方向余弦

Error analysis of direct georefencing is divided into two parts: for attitude angle error, formula is determined by the error of the direction cosine matrix, for other errors, formula is determined by covariance matrix.

为了分析各误差因素对定位精度的影响，分两步建立各误差因素和定位精度的表达式，对于姿态角误差的影响，为避免欧拉角之间的耦合，按照方向余弦矩阵误差定义求取，对于其余误差的影响，采用协方差矩阵求取。

The updating algorithm of Strapdown matrix is one of the crucial techniques of SINS. There are several kinds of attitude updating algorithms of SINS, such as direction cosine algorithm and quaternion algorithm.

捷联矩阵更新算法是捷联系统的关键技术之一，捷联惯导系统姿态算法有欧拉角法、方向余弦法、四元数法和圆锥补偿算法等几种方法。

In this paper, the modeling theory of multi-rigid-body dynamics was thoroughly investigated in order to make up the shortcoming in the above modeling method. The major research achievements are as follows:①Based on the matrix of direction cosine between the body-fixed base and the reference base, and Poisson equation of a rigid body rotating, the coordinate transformation method for the modeling of treelike multi-rigid-body dynamics is derived. The method is very routinization and easy to use the computer to carry on the symbol derivation.

本文针对上述建模方法存在的不足，深入地研究了多刚体系统动力学的建模方法，并将所研究的新方法应用于惯性振动设备的建模，取得的主要研究成果如下：①基于刚体连体基关于参考基的方向余弦矩阵和刚体转动的Poisson方程，导出了建立树形多刚体系统动力学方程的坐标变换法，其过程极其程式化，便于利用计算机进行符号推导。

Now there have been a certain number of works on the research for thekinematic synthesis of spatial RSSR mechanism for causing the driving and driven linkscorresponding angle displacement such as the direction cosine matrix method and rotationvector method.

目前已有若于著作研究了实现主从动杆对应角位移的空间RSSR机构的运动综合问题，如方向余弦矩阵法［1］、回转向量法［2］。

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。

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。

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。