Search NASA⌕ Search

SEARCH · Search NASA

Results for “mathematical programming”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

STABCAR: A program for finding characteristic root systems having transcendental stability matrices

STABCAR can be used to determine the characteristic roots of flexible, actively controlled aircraft, including the effects of unsteady aerodynamics. A modal formulation and a transfer-matrix representation of the control system are employed. Operable in either a batch or an interactive mode, STABCAR can provide graphical or tabular output of the variation of the roots with velocity, density, altitude, dynamic pressure or feedback gains. Herein the mathematical model, program structure, input requirements, output capabilities, and a series of sample cases are detailed. STABCAR was written for use on CDC CYBER 175 equipment; modification would be required for operation on other machines.

Adams, W. M., Jr.↗

Program Calculates Forces in Bolted Structural Joints

FORTRAN 77 computer program calculates forces in bolts in the joints of structures. This program is used in conjunction with the NASTRAN finite-element structural-analysis program. A mathematical model of a structure is first created by approximating its load-bearing members with representative finite elements, then NASTRAN calculates the forces and moments that each finite element contributes to grid points located throughout the structure. The user selects the finite elements that correspond to structural members that contribute loads to the joints of interest, and identifies the grid point nearest to each such joint. This program reads the pertinent NASTRAN output, combines the forces and moments from the contributing elements to determine the resultant force and moment acting at each proximate grid point, then transforms the forces and moments from these grid points to the centroids of the affected joints. Then the program uses these joint loads to obtain the axial and shear forces in the individual bolts. The program identifies which bolts bear the greatest axial and/or shear loads. The program also performs a fail-safe analysis in which the foregoing calculations are repeated for a sequence of cases in which each fastener, in turn, is assumed not to transmit an axial force.

Buder, Daniel A.↗

Engineering description of the OMS/RCS/DAP modes used in the HP-9825A High Fidelity Relative Motion Program (HFRMP)

Simplified mathematical models are reported for the space shuttle's Orbital Maneuvering System (OMS), Reaction Control System (RCS), and on-orbit Digital Autopilot (DAP) that have been incorporated in the High-Fidelity Relative Motion Program (HFRMP) for the HP-9825A desk-top calculator. Comparisons were made between data generated by the HFRMP and by the Space Shuttle Functional Simulator (SSFS), which models the cited shuttle systems in much greater detail. These data include propellant requirements for representative translational maneuvers, rotational maneuvers, and attitude maintenance options. Also included are data relating to on-orbit trajectory deviations induced by RCS translational cross coupling. Potential close-range stationkeeping problems that are suggested by HFRMP simulations of 80 millisecond (as opposed to 40 millisecond) DAP cycle effects are described. The principal function of the HFRMP is to serve as a flight design tool in the area of proximity operations.

Wilson, S. W.↗

Solar flat plate Final report

Computer program and mathematical model for calculating performance characteristics of solar thermoelectric energy conversion plate

Source record↗

Power processing methodology

Discussion of the interim results of a program to investigate the feasibility of formulating a methodology for the modeling and analysis of aerospace electrical power processing systems. The object of the total program is to develop a flexible engineering tool which will allow the power processor designer to effectively and rapidly assess and analyze the tradeoffs available by providing, in one comprehensive program, a mathematical model, an analysis of expected performance, simulation, and a comparative evaluation with alternative designs. This requires an understanding of electrical power source characteristics and the effects of load control, protection, and total system interaction.

Fegley, K. A.↗

Constrained sloshing of liquid mercury in a flexible spherical tank

The mercury propellant tank system developed for use with solar electric propulsion was studied to analytically determine the resonant frequencies of the tank system and compare them with the anticipated control natural frequency of the spacecraft. The system consisted of a stainless steel spherical shell and a hemispherical elastometric diaphragm. The major analytical tool used was the NASTRAN program. Six mathematical models were developed. Resonant frequencies for six harmonics were obtained for each of the six models considered. The results show that the lowest resonant frequency for the tank system is about an order of magnitude greater than the anticipated control frequency of the spacecraft.

Lestingi, J.↗

Constrained sloshing of liquid mercury in a flexible spherical tank

The mercury propellant tank system developed for use with solar electric propulsion was studied to analytically determine the resonant frequencies of the tank system and compare them with the anticipated control natural frequency of the spacecraft. The system consisted of a stainless steel spherical shell and a hemispherical elastomeric diaphram which separates the mercury propellant and the gaseous nitrogen pressurant. The major analytical tool used was the NASTRAN program. Six mathematical models, which represent various amounts of mercury in the tank system were developed. Resonant frequencies for six harmonics were obtained for each of the six models considered. The results show that the lowest resonant frequency for the tank system is about an order of magnitude greater than the anticipated control frequency of the spacecraft.

Lestingi, J.↗

Global Earth Response to Loading by Ocean Tide Models

Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.

Estes, R. H.↗

A new approach to the minimum weight/loss design of switching power converters

A new technique using the mathematical nonlinear programming ALAG is proposed to facilitate design optimizations of switching power converters. This computer-aided approach provides a minimum weight (or loss) design down to the details of component level and concurrently satisfies all related power-circuit performance requirements. It also provides such design insights as tradeoffs between power loss and system weight as the switching frequency is increased.

Lee, F. C.↗

Verification of Numerical Algorithms

The following strategy is suggested for specification and proof: (1) Defer the construction of a formal program specification with respect to I/O assertions unit the correctness of the program with respect to an abstract mathematical model of program intent is demonstrated. (2) Prove that an abstract machine (using infinite precision arithmetic) would compute that object exactly. (3) Prove that the computational sequences of arithmetic operations that occur in the abstract machine must be precisely the same at every step as those occurring on an actual machine (with finite precision arithmetic), executing the same program. (4) Use a Verification Conditions VC-generator that knows about the semantics of arithmetic operations to annotate the program with assertions that bound (or in some circumstances estimate) the difference between the actual machine state variables and the corresponding ones of the abstract machine. Construct the formal program specification by combining the verification conditions into theorems about computational error that can be proved with mechanical assistance.

Source record↗

Optimization of payload mass placement in a dual keel space station

In order to keep a Space Station in a stable low-Earth orbit, angular momentum storage and translational attitude control systems will have to be used. In order to minimize the size of these attitude control systems, the induced gravity gradient torque effects will have to be minimized. This can be done by minimizing the cross-products of inertia of the Station through the management of payload placement with the Station geometry. A derived and automated methodology is presented which utilizes mathematical nonlinear programming techniques. An optimal arrangement of a set of five payloads on a Dual Keel Space Station was found that minimized the cross products of inertia and thus the required controllability resources.

Ferebee, Melvin J., Jr.↗

Predicting Temperatures In Ball Bearings

Computer simulations speed design studies. Analyses performed in two or three dimensions. Sizes and shapes of components approximated by zones or nodes connected by gridlines. From geometric information about grids and boundary conditions, properties of bearing and lubricant materials, and information supplied by users, thermal-analysis programs generate mathematical models for thermal transport. Thermal analysis of high-speed rolling contact bearings matured so much that computerized numerical simulations replace expensive time consuming full scale experiments.

Wagner, William R.↗