坐标的变换公式

On this basis,the PDC bit's fivepoint survey theory is developed,and a series of formulas are derived,applying PDC bits' geometry and analytic space geometry.

在此基础上，运用PDC钻头几何学和空间解析几何学中的四点共面、行列式、坐标变换的知识，提出并推导出了PDC钻头的五点测绘理论及系列公式。

The former applies to those situations that the formulas of two projections are simple and easy to find out the direct relation of the plane rectangular coordinate.

数值变换法应用范围较广，它可以避开较复杂的投影坐标公式的反解问题，求出两个不同投影平面场上点的对应关系。

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

Derived from Mindlin solution, the deformation formula induced by torque between cutterhead and soil is obtained by integration and coordinate transformation, which leads to the total deformation formula induced by shield tunneling.

基于盾构施工过程，利用弹性力学Mindlin解，通过坐标变换经积分推导刀盘与土体之间摩擦力所引起的地面变形计算公式，并得到盾构施工引起的总地面变形计算公式。

In this research, we find that because of the changes of parameters and structure in GNSS, the error origins are very different of them in foretime.

在研究中发现，由于GNSS系统本身参数和结构改变，加上坐标变换的问题，使得误差来源发生变化，导致原有误差公式不再适用。

Applications of homogeneous coordinates in the variable system classifications of structures;2. According to the homogeneous coordinate transition,we deduce the formula for computing target pose under the absolute coordinate system an.

在此基础上，进一步建立空间动态目标全姿态激光跟踪测量的模型，基于空间坐标系的齐次坐标变换，推导出目标分别在绝对坐标系和相对坐标系下的姿态计算公式。

A fault calculation method to determine faults with the conversion matrices in phase coordinates, to determine multiple faults with equal time and elements with unsymmetrical parameters is developed with the sequence network decoupled from symmetrical components coordinates.

利用对称分量变换将相分量坐标下的故障处理方法和计算公式转换到对称分量坐标下，提出了完全使用对称分量坐标系的多态对称分量法。并利用反映网络等效变换的方程降阶方法进一步提高计算效率。

Firstly, based on the force acting on a single-particle, establish a discriminant formula of the sand threshold, and prove that the sand threshold belongs to the cusp catastrophe. Then establish the basic equation of the cusp catastrophe using coordinate transformation and catastrophe theory. Finally, while particle Reynold number and equivalend diameter are the state variables and Shields parameter is the control variables, we can obtain the model of cusp catastrophe of sand threshold, putting those variables into the basic equations of the cusp catastrophe. The model is derived from the mathematics, which has a certain mathematical theory foundation.

首先从单颗沙粒受力分析出发，建立沙床沙粒起动条件判别公式，进而证明了风沙起动属于尖点型突变；然后通过坐标变换和突变理论建立了尖点突变的基本方程；最后本文选择颗粒雷诺数和等效粒径作为控制变量，希尔兹参数作为状态变量，并把它们代入尖点突变的基本方程，经过拓扑变换得到风沙起动的尖点突变模型，并与前人的公式及实验数据进行比较。

A correction formula for target deviations is derived by using the coordinate transform and its suitable conditions are proposed. Experiments show that it is coincident with the spherical trigonometry well.

分析了目前采用的脱靶量修正模型的适用条件，采用坐标变换法推导出经纬仪脱靶量修正公式，获得了与球面三角学相一致的推导结果，并在此基础上推导出成像系统无照准轴平行约束条件的通用脱靶量合成公式。

From Maxwell's equations, with material constitutive relation of optically active crystal and boundary conditions of electric field on the boundary between isotropic media and crystal, through coordinate transformation, the formula of the direction of refracted wave for arbitrary direction incident monochromic plane wave was derived. Furthermore, based on the unit vector of direction of refracted wave, eigen waves of electric field, electric displacement vectors and direction of energy flow can be easily obtained.

从麦克斯韦方程组出发，结合旋光晶体的物质方程以及单色平面波从各向同性介质入射到晶体界面时电场的连续性边界条件，通过晶体主轴坐标系和界面坐标系的坐标变换，推导了任意入射方向的单色平面波在晶体界面上的折射方向的求解公式，进而利用所得的折射方向求解晶体中折射波的电场本征模、电位移矢量本征模和光线方向。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。