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Results for “Two-point Boundary Value Problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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128 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Singular trajectories for time-optimal half-loop maneuvers of a high alpha fighter aircraft

Consideration is given to the problem of deriving a time-optimal open-loop control for the half-loop maneuver of a high-alpha aircraft, with initial conditions Mach 0.6 and 15,000 feet. Pontriagin's maximum principle is used to derive candidate optimal solutions. Using the two-point boundary-value algorithm, the flight path angle is maximized for various increasing specified final times until a final time of 13.6 sec yields a 180-deg flight-path angle. As the final time increased from 0.0 to 13.6 sec, the optimization process revealed 13 distinct switching structures of the control law, of which 11 contained singular arcs, and two had double singular arcs.

Hoffman, Eric↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Lancaster, J. E.↗