Vector kinematics are applied to translation and rotation of rigid bodies.
向量运动学是应用于刚性物体的转化和旋转。
As far as conversion of bone rotation is concerned, two methods are provided: inverse kinematics method using two-link planar chains and vector mapping method.
关于骨头旋转度的转换，给出了两个方案：借助双链接平面链的倒转运动学方法和向量匹配方法。
The horizontal north vector is tangent to the earth and hence the rotation is the result of earth curvature.
由于地球旋转而引起的离心力随纬度θ到地轴距离的变化而变化以及由极向扁率引起的地球半径的变化而对重力资料进行的校正。
In partial celestial sphere celestial Star-Identification, the initial attitude is known. With a certain angular and distance tolerance, the separation angle of the observed stars and that of the catalog stars are matched, then, the star triangles are composed in real time. According to the rules of vector rotation, the inconsistent rotation star triangles are removed. After that, put the star triangles with public vertex into star polygon.
在局部天球星图识别方面，因为已知初始姿态，在一定角距容差和星对容差范围内和已知视轴附近的导航星角距表进行角距匹配，实时组成星三角，根据矢量法则剔除旋转方向不一致的星三角后，再把拥有公共顶点的星三角组合成星多边形。
Kuehl`s triangle Star-Identification, some improvement had made. With a certain angular and distance tolerance, the separation angle of the observed stars and that of the catalog stars are matched, then, the star triangles are composed in real time. According to the rules of vector rotation, the inconsistent rotation star triangles are removed. After that, put the star triangles with public vertex into star polygon.
Kuehl的三角形星图识别的基础上进行了改进，即在一定角距容差和星对容差范围内和整个导航星角距表进行角距匹配，实时组成星三角，根据矢量法则剔除旋转方向不一致的星三角，把拥有公共顶点的星三角组合成星多边形。
A new method, based on the Wold texture model and support vector machines, is proposed for texture recognition to alleviate the difficulties of charactering texture with different rotation and scale changes.
提出一种基于Wold模型和支持向量机的纹理识别新方法，有效解决了方向和尺度变化给纹理识别带来的困难。
In the Cartesian coordinate system, compute the image plane revolution vector quantity caused by scan mirror's rotation applying coordinate conversion and geometrical optics.
在笛卡尔坐标系中，通过数学坐标变换和几何光学的方法对不同工作方式的航空相机由扫描反射镜沿俯角方向旋转引起目标像旋转问题作定量计算，为偏流补偿机构工程应用提供理论依据。
The details and the conclusions as follow: Through the theory of differentiable manifolds and Lie group, a geometrical description has been given on kinematics and dynamics of single and dual robot manipulators. This means the motion variables and force variables of the system have more explicit geometrical meaning. In particular, in order to solve the problem of rotation order brought by Euler angles representation, we define the pose vector, which can represent the rotation motion of rigid body continuously.
本文在已有的双／多机械手协调控制的研究结果上，着重对双／多机械手在紧抓持情况下操作刚体和柔性物体的协调和控制问题进行了研究，所取得的研究成果和结论如下：利用微分流形和李群理论建立了对单、双机械手系统运动学和动力学的几何描述，使整个系统的各运动变量和力变量的几何意义更加明确。
Rotation rings appear at one end of the selected clip vector ghost (figure 8-9, A).
旋转环出现在被选择幽灵矢量的一端。
X, Y and Z describe a vector which is the axis of rotation.
注意，对于这里的旋转轴而言，是有方向区别的。
As the current and voltage have the same basic frequency, the unit voltage Park vector and its conjugate are used to rotate the current Park vector. During the course of rotation, the fundamental positive sequence component in the current Park vector can be filtered out but the others remain.
利用电压与电流基波频率相等，用单位电压Park矢量及其共轭对电流Park矢量进行旋转变换，从而将电流Park矢量的基波正序分量完全滤除而不影响其他的谐波分量。
Magnetic acoustic emission makes use of the phenomenon that reciprocating oscillation and rotation of magnetization vector occurring in magnetic domain walls in ferromagnetic materials under the influence of external magnetic field could produce stress waves to cause acoustic emission.
磁声发射利用了铁磁材料中的磁畴壁在外磁场作用下往复震荡和磁化矢量的转动而产生应力波从而导致声发射现象。
Inscribed polygons are used to approximate a circle, and the number of line segments compose the polygon is detemined by the radius and its image of a circle. Calculation of rotation angles between circle and world coordinate systems with normal vector of circles is also discussed. The proposed approach is tested with several real image data, and results are very satisfying.
讨论了利用空间圆所在平面的法向向量计算空间圆局部坐标系相对于物方坐标系的两个旋转角的方法，系统论述了基于物方直接解和直线段最小二乘模板匹配方法进行空间圆匹配与重建的数学模型，并利用实际图像数据进行了重建实验，取得了较好的重建结果。
According to the different orientations of domain walls with respect to the (100) observation plane of a foil, 90°domain boundaries may be divided into two kinds. one is thin lens or ring shaped a-a 90°domain boundary, and the domain wall lies on the {110} plane; Usually, most of these domain boundaries are uncharged; according to the extinction rules for the (011) domain walls, the displacement vector 〓 along 〓 can be dertermined, which is parallel to the line of intersection between the domain wall and the plane consisting of spontaneous polarization vectors on both sides of domain boundary; from selected area electon diffraction of crystals including domain boundary, we not only examine slight difference in the crystal parts on both sides of the domain boundary, but also obtain crystallographic relationship between them, that is, there exists a 180°rotation symmetry operator along a normal of domain wall. The other is Z or ring shaped a-c 90°domain boundary along {010} direction, and the displacement vector 〓 runs along 〓 direction.
根据界面相对于样品中(100)观测面取向的不同，90°畴可分为两类：一类为薄透镜片状或环状的a-a90°畴，其界面平行于{110}，多数不带电，由消光规律可确定其位移矢量平行于畴界面与自发极化所在平面的交迹，即，〓方向，而从包含畴界的选区电子衍射图可知，这种不带电的90°畴界两侧存在微小的取向差，其界面两侧的结晶学关系为以界面法线为二次轴的旋转关系；另一类为Z状或环状的a-c90°畴，其界面平行于[010]或[001]，相应的位移矢量为〓方向。
The E-vector makes one complete rotation as the wave advances through one wavelength.
当波前进了一个波长之后，E矢量转了一整周。
Based on the vector module`s characteristics of invariance of translation and rotation coordinate transformation, a new fragment matching method is brought forward.
根据向量模在平移、旋转等坐标变换中具有不变性的特征，给出了一种新的碎片匹配算法。
Discussed results show that the feature vector is invariable for images in complex transformations on translation, rotation, noise adding and differences in resolution, and can be used as the features in the application of imaging matching location.
综合得出，在一定的条件下，该特征向量对平移、旋转、加噪、分辨率变化等多种复合变换下的图像具有不变性，可以作为成像匹配定位应用的特征量。
The main results are: If only a single image of a single parallelogram is known, the rotation matrix and direction of the translation vector from the camera system to the object system can be determined.
主要结论有：如果平行四边形的两组边长均未知的话，则从该平行四边形的单幅图像，仅可以确定物体坐标系与摄像机坐标系之间的旋转矩阵和平移向量的方向，平移向量的大小无法确定。
In order to overcome the defects of general image retrieval that using same texture feature vector and existing accumulative error in similarity measure, a novel Rotation Invariant Texture Retrieval Method Based on Learning Log-Gabor Subspace Feature Optimization was proposed.
针对传统基于内容的纹理图像检索方法中抽取固定特征和相似性度量存在累积误差的不足，提出一种新的基于学习的Log-gabor子空间特征优化的旋转不变纹理图像检索方法。
Topics on construction of Complex representation, especially analytic signal of real signal are studied from the viewpoint of vector rotation.
从矢量旋转的角度出发，来考察实信号的复数形式，特别是新的解析信号的构造问题。