A SOLUTION OF THE GODDARD PROBLEM
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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The problem of optimizing the thrust of a vertically ascending rocket is solved here under the assumption of isothermal atmosphere in two important cases 1 the jet Mach number is sufficiently large and 2 the drag is a convex function of the velocity. The first case embraces all physical drags and is valid for the Earth the second extends to all atmospheres, but is restricted to drags that are fairly common. With impulsive boosts in velocity admitted, the solution is shown to contain a finite number of such boosts in the sonic region of the rocket velocity, and to contain no coasting arcs except in the terminal stage. An absolute minimum is proved with the aid of a sufficient condition applicable to problems of optimum control.
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