The extension of Lawden's primer vector theory from the two-body to the three-body problem is obtained by means of a peculiar approach to the optimization of impulsive maneuvers. The trajectory is considered to be composed of ballistic arcs that connect at "corners" where the spacecraft velocity undergoes jumps; no explicit control is present, but the necessary conditions for optimality are nevertheless provided by the optimal control theory. Thrust is applied parallel to the velocity adjoint vector, or primer vector, at the corners, where the primer must have unit magnitude; in time-free problems the time-derivative of the primer magnitude must be null in correspondence to the corners. Numerical examples deal with simple DELTAV-Earth-gravity-assist maneuvers, that are two-burn (departure and deep space) time-free transfers in the three-body problem; an inequality constraint ensures a surfficient distance from the Earth during the flyby. Results are compared to similar results obtained by using the patched-conic approximation. A powered flyby is performed when the primer magnitude suggests an additional burn in close proximity to the Earth.
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