Controlling space vehicle reorientation with minimal energy integral

We consider the optimal control problem for spatial reorientation of a space vehicle (SV) from an arbitrary initial to a given final angular position. The reorientation time is known in advance, so we are minimizing the rotation energy integral. We present an analytic solution of the proposed problem. With the method of quaternions, we have obtained formal equations and computational expressions for constructing the optimal reorientation program. For a dynamically symmetric SV, we give a complete solution of the SV reorientation problem in closed form. We give an example and mathematical modeling results for SV motion dynamics under optimal control. These results demonstrate that the developed method of controlling SV spatial orientation is feasible in practice.