轴矢量

角动量是一种轴矢量。

Angular momentum is an axial vector quantity .

用轴矢量R作为序参量来描述反铁电相便是对称性的变化，对于已得到的晶体相变前后的对称点群，应用居里原理，得到了理想结果。

An axial vector R is selected as the order parameter to reflect the change of symmetry in anti-ferroelectric phase transition . According to Curie principle , the satisfying results are obtained relative to the change of symmetry group in the phase transition .

主要研究内容和结论有：利用矢量瑞利-索末菲（RS）衍射积分公式，推导出非傍轴矢量高斯光束通过圆环衍射的解析式。

The major contents and results are as follows : Starting from the vectorial Rayleigh-Sommerfeld ( RS ) diffraction integrals , the analytical expressions of vectorial Gaussian beams through an annular aperture are derived .

研究了通过优化一组刀位文件的综合误差度来确定工件坐标系定位矢量的方法，提出了基于刀轴矢量的Descartes空间插补算法。

The location vector of the workpiece coordinate systems was found by optimizing the error of the cutter location using an interpolation algorithm in the Descartes coordinate system based on the cutter axes vectors .

根据Porras的非傍轴矢量矩理论，对双异质结半导体激光器的光束质量进行了研究。

The beam quality of double heterostructure injection lasers was studied based on non paraxial vectorial moment theory developed by Porras .

轴矢量自身可参与矢积。

An axial vector may itself enter into a vector product .

从弹轴矢量出发，推导了姿态角的数学公式。

Starting with the axis vector , the attitude angle is derived .

极矢量与轴矢量的区别在于它们的反演性质不同。

Polar vectors and axial vectors are distinguished by their inversion properties .

非傍轴矢量衍射光束的光强及其能量传输的研究

The Study of Light Intensity and Energy Transmission of Non-paraxial Vector Diffraction Beam

有限角位移真是轴矢量吗

How can finite angular displacements be axial vectors

叶轮四坐标数控加工中刀轴矢量的计算

Calculation of cutter - axes vector for 4 - axis numerical control machining of impeller

一类开式整体叶轮五坐标数控加工刀轴矢量生成及其光顺方法的研究

Generation and the Smoothing Method of 5-axis NC Machining Tool Orientation for the Open Integrated Impeller

刚体定点运动的有限转角应是轴矢量

The limited rotative angle of a rigid body motion with a fixed point should be axial vector

同时，引入了刀轴矢量平滑化的概念，提出了基于四元数向量插值的新算法；

The concept of tool axis vector smoothing was introduced and the quaternion vector interpolation algorithm was proposed .

对于任意曲面叶轮的四坐标加工，提出了一种计算刀轴矢量的方法。

A calculation method of cutter-axes vector for 4-axis numerical control machining of arbitrary surface impeller is presented .

然后我们计算了轴矢量，矢量和张量真空磁化率。

Then we use the expressions to the calculation of the axial vector , vector and tensor vacuum susceptibilities .

计算出了走刀行距、走刀步长以及刀轴矢量，最后得到了刀位轨迹。

Finally the tool path is generated after calculating path interval , path step-length and cutter axial vector . 3 .

介绍用双三次参数曲线拟合曲面、平头铣刀的直径、铣削的步长及行距选择、刀位点和刀轴矢量的计算。

It introduced imitating surfaces with bicubic parametric curves , feed length , cutter location and vector of cutter location .

提出了一种新的刀轴矢量函数的生成算法，可以保证全局刀轴矢量连续光顺。

A tool-axis vector generating algorithm is proposed . The algorithm can ensure the continuity and smoothness of the global tool-axis vector .

基于柱状刀侧铣不可展直纹面的亮点偏置法给出了刀轴矢量的计算方法。

Calculation method of tool axis vector was given according to the two-point offset of cylindrical milling cutter milling undevelopable ruled surface .

结果表明，该刀轴矢量光顺方法可以避免刀轴方向频繁变换，同时也可有效地提高加工精度。

The results show that this method can avoid frequent orientation change of the cutter , and can improve the process precision efficiently .

提出用特征偏置法求取刀轴矢量，以使加工误差在刀具与被加工面切触状态下趋于最小；

For finding the tool axis vector , a feature offset method is proposed to minimize machining tolerance under the condition of circumferential milling .

同时解决了曲面法矢垂直于回转平面时刀轴矢量难以确定的关键问题。

Also , a solution is offered to solve the problem of generating tool axis vector when the surface normal ts perpendicular to rotary plane .

在这组矢量中，求出与由曲面几何量计算出的刀轴矢量最相近的矢量，并且使刀具处于该刀轴矢量时与叶片不发生干涉，将这个矢量作为最终的刀轴矢量。

To calculate the nearest vector and make sure there is no interference between cutter and blades , then this vector is the final cutter-axes vector .

后者通过设置刀轴矢量变化的阈值并采用集合碰撞体，实现了刀位的跳点检查和集合运算检查。

The second algorithm , depending on setting the threshold controlling tool-axis vector and using solid based on Boolean-operation , realizes unsafe CL-points and Boolean-operation check .

为了解决数控刻楦中刀轴矢量方向相对鞋楦表面法向频繁变换而造成冲击或发生干涉等问题，提出一种刀轴矢量平滑化插值方法。

In order to avoid striking or collision caused by incessant changing of tool orientation in shoe last carving , a tool orientation smoothing approach was proposed .

对两个相邻叶片的直母线进行插值后，得到的刀轴矢量能完全避免刀具与叶片之间的干涉问题。

The cutter orientation vector , which was got from interpolating the two ruled lines of adjacent blades , could entirely avoid the interference between cutter and blade .

针对直纹面叶片侧铣加工进行刀具轨迹规划，通过偏置法计算圆柱铣刀的刀轴矢量，计算刀心点坐标和走刀步长。

Plan tool path based on flank milling the ruled surface blades . Calculate the tool axis vector of the cylindrical cutter with the offset method and tool center point coordinates and the step-length .

由于四坐标铣床自由度的限制，根据曲面上接触点的几何量计算出的刀轴矢量，不一定能在四坐标系床上实现。

Because of the restriction of freedom degree in 4-axis NC machine tool , the cutter location calculated by geometry characteristic of cutter contact point on surface may not be implemented on 4-axis machine tool .

在叶片曲面侧铣精加工方面，分析了过切误差，并采用旋转初始刀轴矢量的干涉控制方法，提高了叶片曲面的加工精度。

During the blade surface finish machining , the over-cut error is analyzed and by means of rotating initial tool axis vector to control the interference . Therefore , the impeller machining precision is improved .