Euler parameter is the normalized quaternion.

欧拉参数是规范四元数。

Through it, we can get quaternion some characteristics.

通过它，可以掌握四元数的一些特征。

Replaces the current quaternion with its natural logarithm.

用当前四元数的自然对数替换此四元数。

The basic theory and the usage of quaternion are also been introduced.

介绍了四元数法的基本原理及其在捷联系统中的用法；

To answer that, you first need to calculate the norm of your quaternion.

答案在这，你首先需要计算你的四元数的平均值。

In this paper, decomposition of a quaternion matrix is systemically studied.

本文系统的研究了四元数矩阵分解理论。

In this aspect, the quaternion theories and methods perhaps are appropriate.

在这方面，四元数的理论和方法或许是合适的。

In this paper, we study the existence for right eigenvalue of quaternion matrix.

本文讨论四元数矩阵右特征值的存在性问题。

Quaternion is used rather than Eular angles to avoid the problem of singularity.

使用四元数避免了欧拉角法的奇异问题；

In this paper, we obtain some inequalities for norm and traces of quaternion matrices.

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。

Both are expected to facilitate the future dual quaternion-based integrated navigation filter.

这两个误差模型可用来搭建基于对偶四元数的组合导航滤波器。

The satellite dynamics equation and kinematic equations are built with the method of quaternion.

用四元数方法建立起卫星动力学方程和运动学方程。

Quaternion is used to describe the orientation of a rigid body, and attitude motion is modelled.

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。

The electromagnetism laws and the relativistic mechanics are described by the double quaternion.

用双四元数表述了相对论力学和电磁规律。

Two control laws are presented for attitude regulation of a rigid body expressed by unit quaternion.

给出了用四元数表示的刚体姿态调节问题的两种控制规律。

Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.

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。

Some inequalities of eigenvalues for weak cycle products of self-conjugate quaternion matrices are given.

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。

Angle a number, passed by reference, that identifies the Angle of rotation, in radians, of the quaternion.

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)。

This represents an attempt in introducing quaternion methods in the study of cases involving space engagement.

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。

So, dual Euler method is better than quaternion method in the solution of the singularity of the Euler equation.

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。

It proves that the estimate sectional curvature of a quaternion manifold is very useful for Riemann symmetric space.

它进一步说明一个四元流形的截面曲率的估计对许多对称黎曼空间都是有效的。

Finally, the necessary and sufficient condition is shown for similarity and consimilarity of matrices over quaternion field.

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。

The quaternion matrix singular value perturbation theorem is generalized and these results are also new one for complex matrix.

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。

A new effective method which makes use of quaternion theory is presented to implement location transformation of a plane curve.

利用实四元数理论，提出了一种将一般位置平面曲线变换到空间任意指定位置的一种简捷方法。

The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix.

利用与每个四元数矩阵相关联的复伴随矩阵，问题被简化为关于复数矩阵的并行问题。

The state equations of the system are established on the basis of the relation between attitude error quaternion and the gyro drift.

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；

Quaternion method, which has been successfully applied to the Strapdown Inertial Navigation and Guidance for tens year, is classical.

数十年来，四元数及其解法成功地应用于捷联惯性导航和制导系统中，成为经典的算法。

When optimizing synchro update of the quaternion, the quaternion differential equation is calculated by using minimum parametric method.

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。

The sample and static error compensation, quaternion and attitude updating and algorithm of station and velocity updating were researched.

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。