Optimal spacecraft terminal attitude control synthesis by the quaternion method

We consider an optimal control problem of spacecraft retargeting from an arbitrary initial position to a given terminal angular position. The objective is to minimize a path functional. Using the quaternion method, we obtain an analytic solution of this problem and present formalized equations and computational expressions for synthesizing an optimal manoeuvre program. We also present an example and the results of mathematical simulation of the spacecraft motion dynamics under an optimal control, which demonstrate the practical implementability of the control method developed in the present paper.