Analytical approximate solution of the problem of a spacecraft's optimal turn with arbitrary boundary conditions

The problem of the optimal turn of a spacecraft as a rigid body having an arbitrary dynamical configuration, with arbitrary boundary conditions on the attitude and on the angular velocity of the spacecraft in the quaternion formulation is considered. As an optimality criterion we use a functional that combines time and power spent in order to turn the spacecraft. In the class of generalized conic motions, the problem of the optimal turn is modified in such a way that the analytical solution of this problem can be obtained. The analytical solution of the modified problem can be considered as an approximate solution of the traditional problem of the spacecraft's optimal turn. Numerical examples that demonstrate the close agreement of the solutions of two these problems are presented.