Fuel-Optimal Rendezvous in a Central Force Field with Linear Drag

In this paper we consider the fuel-optimal rendezvous between a satellite and a spacecraft in a central force field with a drag force that is linear in the velocity. In this general setting we linearize the equations of motion of the spacecraft and show that they can be reduced effectively, in the case of a linear drag, to one second order linear differential equation. We then specialize to the case of inverse square laws. Under certain simplifying assumptions a state-transition matrix can be found in terms of integrals. The work can then be placed in the context of various control models that have been developed in previous work.