Making Matrix Structures Work - From Theory to Practice: Jet Propulsion Laboratory (JPL) Use Case
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Ward, Patrick↗
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Lie theoretic aspects of the Riccati equation
Various features of the application of Lie theory to matrix Riccati equations, of basic importance in control and system theories, are discussed. Particular consideration is given to centralizer foliation, the Cartan decomposition, matrix Riccati equations as Lie systems on Grassmanians, local analysis near a zero point of a vector field, linearization in homogeneous space, the tangent bundle in terms of partitioned matrices, and stability properties of fixed points of Riccati vector fields.
Hermann, R.↗
On the fixed point probability vector of regular or ergodic transition matrices.
Fixed point probability row vector of regular or ergodic transition matrices simplified using generalized matrix inversion theory
MATRIX ANALYSIS↗
FORTRAN 4 subroutines for coupling coefficients and matrix elements in the quantum mechanical theory of angular momentum
FORTRAN 4 subroutines for coupling coefficients and matrix elements in quantum mechanical theory of angular momentum
Braley, R. C.↗
Analysis of metal-matrix composite structures. I - Micromechanics constitutive theory. II - Laminate analyses
The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.
Arenburg, R. T.↗
Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.
An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.
Kattawar, G. W.↗
Radiative transfer in realistic planetary atmospheres
Some 40 publications that appeared in scientific journals from 1973 to 1981 as well as 45 scientific reports issued during the grant period are listed by title. Topics cover the development of a matrix operator theory of radiative transfer which made possible the exact model calculations of the radiance as a function of height in planetary atmospheres; calculation of the Mie phase matrix for various types of particles as well as for radiance and polarization in planetary atmospheres; analysis of high dispersion spectroscopic observations of Venus; calculation of curves of growth for Venus; the development of a theory for calculating radiative transfer in spherical shell atmospheres; investigations of zonal winds on Venus; and examination of Rayleigh scattering.
Plass, G. N.↗
Robust root clustering for linear uncertain systems using generalized Lyapunov theory
Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.
Yedavalli, R. K.↗
An application of generalized matrix inversion to sequential least squares parameter estimation
Generalized matrix inversion theory used in formulating recursive algorithm for least squares parameter estimation
INVERSION↗
Modified Matrix Method for Calculating Steady-State Span Loading on Flexible Wings in Subsonic Flight
A method is presented for shortening the computations required to determine the steady-state span loading on flexible wings in subsonic flight. The method makes use of tables of downwash factors to find the necessary aerodynamic-influence coefficients for the application of lifting-line theory. Explicit matrix equations of equilibrium are converted into a matrix power series with a finite number of terms by utilizing certain characteristic properties of matrices. The number of terms in the series is determined by a trial-and-error process dependent upon the required accuracy of the solution. Spanwise distributions of angle of attack, airload, shear, bending moment, and pitching moment are readily obtained as functions of qm(sub R) where q denotes the dynamic pressure and mR denotes the lift-curve slope of a rigid wing. This method is intended primarily to make it practical to solve steady-state aeroelastic problems on the ordinary manually operated desk calculators, but the method is also readily adaptable to automatic computing equipment.
Gainer, Patrick A.↗
A unified process for systems identification based on performance assessment
Many modern spacecraft are complex multi-body dynamic systems where the bodies are connected by several active control systems for pointing and isolation. Mission requirements indicate that many structural modes and possibly some nonlinear effects will require characterization. Thus, even characterization at the subsystem level will become more difficult than usual. System level characterization difficulties will be compounded by the fact that only limited ground testing will be possible on the full up system, and flight testing will be restricted by an extremely limited measurements set. The object of the present discussion is the application of matrix majorant theory to the problem of assessing dynamic system performance when knowledge of the system is uncertain. We show how majorants provide an effective tool to relate required performance output to system identification test quality in terms of residual uncertainty in input-output relations, parameter values, nonlinearities, and interactions. The underlying machinery consists of the block-norm matrix which is a nonnegative matrix each of whose elements is the norm of a block of a suitably partitioned matrix. A matrix which bounds the block-norm matrix in the sense of nonnegative matrices, i.e., element by element is known as a majorant.
Hyland, C.↗
Influence matrix program for aerodynamic lifting surface theory
A users manual is described for a USA FORTRAN 4 computer program which computes an aerodynamic influence matrix and is one of several computer programs used to analyze lifting, thin wings in steady, subsonic flow according to a kernel function method lifting surface theory. The most significant features of the program are that it can treat unsymmetrical wings, control points can be placed on the leading and/or trailing edges, and a stable, efficient algorithm is used to compute the influence matrix.
Medan, R. T.↗
Improved solution for system identification equations by Epsilon-Decomposition
Matrix eigenvalue theory is used to examine the source of ill-conditioning in linear algebraic equations. This approach highlights the crucial role played by the zero and near-zero eigenvalues and corresponding eigenvectors of poorly conditioned systems. Insight gained from this approach is used to significantly improve a recently developed solution procedure called Epsilon-Decomposition (E-D). E-D is an efficient alternative to Singular Value Decomposition (SVD) for ill-conditioned systems arising in parameter estimation and system identification studies. The efficiency of the improved E-D over SVD resides in the need to only obtain the zero and near-zero eigenvalues of the coefficient matrix as opposed to all of its eigenvalues and vectors (as required by SVD). Thus, the efficiency of E-D is significant for large matrices with small rank deficiency.
Ojalvo, Irving U.↗
Irreducible realizations and the degree of a rational matrix.
Equivalence of irreducible realization in control theory and degree of rational matrix in network theory
COMPLEX VARIABLE↗
On the existence of Liapunov functions for the problem of Lurie
Control theory and matrix analysis for existence of Liapunov functions for problem of Lurie
LIAPUNOV FUNCTION↗
Birefringent filter for millimeter waves.
Birefringent filter design for millimeter wavelengths using second order theory and matrix method
Schiffman, B. M.↗
Varied statistical problems and tests, volume 2
Multivariate statistical analysis including divergence, probability of misclassification, information theory, and matrix analysis
Source record↗
Phase matrix induced symmetrics for multiple scattering using the matrix operator method
Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.
Hitzfelder, S. J.↗