The paper considers the application of the method for analytical design of optimal controllers as formulated by of A.A. Krasovsky (optimization according to the criterion of generalized work) for the control synthesis of spacecraft reorientation from an arbitrary angular position to a given attitude during a fixed time period. A predictive algorithm model was selected as a numerical implementation for the analytical design according to the generalized performance criterion. In order to investigate the angular motion optimization methods experimentally, a model of the spacecraft reorientation control process was developed and implemented in C#. Numerical experiments demonstrated that the generic algorithm does not ensure the specified accuracy of the final orientation, and an increase in the weight coefficients in the terminal member in order to reduce the orientation errors leads to a loss of stability of the dynamic process. The paper proposes a modification of the prediction algorithm — a recurrent-iterative algorithm for exact reorientation of a spacecraft in a fixed time period. The approach used in this case involves organizing an iterative procedure for synthesizing the optimal control of the spacecraft reorientation based on a prediction algorithm. The optimal control calculated at each iteration is used at the next step of the iterative procedure as the next additive component of programmable control. Numerical experiments demonstrated that the recursive-iterative method for reorienting a spacecraft ensures the angular motion stability of the spacecraft and the specified accuracy of the final orientation in a wide range of boundary conditions. The scope of the proposed algorithm is limited to control objects with continuum end-effectors. An example of such a control object is a remote sensing satellite with power gyroscopes (gyrodines) in the orientation system.