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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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Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.
Several aerospace problems are solved using various reliability methods. The problems considered are associated with distribution functions, sampling, accelerated life testing, and accept/reject decisions with sequential testing. In addition, two reliability case histories are described in detail. They include the second space Electric Rocket Test (SERT II), and the Microthruster Power Conditioner (MTPC) life test, both conducted by the Lewis Research Center.
A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.
Extension of Allen and Wing's (1970) previous work on problems of transport in periodic media to the matrix case. A method in the form of a complete set of equations is presented that may be used without any further analytical work by investigators interested in computing solutions to problems of the type the method is designed to handle. All the formulas have been checked out numerically, and their effectiveness is demonstrated by numerical examples.
New ideas and techniques recently put to use at the Jet Propulsion Laboratory for structural dynamics of spacecraft are presented. This paper deals with practical problems rather than elaborate mathematical theories and is concerned with the system approach for structural dynamics, an approach which has received attention in the recent past owing to the use of the fast Fourier transform algorithm which permits an economical use of digital computers. Concept of dynamics mass in the frequency domain is introduced. Reaction forces and moments at the base of a spacecraft in boosted flight configuration are determined. A combination of digital and analog techniques for special problems is presented. The examples reported are on actual spacecraft.
Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
This paper presents a state-space approach to the multivariable 'type one' servomechanism problem. Necessary and sufficient conditions for the controllability of such systems are derived and applied to the observability of the (dual) state reconstructor problem for a system with an unknown constant input. The paper also presents a simple systematic design algorithm which provides type one servomechanism performance to command inputs, together with pre-specified closed-loop pole locations. Examples are given to illustrate the utility of the design procedure.
A technique is presented by which one can apply the Minimum Principle of Pontryagin to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being essentially deterministic. The technique is applied to systems with quadratic and non-quadratic costs to illustrate its use.
Reviewed are some current problems in modeling man-machine control behavior in a biodynamic environment. It is given in two parts: (1) a review of the models which are appropriate for manual control behavior and the added elements necessary to deal with biodynamic interfaces; and (2) a review of some biodynamic interface pilot/vehicle problems which have occurred, been solved, or need to be solved.
The inverse scattering problem is introduced in the context of the Schroedinger equation. The emphasis is on the Gelfand Levitan approach to the nonrelativistic problem at fixed angular momentum.
Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.
The activities of the Social Sciences Group in solving earth resources management problems as related to social factors, are reported. Major efforts of the Group revolved around identifying potential users of ERTS data, ascertain the user's needs, and assay the organizational impacts of new and technologically advanced sources of information. Attempts were also made to develop a linear programming model to be used in decision making with respect to resources being observed by ERTS and other remote sensing vehicles. The cost effectiveness of solving these management problems is discussed.
It is pointed out that too frequently during the design and development of mechanisms, problems occur that could have been avoided if the right question had been asked before, rather than after, the fact. Several typical problems, drawn from actual experience, are discussed and analyzed. The lessons learned are used to generate various suggestions for minimizing mistakes in mechanism design.
The Schwarz-Neumann alternating method is employed to obtain stress intensity solutions to two crack problems of practical importance: a semi-infinite elastic plate containing an edge crack which is subjected to concentrated normal and tangential forces, and an elastic half space containing a semicircular surface crack which is subjected to uniform opening pressure. The solution to the semicircular surface crack is seen to be a significant improvement over existing approximate solutions. Application of the alternating method to other crack problems of current interest is briefly discussed.
A study was conducted to investigate the feasibility of using combined subsonic and supersonic linear theory as a means for solving unsteady transonic flow problems in an economical and yet realistic manner. With some modification, existing linear theory methods are combined into a single program and a simple algorithm is derived for determining interference between lifting surface elements of different Mach number. The method is applied to a wide variety of problems for which measured unsteady pressure distributions and Mach number distributions are available. By comparing theory and experiment, the transonic method solutions show a significant improvement over uniform flow solutions. It is concluded that with these refinements the method will provide a means for performing realistic transonic flutter and dynamic response analyses at costs which are compatible with current linear theory based solutions.
The Boltzmann equation is considered in terms of the problem of relaxation of some initial distribution function which depends only on velocities, to Maxwell's distribution function. The Boltzmann equation is given for the relaxation problem in which the distribution function f(t, u, v) is time dependent and is also dependent on two other variables u and v (the velocities of rigid spherical molecules). An iteration process is discussed in which the velocity space u, v is subdivided into squares, the distribution function in each square being approximated by the second-order surface from the values of the distribution function at nine points. The set of all of these points forms a network of u, v values at the nodes of which the distribution function can be found.
Results of a three-year research effort on retrieval and deployment problems associated with orbiting payloads are summarized. Answers to several basic questions about rendezvous, docking, and deployment dynamics and controls were obtained. A basic retrieval mission profile was formulated in order to develop relevant technology. A remotely controlled retrieval package was conceived. Special deployment dynamics problems associated with high altitude deployment were investigated, and new knowledge of payload spin reorientation was obtained.