四元

A conception of "standard quaternion" is proposed and its significance in attitude simulation is also discussed.

最后讨论了用四元数实现姿态描述惟一性的问题，并提出了"标准"四元数的概念。

Accordingly, it is also very important for quaternion matrix theory.

同样地，对于四元数体上矩阵的理论研究和计算而言，四元数矩阵分解也占有十分重要的地位。

The result of numeric computation demonstrates that the approximate directional algorithm is robust, the result of Monte Carlo simulation shows that the performance of the optimum four-element array structure is better than the common one or the regular tetrahedron one.

数值计算结果表明，提出的近似定向算法是可靠的；计算机蒙特卡罗仿真结果表明，导出的最佳四元阵列性能优于普通的四元阵和正四面体阵。

We work out generalized Schur decomposition of quaternion matrix pencil and give out a sufficient condition for simultaneous unitary diagonalization of two quaternion matrices.

2得到了四元数矩阵束的广义Schur分解及两四元数矩阵可同时酉对角化的一个充分条件。

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。

These houses generally have a square十五六size, usually in monthly rent一百四五十yuan, 56 yuan per person per month to add the water and electricity for each unit of the Pentagon to seven angle, if there is cable TV subscription fees, toilet fees, one month down, one house at least monthly expenditure一百六七十million, more than close to 200 yuan.

这些房屋通常有十五六平方米大小，通常在每月租金一百四五十元， 56元，每人每月增加的水费，电费为每单位五角大楼至7角，如果有有线电视收费费，厕所费，一个月下来，一所房屋，至少每月支出一百六七十亿美元，超过近200万元。

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。

If now the case, let alone a four-yuan, 400 yuan of money that is a party, then people are not allowed toward that lire.

要是现在的话，别说是四元钱，就是四百元钱一方的话，老百姓也不准往那里拉。

By using it, we solve the Yamabe problem on quaternionic contact manifolds when the Yamabe invariant is smaller than that of the sphere.

我们还建立了四元切触流形的分析基础，应用建立的分析工具，在流形Yamabe不变量与球面的不同时，解决了四元切触流形上的Yamabe问题。

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。