Optimality and guidance for planar multiple-burn orbit transfers

An analysis of the second variation for extremal orbital transfers is presented, as well as a discussion of a multiple-burn guidance scheme that may be implemented for such transfers. The second variation analysis includes the examination of the conditions for free final time transfers. A continuous burn transfer is shown to have neighboring extremals through these conditions. An implicit guidance scheme is explored, which implements a neighboring optimal feedback guidance strategy to calculate thrust direction and thrust off-times. A new time-to-go formulation is introduced, which has improved performance for this transfer. This continuous burn guidance scheme is adapted to multiple-burn transfers. A two-burn guidance problem is simulated. (Author)