Necessary and Sufficient Conditions are known for the problem of the impulsive minimization of the total characteristic velocity of a spacecraft subject to linear equations of motions. These conditions are global in the sense that the primer vector must be known over the entire flight interval. The purpose of the present paper is to present new localized necessary and sufficiency conditions that are derived from the original ones, but requires calculation of information about the primer vector only at a few specific points. These new necessary and sufficiency conditions have both theoretical and practical value.
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