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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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A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
Spacecraft guidance - multistage rocket trajectories
Spacecraft guidance - boundary value problem
Control optimization of guidance systems and trajectories
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.
Definitions of extremaloids in relation to optimal control problems and Lagrange problems based on Pontryagin principles
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.
A bibliography is presented of publications and reports resulting from the research project.
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.
Time dependent hypervirial theorem for variational wave functions - variational calculus
Ascent from lunar surface problem with solution by variational calculus
Methods to approximate variational calculus solutions in Saturn guidance
Caratheodory unified approach to Hamilton-Jacobi theory in variational calculus problems of optimal control
Optimizing lift-to-drag ratio of slender, flat-top wing of given planform in hypersonic flow by using variational calculus methods
Optimal design of RC lines distributed parameter systems using gradient technique and variational calculus
Equivalence of perturbation method, Newtons method, and adjoint-perturbation method for solving boundary value problems from variational calculus treatment of optimal control problems
Three-dimensional slender wings of maximum lift/ drag ratio in hypersonic flow studied by variational calculus under several lift and volume conditions
Perturbation theory-variational calculus analysis of optical rotatory power of molecules based on wavefunction badness