四元数的核心矩阵及其在航天器姿态控制中的应用

 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。以此为中心,首先导出了核心矩阵本身、逆、行列式及其导数的若干关系式,然后应用核心矩阵得到了四元数姿态误差及其运动学关系的非常简洁的表示形式,最后利用核心矩阵证明了用缩减四元数为广义坐标和以常规 Euler角为广义坐标对描述航天器姿态动力学的等效性。研究结果可应用于航天器的快速、大角度和三维姿态机动控制

KERNEL MATRIX OF QUATERNION AND ITS APPLICATION IN SPACECRAFT ATTITUDE CONTROL

A concept of kernel matrix of quaternion is proposed, which is based on rotation group algebra and with spacecraft attitude control as its background. Centering around it, some related expression of kernel matrix itself, its inverse, its determinant and its derivative are derived first;then the concise expression of quaternion attitude error and its kinematic relationship are obtained with kernel matrix; finally, also proved is the equivalence of spacecraft attitude dynamics described with reduced quaternion as its generalized coordinate to that described with normal Euler angles as its generalized coordinate. The result of this paper can be used in rapid, large angle and three dimensional attitude maneuver control of spacecraft.