On verification of fuel-optimal space trajectories

Candidate fuel-optimal trajectories for rendezvous in space are obtained with a parameter optimization method. These trajectories, which may include a minimum radius constraint, are verified against necessary conditions for optimality. Necessary conditions are presented in the form of requirements on a primer vector and in terms of requirements on the jumps in the costates when the constraint is encountered. In addition, criteria due to Lion and Handelsmann indicate how to improve candidate trajectories which prove non-optimal so that they become locally optimal. Numerical results are presented which show that the candidate solutions must be obtained to a high level of accuracy before primer vector tests are valid.