方向余弦

Then,the cosine value of central angle between the spacecraft and the descending node is solved by using cosine theorem of spherical geometry to avoid the cumbersome solving process by judging the flight direction of a satellite and the latitude of sub-satellite point in an original calculation model of image motion speeds.

通过球面几何的余弦定理直接求解航天器与降交点相对地心夹角的余弦值，避开了原像移速度计算模型中通过判断卫星飞行方向和星下点纬度来求解航天器与降交点相对地心夹角余弦值这一过程。

For every ULA, the wide-band signals are sampled in spatial and temporal, then 2-D discrete Fourier transform is carried out. A projection operation on 2-D representation of wide-band signals is applied in the spatial-temporal frequency domain. The direction cosine relative to the ULA axes is estimated by MUSIC algorithm.

该方法采用3个共面的均匀线阵，每一均匀线阵对宽带信号空间采样，然后进行空时二维DFT变换，在空时频率域对宽带信号进行投影变换，用MUSIC算法实现宽带来波信号方向余弦的估计。

The forward kinematics is analyzed by choosing one of the mechanisms which have one, two,three or zero angle constraint.Wherein,3-CCC is a new parallel mechanism which has three angle constraints and three distance constraints, Calay\'s formular and direction cosine matrix are used to describe the rotation matrix respectively.By setting Dixon\'s and Sylvester\'s resultant with the three angle constraint equations respectively and using parameters replacement to deal with the distance constraint equations,the 64 order input-output equation of the forward kinematics is obtained under both of the methods.Numerical example confirms these theretical results and the motion simulation is shown in VC++ by integrating OpenGL.

3对高小山提出的广义并联机构进行了研究，以其中具有角度约束的并联机构进行了分析，选取具有一个、两个、三个和零个角度约束类型中各一个机构进行了运动学正解求解，其中3-CCC是一种全部由圆柱副构成的具有三个线线角度和三个距离约束的新型并联机构，文中分别用Calay公式和方向余弦两种旋转矩阵建模方法对其位置正解进行了分析，通过对三个角度约束方程分别构造Dixon结式和Sylvester结式，以及对三个距离约束方程进行变量代换分别导出了位置正解输入输(来源：4040ABC论文网www.abclunwen.com)出方程，得出64组位置正解，并使用数值算例验证了其全部根。

Earthworks zero line is determined by constructing the spatial gridding curved surface model of the original terrain and the field leveling design terrain by digital elevation mode. The DEM data of original terrain are obtained by actual measurement. The mathematical correlation is deducted to demonstrate the relationship between the coordinates of any point on spatial line and the direction cosine by the spatial linear equation. DEM data obtaining program is compiled by Fortran9.0 and it is applied automatically to obtain the DEM data of field leveling design terrain.

目的 利用数字高程模型(digital elevation model， DEM)构造原始地形和场平设计地形的空间网格曲面模型，确定土方工程中的零线方法通过实测提取原始地形DEM数据；依据空间直线方程，推导空间线段土任意点的坐标与方向余弦的数学关系式，采用Fortran90程序设计语言编写DEM数据提取程序，自动提取场平设计地形DEM数据；应用Surfers8.0和MapInfo软件构造规则的网格空间曲面模型并导出网格节，点数据；擦除场平设计范围外数据。

The normal transformation polynomial is used by some researcher in practical probabilistic analysis in structural or civil engineering; especially when multivariate random variables with the probabilistic characteristics expressed using only statistical moments are involved.

本论文提出了两种样本点选取策略，即方向余弦策略和有限步长策略，对响应面法进行改良；本方法一次性拟合响应面方程，避免了常规响应面法的复杂迭代运算，且对高非线性问题有较好的适用性。

Where 、and is the direction cosines of the normal vector of the directed surface at the point .

其中、、是有向曲面在点处的法向量的方向余弦。

In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related respectively to the direction cosines of the ith source relative to the x and y-axes.

在算法最后阶段构造一个矩阵，其第i个特征值的实部和虚部分别与第i个信号源相对X轴和Y轴的方向余弦一一对应。

Using the direction cosines relative to three ULA axes, the correct pair is obtained, then the azimuth and elevation are estimated.

利用3个方向余弦估值进行配对，然后求得来波的方位角和仰角估计。

Using the direction cosines relative to the three URL axes, the correct pair is obtained, and the azimuth and elevation angles are estimated.

利用三个方向余弦估值进行配对，然后求得来波的方位角和仰角估计。

The point of intersection of three light-source on tested body is used as basic point, the mathematical model of line displacement is established.

并以固结在被测体上的三个激光器的交点为基点，建立其线位移数学模型；以方向余弦法来确定被测体的角位移，建立其角位移数学模型。

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。