quaternion

Quaternion definition and geometry meaning were described and quaternion movement equation was introduced.

阐述了四元数的定义、几何意义及四元数表示的运动学方程.

A quaternion can be used to represent any arbitrary rotation.

四元数可用来表现所有形式的旋转.

The quaternion feedback control laws was studied for the three-axis stabilization control using reaction wheels, a design method for the PID controller parameters was presented and the simulation results indicated that the control algorithm works efficiently.

针对以反作用飞轮作为执行机构的三轴稳定控制情形，研究了四元数反馈控制算法，给出PID控制器参数的设计，仿真结果验证了控制器设计是合理的。

Considering the target angle rate changing, an adaptive attitude tracking control law was designed based on the error quaternion, and the corresponding close system stability was also proved.

考虑目标姿态角速度可以时变的一般情形，设计了基于误差四元数的自适应姿态跟踪控制律，给出了稳定性证明。

The theoretical analysis results are verified by the performance comparison simulation between the conventional specific force integration algorithms and the dual quaternion algorithms under typical angular vibration and accelerated motion conditions. 3.

通过典型角振动及加速运动条件下传统捷联惯性导航算法和对偶四元数导航算法的仿真比较，对理论分析结果进行了验证。

The quaternion attitude algorithms are studied in this paper. The scale error, skew error and drift error for algorithms of different kind are clearly described by using US fraction of attitude matrix.

该文对姿态计算四元数方法进行了研究.通过对计算姿态矩阵的US分解，清楚地表达了不同算法的标度误差、歪斜误差和漂移误差；

All the existing Methods : Utilize quaternion algebra to iteratively compute M-sets'boundaries.

用文中提出的体绘制算法绘制了三元数法和四元代数法所构造的三维M集.

Applying the theories of abstract groups and permutation groups, the following results are obtained: ( 1) If a finite group G acts transitively on all the minimal subgroups by conjugation, G is then a cyclic p-group or a generalized quaternion.

运用抽象群和置换群的理论得到：（1）如果有限群G共轭作用在它的所有极小子群上传递，G一定是循环p-群或广义四元数群；

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 third phase of the form of intermediate code using easy-to-read type Quaternion.

第三阶段中间代码的形式采用便于阅读的四元式.

Thetheory includes Euler angular algorithm, direction cosine algorithm, quaternion algorithm and rotation vector algorithm.

基本理论包括欧拉角算法 、 方向余弦算法 、 四元数算法和等效旋转矢量算法.

For AUV and mass-varying AUV in 6 degrees of freedom ( DOF), the dynamic equations of motion with applying generalized vector notation are derived. In these equations, the attitudes are represented by the 4-parameter unit quaternion ( Euler parameters) and Euler angles.

建立了基于广义矢量参数形式的水下航行器的空间运动方程以及变质量航行器的空间运动方程，并考虑到实际需要，分别使用欧拉角和四元数形式对其进行表示。

Eight , design SAMPLE language grammar, semantic analyzer, the output quaternion type of intermediate results.

设计SAMPLE语言的语法 、 语义分析器, 输出四元式的中间结果.

MATLAB simulation shows that the quaternion makes the calculation and control of spherical motor simple, motor rotates along the given trajectory, and it is an efficient method.

MATLAB仿真表明，利用四元数的数学工具简化了球形电机的计算与控制过程，可以使电机按预定轨迹转动，是一种行之有效的方法。

Application of quaternion matrix in resolution of aerospace camera image plane position

四元数矩阵在航天相机像面位置求解中的应用

Finally, the 3-D M-sets generated by the ternary number and quaternion algebra are both rendered by our new algorithm.

用文中提出的体绘制算法绘制了三元数法和四元代数法所构造的三维M集。

The norm of a quaternion is similar to that of a vector.

四元数的平均值与矢量的有点相似.

It is realized by real quaternion overrides the weakness of matrix such as unintuitionistic, complex calculation.

此算法采用实四元数组实现,克服了采用矩阵实现时的非直观性 、 计算复杂等弱点.

Ion: To realize the optimal control of ships guise-angle, Integrating the quaternion arithmetic with the theory of optimal control and deriving Hamilton function, a mathematic model is obtained, which is applicable to the control of ship's guise-angle.

为实现舰船姿态角控制效果的最优化，将四元数算法和最优控制理论有机的结合，构造哈密顿函数，得出了适用于舰船姿态角控制的数学模型。

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

Mixed Operation of Quaternion, Special Function Differentiation and Application of Rolle's Theorem in Mizar

四元数混合运算及特殊函数的微分公式和洛尔定理应用的Mizar实现

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.

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.

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。

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.

Quaternion can avoid gibbs lock if you use euler angle to rotate 3 d model.

四元数可避免吉布斯锁如果您使用的欧拉角旋转三维模型.

Analysis of Spherical Mechanism through Quaternion Transformation

四元数变换分析球面机构

The method of adjusting screen-coordinate and object-coordinate of plane model with quaternion is discussed.

论述了以四元数法调整模型的屏幕坐标和物体坐标的方法.

In this paper, we firstly consider a quaternion algebra.

本文首先考察某个四元代数.

The Geometry Representation of Quaternion in Euclidean Three-space

四元数在三维空间的几何表示