Programs of time-optimal control in the problem of rendezvous transfer of spacecraft with low transversal thrust

We study the problem of determining time-optimal control of in-plane rendezvous transfer of spacecraft with low transversal thrust. We use the Pontryagin maximum principle to determine the optimal control program. Motion is considered in the vehicle centric system with linearized equations. We recognize secular and periodic components of relative motion. Motion control is accomplished by the reversal of the thrust acceleration component. We study the general problem – controlling the periodic and secular components at the same time (joint optimal control program). Also we study partial problems – determining separate control programs for secular and periodic components of planar motion. Solving partial problems made it possible to determine the structure of the joint optimal control program. We found that the adjustment of secular motion components contains no more than two phases of constant acceleration. The adjustment of periodic motion components consists of a sequence of boost and deceleration phases, the number of which in a single pass does not exceed three.