Abstract: 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.

Key words: quaternion, at t itude erro r, generalized coo rdinate, spacecraft at t itude dynam ics, at t itude cont ro l