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adjoint system assumed Ballistics Bliss introduced Bryson calculating differentials calculus of variations Calif choosing a route Class notes coefficient Computational constants constraints control variable Convergence criterion Curves DETERMINING OPTIMUM SHIP differential equations discussed dose dt J0 end values equivalent Euler equation extremum f Ay f dt fallout Faulkner formulas Frank function Guess hence initial values integrand Integrate involved iteration Kelley Kopp Lagrange larger value Mathematics and Mechanics maximum speed method minimize the probability minimum Monterey multipliers Naval Postgraduate School neighboring Numerical OPTIMUM SHIP ROUTES path probability of detection problem of sending programmed and run rank related problems rendezvous RESEARCH PAPER routine satisfies the relation sending the ship simplify solution specified Supported by ONR system of differential terminal values tion trajectories transversal condition ucos UNITED STATES NAVAL values must satisfy vectors versal condition Xsin