四元数

After analysing the existing smooth orientation interpolation methods we proposed a smooth orientaion interpolation method based on cubic cardinal spline in quaternion space. This method possesses the following advantages: interpolation, C〓 continuity, accurate evaluation of the quaternion value at arbitrary parameter, transparent to the users, adjustable parameters for controlling the velocity of orientation change.

在分析现有的朝向光滑插值方法基础上，提出了基于四元数空间三次C样条的朝向光滑插值方法，该方法具有插值、C〓连续、任一参数处的四元数值可精确求得、对用户透明、可以用参数调节关键帧处物体朝向变化的速度等优点。

In practical terms, an octonion is simply an octuple of real numbers

定义在八元数上的加法和乘法运算推广了在四元数上的加法和乘法运算。

This paper first elaborated the principle of SINS, some interrelated information,and the affect of renewed arithmetic to the system"s precision. Then, we studied thequaternion in traditional renewed attitude arithmetic. The quaternion is simple, andwhen run it into computer, it"s time saving. So, this arithmetic is often adopted byengineering. However, the quaternion brought unexchangeable error inevitably. Whenthe carrying body moves in highly dynamic situation, the error would become larger.So we should take effective measure to get over it.

本文首先论述了捷联式惯性导航系统的工作原理及相关知识，捷联惯导系统姿态更新算法对系统精度的影响；其次研究了传统的姿态更新算法中四元数法，该算法简单，计算量小，因而在工程中经常被采用，但是在四元数法中不可避免的引入了不可交换性误差，特别是在载体处于高动态环境时，这种误差就会很大，必须采取有效措施加以克服。

Results Vector algebra and vector analysis are the production of quaternions and the result of seeking mathematical indication of physical phenomenon, it′s the historic certainty as well as the effect of some accidental elements.

结果现代向量系统是从四元数发展而来的，是寻找物理现象的数学表示的结果；通过对哈密顿四元数与格拉斯曼系统的对比分析指出其历史的必然性。

We give different kinds of iterative methods of some quaternion matrix equations,and using structure-preserving property for complexification operator of the quaternion matrices,which analysis and character the convergence of various algorithms.

给出了若干类四元数矩阵方程的多种迭代算法，并利用四元数矩阵复表示运算的性质与保结构特性，分析和刻画了各种算法的收敛性。

We investigate mixed totally umbilical QR-submanifolds in a quaternionic space form and also study the pseudo-umbilical QR-submanifolds of a quaterninoic space form with some additional conditions.

考查四元数空间形式中混合型全拟脐QR子流形并研究了四元数空间形式中具有某种条件下的混合型伪脐QR子流形。

Specifying a rotation directly as a quaternion is completely unintuitive, so what you\'ll want to do is convert quaternions to and from other representations.

四元数并不天生就具有旋转的特性，因此你还要做一些转换四元数或其它的一些必要工作。

The conjugation by a unit quaternion (a quaternion of absolute value 1) with real part cos is a rotation by an angle 2''t'', the axis of the rotation being the direction of the imaginary part.

单位四元数（绝对值为1的四元数）若实部为 cos，它的共轭作用是一个角度为2''t''的转动，转轴为虚部的方向。

As it is expected, the main obstacle in the study of quaternion matrices is the non-commutation in multiplication of quaternions.

实四元数矩阵研究的主要难点是四元数乘法的不可交换性。

INS with single axis stablization is analyzed using quaternions, and system quaternions error model is worked out.

应用四元数方法分析了单轴稳定惯导系统，建立了系统的四元数误差模型。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。