，通过分析三个传播方向上出现横波分裂的差异，以及出现最大或最小快慢横波振幅的偏振方向发现，可从横波偏振方向和速度值判断出纹理砂岩和裂隙大理岩样品存在不同程度的速度正交各向异性和裂隙方向等特征，认为这两种岩石的正交特性的原因是岩石的层理或裂隙与岩石本身的结构构成的。

In order to be fit for the calculation of wave transformation in harbor basin with irregular solid boundary, the governing equations and the boundary conditions of the present model are transformed by a non--orthogonal coordinate. Comparisons with the theoretical solutions indicate that the transformation is correct.

其次对上述完全型波浪绕射折射控制方程及边界条件进行非正交坐标变换，以适应存在固体边壁的港内水域波浪传播变形计算，经与理论解的验证比较，本文采用的坐标变换算法是正确的。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。