3D geosynchronous transfer of a satellite: Continuation on the thrust (Q597206)

The minimum-time three-dimensional transfer of a satellite from a low and eccentric initial orbit to high geostationary orbit is studied by assuming that the available thrust is very small (e.g., 0.3 Newton for an initial mass of 1500 kg). To solve the problem numerically, an optimal control mode is studied, and a homotopic procedure is introduced. Then, in the framework of parametric optimal control, the differentiability of the transfer time with respect to the thrust is investigated under specific assumptions. Numerical results obtained by coupling the continuation technique with a single-shooting procedure are detailed.