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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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Technique based upon matrix representation and matrix collapsing calculates the probability of successfully completing manned missions and of returning the spacecrew safely to earth. This technique provides analytic expressions for each subsystem, making it possible to relate changes in subsystem reliability directly to mission success and crew safety.
Matrix identity associated with linear digital filtering and recursive estimating determined using matrix projection operators and properties
Matrix system utilizing unique digital code enables drawing block diagrams with parallel blocks. Complete freedom is obtained in laying out diagram, and it is possible to go directly from matrix to finished drawing. Need to rough out diagram is eliminated and time involved is greatly reduced.
Magnetic matrix memory system for nondestructive reading of information contained in matrix
Density matrix components for multiconfiguration wave functions, constructing N electron /spin free/ Hamiltonian configuration interaction matrix
A point matrix kernel for radiation transport, developed by the transmission matrix method, has been used to develop buildup factors and energy spectra through slab layers of different materials for a point isotropic source. Combinations of lead-water slabs were chosen for examples because of the extreme differences in shielding properties of these two materials.
Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.
A common problem for experimental space physicists is the determination of the attitude matrix T which transforms vectors between representations in X and X' coordinate systems according to (vector V sub X) = (T sub XX')(vector V sub X'). A straightforward, simple, and efficient solution for the transformation matrix is a double-cross transformation. It is calculated from any two directions A and B, which are vectors normalized to unit length and are known in both X and X' coordinates. The B direction need be known only well enough to define the plane in which vectors A and B lie. The problem of the intersection of two cones as applicable to attitude solutions is also discussed.
In theories of numerical stability, roots to a characteristic polynomial are sought, which, in the case of the predictor with iterative correction method of numerical integration, are eigenvalues of a matrix whose elements depend on the coefficients used in the integration process. The characteristic polynomial is displayed explicitly in terms of the elements of the characteristic matrix.
An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.
The empirical data used in the 1969 Smithsonian Standard Earth (2) are presented. The variance-covariance matrix, or the normal equations, used for correlation analysis, are considered. The format and contents of the matrix, available on magnetic tape, are described and a sample printout is given.
The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.
An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities.
A significance criterion is proposed that compares the strength parameter against the parameter expected from a random group of vectors in variance matrix applications. The variance matrix technique for determining preference or avoidance directions in space for a group of vectors gives only the parameter indicating the strength of the preference or avoidance, and the proposed criterion is shown to be of help in the achievement of reliability.
Demonstration that the vanishing of certain coupling matrix elements at level crossings follow from angular momentum commutation relations. A magnetic dipole transition having delta M = plus or minus 1, induced near a crossing of the levels in a nonzero magnetic field, is found to have a dipole matrix element comparable to or smaller than the quotient of the level separation and the field. This result also applies in the analogous electric field electric dipole case.
Analytical models of three structures were used to test mass matrix-reduction schemes. Accuracy of four mode shapes and frequencies was tracked through successive mass matrix-reductions with diminishing numbers of indicator degrees of freedom. Results were consistently disappointing. Two new procedures were developed in attempt to improve accuracy.
The method used in computing the structural influence coefficient matrix of the computer program of Reference 1 (appendix A of the Summary Report) is reported. This matrix is computed for complete wing-body-tail configurations by assuming that all major airplane components can be structurally represented by a slender beam called the elastic axis. A structural influence coefficient is defined as the rotation about the Y-stability axis at panel j induced by a unit load on panel k. A description of how a structural breakdown is performed in detail is included.
Expressions are derived for computing the aerodynamic influence coefficient matrix for nonplanar wing-body-tail configurations. An aerodynamic influence coefficient is defined as the load in lbs. induced on a panel as a result of a unit angle of attack on another panel. Fuselage, wing and tail thickness are assumed to be small with the result that the thickness effect on the flow-field is negligible. The method for determining the aerodynamic influence coefficient matrix is based on the lifting solution to the small perturbation, steady potential flow equation.