Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Derived 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.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Computing the projected area of a spacecraft solar array with matrices

Matrix methods for computing the projected area of a solar array as a function of the rotational position of a spacecraft and of array position on a spacecraft are presented. Formulas are derived which provide the optimum solar array pitch, cant and tracking angles for a given spacecraft configuration and orbit. These formulas are general and applicable to many spacecraft. Formulas are also provided for determining the energy output from an array for a given orbit and the resultant energy available to spacecraft loads. Results are simply obtained and realizable with a hand calculator. The methods above can be extended to the case of computer analysis of solar array shadowing. How this can be done is outlined and results are presented from a spacecraft study program.

E. M. Gaddy↗
NASA NTRS1991

On the symbolic manipulation and code generation for elasto-plastic material matrices

A computerized procedure for symbolic manipulations and FORTRAN code generation of an elasto-plastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

Chang, T. Y.↗
NASA NTRS1992

Polymeric precursors for fibers and matrices

Candidate polymeric precursors for ceramic fiber and matrix processing are discussed, with a view to the advantages and disadvantages of this approach relative to existing alternatives. The properties of ceramic products thus derived are noted to strongly depend on the molecular weight and structure of the starting polymer; in particular, the ceramic's composition and morphology are dependent on the character and extent of crosslinking, as well as on the path of pyrolysis. While large and complex structural ceramic components may ultimately be obtainable by these means, the polymer-precursor method is still in its developmental infancy.

Hurwitz, Frances I.↗
NASA NTRS1986

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

Reddy, T. S. R.↗
NASA NTRS1972

Multivariable control theory applied to hierarchial attitude control for planetary spacecraft

Multivariable control theory is applied to the design of a hierarchial attitude control system for the CARD space vehicle. The system selected uses reaction control jets (RCJ) and control moment gyros (CMG). The RCJ system uses linear signal mixing and a no-fire region similar to that used on the Skylab program; the y-axis and z-axis systems which are coupled use a sum and difference feedback scheme. The CMG system uses the optimum steering law and the same feedback signals as the RCJ system. When both systems are active the design is such that the torques from each system are never in opposition. A state-space analysis was made of the CMG system to determine the general structure of the input matrices (steering law) and feedback matrices that will decouple the axes. It is shown that the optimum steering law and proportional-plus-rate feedback are special cases. A derivation of the disturbing torques on the space vehicle due to the motion of the on-board television camera is presented. A procedure for computing an upper bound on these torques (given the system parameters) is included.

Boland, J. S., III↗
NASA NTRS1975

Necessary and sufficient conditions for the complete controllability and observability of systems in series using the coprime factorization of a rational matrix

The series connection of two linear time-invariant systems that have minimal state space system descriptions is considered. From these descriptions, strict-system-equivalent polynomial matrix system descriptions in the manner of Rosenbrock are derived. They are based on the factorization of the transfer matrix of the subsystems as a ratio of two right or left coprime polynomial matrices. They give rise to a simple polynomial matrix system description of the tandem connection. Theorem 1 states that for the complete controllability and observability of the state space system description of the series connection, it is necessary and sufficient that certain 'denominator' and 'numerator' groups are coprime. Consequences for feedback systems are drawn in Corollary 1. The role of pole-zero cancellations is explained by Lemma 3 and Corollaires 2 and 3.

Callier, F. M.↗
NASA NTRS1985

Petrology of the Cangas de Onis and nulles regolith breccias Implications for parent body history

The present study of the Cangas de Onis and Nulles H chondrite regolith breccias indicates that the minerals in the matrices and equilibrated clasts have essentially the same compositional distributions, so that much of the material in the castic matrix would have to have been derived from the impact comminution of clats. The apparently exclusive occurrence of H6 clasts in Cangas de Onis, and H4 clasts in Nulles, suggests that, at the locations where these breccias formed, the regolith predominantly consisted of H6 and H4 material, respectively.

Williams, C. V.↗
NASA NTRS1973

Preliminary data on boulders at station 6, Apollo 17 landing site

A cluster of boulders at Station 6 (Apollo 17 landing site) consists of breccias derived from the North Massif. Three preliminary lithologic units were established, on the basis of photogeologic interpretations; all lithologies identified photogeologically were sampled. Breccia clasts and matrices studied petrographically and chemically fall into two groups by modal mineralogy: (1) low-K Fra Mauro or high basalt composition, consisting of 50-60% modal feldspar, approximately 45% orthopyroxene and 1-7% Fe-Ti oxide; (2) clasts consisting of highland basalt composition, consisting of 70% feldspar, 30% orthopyroxene and olivine and a trace of Fe-Ti oxide.

Heiken, G. H.↗
NASA NTRS1977

Infinite order sudden approximation for rotational energy transfer in gaseous mixtures

Rotational energy transfer in gaseous mixtures is analyzed within the framework of the infinite order sudden (IOS) approximation, and a new derivation of the IOS from the coupled states Lippman-Schwinger equation is presented. This approach shows the relation between the IOS and coupled state T matrices. The general IOS effective cross section can be factored into a finite sum of 'spectroscopic coefficients' and 'dynamical coefficients'. The evaluation of these coefficients is considered. Pressure broadening for the systems HD-He, HCl-He, CO-He, HCl-Ar, and CO2-Ar is calculated, and results based on the IOS approximation are compared with coupled state results. The IOS approximation is found to be very accurate whenever the rotor spacings are small compared to the kinetic energy, provided closed channels do not play too great a role.

Goldflam, R.↗
NASA NTRS1996

On the Use of Kronecker Operators for the Solution of Generalized Stochastic Petri Nets

We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of marking-dependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulse-based reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the state-space explosion. In the conclusion, we point out ideas to parallelize our approach.

Ciardo, Gianfranco↗
NASA NTRS2011

TPSAS-NF1676L-12839-DND

Hyper-spectral remote sensors, such as Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI), provides top of atmospheric radiances with high information content on atmospheric and surface properties. In order to analyze these data in real time, fast, and accurate forward and inverse models are needed. We will describe a method of simultaneously retrieving atmospheric temperature, moisture, cloud, and surface properties using all available spectral channels without sacrificing computational speed. The method has been successfully applied to AIRS, IASI, and NAST-I data. By applying the same method to the current and future hyperspectral sounders, the derived products will have less errors due to biases introduced by different retrieval methods. We have compared the retrieved products to radiosondes, aircraft measurements and other validation dataset. Simulations have done to quantify retrieval errors associated with the retrievals. The essence of the method is to convert channel radiance spectra into super-channels by an Empirical Orthogonal Function (EOF) transformation. A Principal Component-based Radiative Transfer Model (PCRTM) developed at NASA Langley Research Center is used to calculate both the super-channel magnitudes and derivatives with respect to atmospheric profiles and other properties. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance matrices and a priori information as constraints. One advantage of this approach is that it uses all information content from the hyper-spectral data so that the retrieval is less sensitive to instrument noise and eliminates the need for selecting a subset of the channels. The PCRTM forward model has also been used to performance end-to-end sensor performance simulations of the Climate Absolute Radiance and Refractivity Observatory (CLARREO).

Xu Liu↗
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
NASA NTRS1988

Prediction of the microyield strength of polymer matrix composites

A theory for the prediction of the creep and the microyield strength of composite laminates with viscoelastic matrices has been developed and tested. Precise creep curves from three laminates with arbitrary orientations provide the necessary input data. The time-dependent lamina properties are derived for subsequent use with standard laminate codes. Both the level and the shape of creep and strain recovery curves can be predicted. Extensions of the theory to include the effects of microcracking are outlined.

Wolff, Ernest G.↗
NASA NTRS1988

System identification using modal residues and roots

This presentation will address an approach for using modal residues and roots, typically derived from vibration testing, to solve for the lumped parameters of a finite element model. The uniqueness of the approach is that the mass, stiffness, or damping matrices of a structure do not need to be known or estimated a-priori. Instead just the connectivity of the structure needs to be estimated. In addition, the presentation will demonstrate how models with orders larger than the number of modes obtained by the test program can be solved. The presentation will start by covering the basis of the approach, then illustrate a trivial application of how it works, and finally illustrate its use on a cantilevered beam using only a fraction of the mode to solve the mass, stiffness, and damping matrices.

Wendler, Bruce H.↗
NASA NTRS1994

Weighted graph based ordering techniques for preconditioned conjugate gradient methods

We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

Clift, Simon S.↗
NASA NTRS1993

Polarimetric radar data decomposition and interpretation

Significant efforts have been made to decompose polarimetric radar data into several simple scattering components. The components which are selected because of their physical significance can be used to classify SAR (Synthetic Aperture Radar) image data. If particular components can be related to forest parameters, inversion procedures may be developed to estimate these parameters from the scattering components. Several methods have been used to decompose an averaged Stoke's matrix or covariance matrix into three components representing odd (surface), even (double-bounce) and diffuse (volume) scatterings. With these decomposition techniques, phenomena, such as canopy-ground interactions, randomness of orientation, and size of scatters can be examined from SAR data. In this study we applied the method recently reported by van Zyl (1992) to decompose averaged backscattering covariance matrices extracted from JPL SAR images over forest stands in Maine, USA. These stands are mostly mixed stands of coniferous and deciduous trees. Biomass data have been derived from field measurements of DBH and tree density using allometric equations. The interpretation of the decompositions and relationships with measured stand biomass are presented in this paper.

Sun, Guoqing↗
NASA NTRS2001

Discontinuous Galerkin Methods for NonLinear Differential Systems

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Barth, Timothy↗
NASA NTRS2002

The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗