Partial derivatives for various scaler functions of matrices
Theorems and their proof are given for the solution of partial derivatives for various scaler functions of matrices.
Quirein, J.↗
SEARCH · Engineering Papers
Results for “matrices”
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.
An interactive graphics package for the automatic node renumbering of finite element matrices
An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with the reordering scheme either defined by the user or automatically generated by the program with the aim of reducing matrix bandwidth and profile. Although the primary application of the package has been to the finite element analysis of structures, it is equally well suited to the many other areas of engineering and science which use sparse matrices.
Boisvert, R. F.↗
Recursive partitioned inversion of large (1500 x 1500) symmetric matrices
A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.
Putney, B. H.↗
Euler angles, quaternions, and transformation matrices for space shuttle analysis
Relationships between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion are analyzed, and equations developed are applied directly to current space shuttle problems. The twelve three-axis Euler transformation matrices as functions of the Euler angles, the equations for the quaternion as a function of the Euler angles, and the Euler angles as a function of the transformation matrix elements are included along with a group of utility subroutines to accomplish the Euler matrix, quaternion matrix, and Euler quaternion relationships.
Henderson, D. M.↗
Shuttle Program. Euler angles, quaternions, and transformation matrices working relationships
A brief mathematical development of the relationship between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion is presented. The analysis and equations presented apply directly to current space shuttle problems. The twelve three-axis Euler transformation matrices are given as functions of the Euler angles, the equations for the quaternion as a funtion of the Euler angles, and the Euler angles as a function of the transformation matrix elements.
Henderson, D. M.↗
Chemiluminescent reactions of sulfur /3P2/ atoms in cryogenic matrices - S + O2 yields SO2 /a3 B1/
Results are reported for thermoluminescence studies of reactions of sulfur atoms in cryogenically deposited solid argon through in situ photolysis of OCS. Analysis of the thermoluminescence spectrum that resulted from photolysis and heating of matrices in which O2 was codeposited with an OCS/Ar mixture shows that the emitter contained oxygen derived from the added O2 and that little SO2 accumulated during photolysis. The observed absence of thermoluminescence or fluorescence in either of the allowed transitions of excited SO2 is taken as definitive evidence that ground-state sulfur atoms can insert into the oxygen molecule with effectively zero activation energy.
Long, S. R.↗
Advanced resin matrices for composites
The selection criteria, and the chemical structure of resin matrices are given along with the processing conditions for resins and laminates.
Kourtides, D. A.↗
Analysis of numerical stability and amplification matrices: Fourth-order Runge-Kutta methods
Amplification matrices, numerical kernels, stable, and exponentially stable numerical solutions are examined. The various techniques involved in these concepts are applied to certain systems that have Jordan forms, which are nondiagonal, with particular interest in the case of imaginary or zero eigenvalues.
Kennedy, E. W.↗
Integrating matrices for arbitrarily spaced grid points
Integrating matrices are derived for arbitrarily spaced grid points using either interpolating or least squares fit orthogonal polynomials. Several features of the equally spaced grid case are also discussed.
Lakin, W. D.↗
The matrices of unequilibrated ordinary chondrites - Implications for the origin and history of chondrites
The matrices of 16 unequilibrated chondrites were examined by optical microscopy, an electron microprobe, and a scanning electron microscope. The fine-grained, opaque, silicate matrix of type 3 unequilibrated chondrites was compositionally, mineralogically, and texturally different from the chondrules and their fragments; it may be the low temperature condensate proposed by Larimer and Anders (1967, 1970). Each meteorite has been metamorphosed by a combination of processes including thermal metamorphism and the passage of shock waves; the appearance of each chondrite results from the temperature and pressure conditions which formed it, and subsequent metamorphic alterations.
Huss, G. R.↗
Absorption and resonance Raman spectra of Pb2, Pb3, and Pb4 in xenon matrices
Matrix isolation techniques are used to investigate the spectra of lead molecules and, in particular, to obtain resonance Raman spectra of lead vapors isolated in solid xenon matrices. The presence of Pb2 is confirmed by the visible adsorption, and Raman spectra yield a vibrational frequency for the ground state of 108 per cm and a dissociation energy of 8200 per cm. A second resonance Raman progression indicates a Pb3 species of D3h symmetry. Finally, two additional Raman features at approximately 111 per cm spacing are evidence for a third species, tentatively identified as Pb4.
Stranz, D. D.↗
Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system
Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.
Tsang, W. L.↗
Investigation of degradation mechanisms in composite matrices
Degradation mechanisms were investigated for graphite/polysulfone and graphite/epoxy laminates exposed to ultraviolet and high-energy electron radiations in vacuum up to 960 equivalent sun hours and 10 to the ninth power rads respectively. Based on GC and combined GC/MS analysis of volatile by-products evolved during irradiation, several free radical mechanisms of composite degradation were identified. The radiation resistance of different matrices was compared in terms of G values and quantum yields for gas formation. All the composite materials evaluated show high electron radiation stability and relatively low ultraviolet stability as indicated by low G values and high quantum for gas formation. Mechanical property measurements of irradiated samples did not reveal significant changes, with the possible exception of UV exposed polysulfone laminates. Hydrogen and methane were identified as the main by-products of irradiation, along with unexpectedly high levels of CO and CO2.
Giori, C.↗
Experimental measurements of hydrodynamic stiffness matrices for a centrifugal pump impeller
The objective of the Rotor Force Test Facility at the California Institute of Technology is to artificially orbit the center of rotation of an impeller enclosed within a volute over a range of frequencies from zero to synchronous and to measure the resulting forces on the impeller. Preliminary data from the first stage experiments in which the shaft is orbited at low frequency is reported. Steady volute forces along with stiffness matrices due to the change in position of the rotor center are measured. Static pressure taps around the volute are used to obtain volute pressure distributions for various fixed positions of the impeller center and for various flow rates. Static pressure forces are calculated from these pressure distributions allowing a more complete analysis of the components of the impeller forces. Comparison is made with various existing theoretical and experimental results.
Chamieh, D. S.↗
Study of alumina-trichite reinforcement of a nickel-based matric by means of powder metallurgy
Research was conducted on reinforcing nickel based matrices with alumina trichites by using powder metallurgy. Alumina trichites previously coated with nickel are magnetically aligned. The felt obtained is then sintered under a light pressure at a temperature just below the melting point of nickel. The halogenated atmosphere technique makes it possible to incorporate a large number of additive elements such as chromium, titanium, zirconium, tantalum, niobium, aluminum, etc. It does not appear that going from laboratory scale to a semi-industrial scale in production would create any major problems.
Walder, A.↗
A minimax approach to spatial estimation using affinity matrices
Estimates made in the plane to improve on noisy unbiased estimates were combined. Only a small fraction of points in a giant grid were used to do this, those that are most like a given point. A component of this process defining an affinity matrix of values, indicating which points are relevant to others. Minimax rules are shown to be based on affinity matrices.
Morris, C. N.↗
Compliance matrices for cracked bodies
An algorithm is presented which can be used to develop compliance matrices for cracked bodies. The method relies on the numerical solution of singular integral equations with Cauchy-type kernels and provides an efficient and accurate procedure for relating applied loadings to crack opening displacements. The algorithm should be of interest to those performing repetitive calculations in the analysis of experimental results obtained from fracture specimens.
Ballarini, R.↗
Comparison of flexural properties of aramid-reinforced pultrusions having varied matrices, pretreatments and postcures
Aramid-reinforced composite materials of equal fiber volume and varied polymer thermoset matrices were pultruded and flexurally tested to failure. The objective was to improve the flexural properties of aramid-reinforced pultrusions. Pultrusions of both sized and unsized aramid fiber with four different resin systems were compared to determine the effects of sizing compounds and postcuring on flexural strength, fiber wettability, and fiber-to-resin interface bonding. Improvements in flexural strength resulting from pretreatments with the sizing solutions used were marginal. The most significant improvements in flexural properties resulted from postcuring. Flexural strengths ranged from a low of 39,647 psi (273MPa) to a high of 80,390 psi (554 MPa), an overall increase of 103 percent. The fact that postcuring improved the flexural properties of the pultrusions of the four resin systems indicates that a full cure did not occur in any of the resin systems during the pultrusion process. The increased flexural strengths of the polyester and vinyl ester pultrusions were the most surprising. The four resin systems examined were Interplastic Corporation VE 8300 vinyl ester, Ashland Chemical Company Aropol 7430 Polyester, and Shell Chemical Company Epon 9302 and Epon 9310 epoxides.
Wilson, Maywood L.↗