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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1968

HICOV - Newton-Raphson calculus of variation with automatic transversalities

Computer program generates trajectories that are optimum with respect to payload placed in an earth orbit. It uses a subroutine package which produces the terminal and transversality conditions and their partial derivatives. This program is written in FORTRAN 4 and FORMAC for the IBM 7094 computer.

Heintschel, T. J.↗
NASA NTRS1972

Bounded state variables and the calculus of variations

An optimal control problem with bounded state variables is transformed into a Lagrange problem by means of differentiable mappings which take some Euclidean space onto the control and state regions. Whereas all such mappings lead to a Lagrange problem, it is shown that only those which are defined as acceptable pairs of transformations are suitable in the sense that solutions to the transformed Lagrange problem will lead to solutions to the original bounded state problem and vice versa. In particular, an acceptable pair of transformations is exhibited for the case when the control and state regions are right parallelepipeds. Finally, a description of the necessary conditions for the bounded state problem which were obtained by this method is given.

Hanafy, L. M.↗
NASA NTRS1992

Sufficient conditions for a local minimum of the Bolza problem with a variable initial point

Sufficient conditions for a weak relative minimum of a form of the Bolza problem of variational calculus are derived. The variational problem considered includes arbitrary numbers of constraints on the initial and terminal points, but assumes no control constraints or interior point constraints. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of previously published sets of conditions. The derivation, though lengthy, is felt to be simpler in concept than previous derivations. The application of these conditions is demonstrated in the context of a simple geometric problem.

Wood, Lincoln J.↗