The direct algorithm for calculating programmed controls of a special form in the problem of guidance of an orbital telescope

The problem is studied for calculating the programmed control of an orbital telescope with two-stage powered gyroscopes as actuators of the control system. Modifications are considered of the direct method for calculating the programmed controls, which is alternative to the method of inverse problems of dynamics. The suggested versions of the algorithm afford either the calculation of smooth controls taking prescribed values at the initial and the finite instant of time or the calculation of piecewise linear programmed controls realizable by the rotation of gyronodes with constant accelerations. The special feature of the dynamic model of an orbital telescope is the availability of the model of an invariant manifold in the space of states. The presented algorithm rebuilds the linearized model at each iteration of the calculation, its boundary conditions, and makes up a collection of independent variables of the state for these conditions.