Optimization of transfers under constraints on the thrust direction: I

Transfers with a low thrust are considered under constraints imposed on the thrust vector direction. These constraints can be caused by peculiarities of the attitude control system and the mode of stabilization of a spacecraft, and, in the general case, they are functions of the time and state vector. The constraints specified by equalities and inequalities are investigated. It is shown that the optimal thrust is directed along the projection of the Lawden’s primer vector onto the restricting set.