本文系统的研究了四元数矩阵分解理论。
In this paper, decomposition of a quaternion matrix is systemically studied.
用当前四元数的自然对数替换此四元数。
姿态运动学和动力学用误差四元数描述。
The attitude kinematics and dynamics are both described by error quaternions.
欧拉参数是规范四元数。
答案在这，你首先需要计算你的四元数的平均值。
To answer that, you first need to calculate the norm of your quaternion.
四元数将三维中旋转的概念扩展到四维中的旋转。
Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions.
两个四元数相等的准则是，它们的数量部分相等。
The criterion of equality of two quaternions is that their scalar parts shall be equal.
用四元数方法建立起卫星动力学方程和运动学方程。
The satellite dynamics equation and kinematic equations are built with the method of quaternion.
当然，你可能也会用到四元数转换的“常规”表示法。
Of course, you'll also need to be able to convert from "conventional" representations to quaternions.
给出了自共轭四元数矩阵的弱圈积的特征值的一些不等式。
Some inequalities of eigenvalues for weak cycle products of self-conjugate quaternion matrices are given.
这是试图把四元数方法引入空间啮合原理研究的一种尝试。
This represents an attempt in introducing quaternion methods in the study of cases involving space engagement.
采用四元数描述刚体姿态，建立了刚体姿态运动的数学模型。
Quaternion is used to describe the orientation of a rigid body, and attitude motion is modelled.
由此，把复数域上矩阵论的若干重要定理推广到了四元数体。
Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.
因此，对于解决欧拉方程奇异性来讲，双欧法要优于四元数法。
So, dual Euler method is better than quaternion method in the solution of the singularity of the Euler equation.
CwMtx中的矩阵包括向量和方阵，其中向量包括空间向量和四元数。
The matrices in CwMtx include vectors and square matrices, where vectors include space vectors and quaternions.
使用四元数的第二个理由，就是其可实现两个状态间的平滑插值。
The second argument that is commonly given for the use of quaternions is the possibility of smoothly interpolating between two orientations.
采用最小参数法求解四元数微分方程，优化了四元数实时更新算法。
When optimizing synchro update of the quaternion, the quaternion differential equation is calculated by using minimum parametric method.
一个按引用传递的数值，标识该四元数的旋转角度(以弧度为单位)。
Angle a number, passed by reference, that identifies the Angle of rotation, in radians, of the quaternion.
研究了采样与静差补偿，以及四元数、姿态、位置和速度更新的算法。
The sample and static error compensation, quaternion and attitude updating and algorithm of station and velocity updating were researched.
四元数就不会遭受万向节锁的痛苦，因为它不用三个分离的轴表示旋转。
Quaternions do not suffer from gimbal lock, because they do not express rotations relative to three separate axes.
对高精度导航系统和大机动场景来说，对偶四元数算法是一个更好的选择。
The new algorithm turns out to be a better choice than the conventional algorithm for high-precision navigation systems and high-maneuver applications.
本文获得了四元数矩阵的范数和迹的一些不等式，改进了近期的某些结果。
In this paper, we obtain some inequalities for norm and traces of quaternion matrices.
同时得到一些关于四元数矩阵的性质，以及体上矩阵相似和合相似的充要条件。
Finally, the necessary and sufficient condition is shown for similarity and consimilarity of matrices over quaternion field.
本文以姿态误差四元数与陀螺漂移误差之间的关系为基础，构建了系统状态方程；
The state equations of the system are established on the basis of the relation between attitude error quaternion and the gyro drift.
本文对四元数体上矩阵奇异值摄动定理给出了推广，且这些结果对复矩阵也是新的。
The quaternion matrix singular value perturbation theorem is generalized and these results are also new one for complex matrix.
基于旋转群代数，以航天器姿态控制研究为背景，提出了四元数的核心矩阵的概念。
A concept of kernel matrix of quaternion is proposed, which is based on rotation group algebra and with spacecraft attitude control as its background.
四元数一实数和一矢量的和的表达式，有四个项，一个为实数项，另外三个为虚数项。
An expression that is the sum of a real number and a vector and that contains four terms, one real and three imaginary.
四元数可能把三维旋转的概念推广到四维(请参阅参考资料，其中有四元数的参考资料的链接)。
Quaternions make it possible to extend the concept of rotation in three dimensions to four dimensions (see Resources for links to quaternion references).
四元数可能把三维旋转的概念推广到四维(请参阅参考资料，其中有四元数的参考资料的链接)。
Quaternions make it possible to extend the concept of rotation in three dimensions to four dimensions (see Resources for links to quaternion references).
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