Constrained multiple-revolution Lambert's problem

A fixed-time, multiple-revolution Lambert's problem is solved under given constraints. For N_max revolutions, there exist 2N_max + 1 mathematical solutions to Lambert's problem. Unfortunately, not all of these solutions are feasible. Practical solutions require that the perigee radius be greater than a minimum value (to avoid Earthimpacting trajectories) and the apogee radius be lower than a maximum value (to avoid expensive changes in eccentricity). In particular, short-path and long-path solutions require different considerations to discriminate between the unfeasible solutions. A solution procedure for the semimajor-axis range is proposed that takes these two constraints into account. Based on the semimajor-axis range, the solutions with a feasible number of revolutions can be easily selected. The case of zero revolutions is also discussed, as the trajectory may be feasible even if not complying with the bounds. Numerical examples show that the number of feasible solutions greatly decreases when considering the constraints.