余弦

The quaternion calculation for spacecraft attitude determination is investigated in this paper,including the transformation between quaternion and the direction cosine matrix,the quaternion differential equation,the selection of time steps for integrating the quaternion equation,and the compensation methods for the noncommutativity error in high dynamic motion.

介绍了四元数计算中的相关问题，包括四元数与方向余弦阵之间的转换、四元数运动方程、求解四元数运动方程时积分步长的选取和高动态应用中非互易误差的补偿，此外还介绍了对偶四元数的发展。

The so called indirect integral operation means that Eular angles can be gotten from the direction cosine matrix which is received by the integral operation of quaternions or direction cosine.

飞行器导航中，姿态角的获取可以通过直接或间接的积分运算求得的，所谓间接获取即是指通过四元数或方向余弦的积分运算求得姿态矩阵，再从姿态矩阵中提取姿态角。

The pressure hydrophone array manifold can be divided into two subarray manifolds,which constitute a rotation pair,and the rotational invariant factors comprise the source's direction cosine.

其中声压水听器阵可以被划分为2个子阵，它们构成旋转对，旋转因子为包含某一轴方向余弦信息的相位延迟因子。

Several common description methods for rotational kinematics are discussed in control point, such as direction cosine matrix, Euler angles, quaternions and Rodrigues/Modified-Rodrigues parameters. Transformation relationships, advantages and disadvantages among those methods are discussed.

从控制角度综评方向余弦、欧拉角、四元数和Rodrigues/修正Rodrigues参数几种常用姿态描述动态方程，指出各种方法的优缺点，及相互转化。

A test scheme of trajectory measurement in security and reliably with OKA,GPS and total station positioning system(TCRA1101) etc is established.Synchronously,a method is presented on two OKA by direction cosine intersection in the measurement,also two different methods are adopted to check up the precision and the expectant results are obtained.

针对模型自由飞的特点，综合利用两台小型激光电视测量系统、GPS、全站仪（TCRA1101）等现有设备，设计了安全、可靠的模型自由飞跟踪、测量方案；利用方向余弦交会算法，对测量的模型自由飞数据进行处理，并采用两种不同的方法进行了测量精度检查，结果表明测试精度满足测试要求。

In this beamline, with the neutron depolarization technique, provides information of the mean domain size, the mean square direction cosine of the magnetic induction in the domains, and the mean magnetization of a magnetic sample.

三维去极化中子仪主要为观察极化中子通过磁性材过程，受到内部磁区的扰动使得极化中子向的方向和大小改变，进分析后可以观察出材内部平均磁区大小、平均感应磁场强、磁区平均方向余弦的平方。

The velocity hydrophone array manifold can also be divided into two subarray manifolds,which constitute a rotation pair with the pressure hydrophone array manifold,and the rotational invariant factors comprise the source's other direction cosine.

振速水听器阵可以被划分为2个子阵，它与声压水听器阵构成旋转对，旋转因子为另一轴方向余弦。

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 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。