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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Pseudo Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler's equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate.

Harman, Richard R.↗
NASA NTRS1999

Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations

The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.

Thomas, J. L.↗
NASA NTRS2004

Pseudo-Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler s equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate. The performance of the two filters is examined using simulated data.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS2017

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗
NASA NTRS1982

Aerothermal modeling

The objectives, approach, and status of a program to develop the computational fluid dynamics tools needed to improve combustor design and analysis are outlined. The calculation procedure selected consists of a finite difference solution of the time averaged, steady state, primitive variable, elliptic form of the Reynolds equations. Standard TEACH type numerics are used to solve the resulting equations. These include hybrid differencing, SIMPLE algorithm for the pressure field, line by line iterative solution using the ADI method and the tridiagonal matrix algorithm (TDMA). Convergence is facilitated by using under relaxation. The physical processes are modeled by a two equation eddy viscosity model for turbulence; combustion is represented by a simple, irreversible, one step chemical reaction whose rate is influenced only by the time scale of the turbulence. The model evaluation procedure is also described.

Sturgess, G. J.↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1990

State-variable models of structures having rigid-body modes

In cases where the equations of motion of a structure having rigid-body freedom are cast in state-variable form, generalized state rigid-body modes may be needed. It is possible to find a linearly-independent set of generalized vectors which transform an n x n matrix into the almost-diagonal Jordan form. Attention is presently given to equations governing these generalized eigenvectors, together with illustrative examples of the damped and undamped structure cases.

Craig, Roy R., Jr.↗
NASA NTRS1996

Computational Simulation of Continuous Fiber-Reinforced Ceramic Matrix Composites Behavior

This report describes a methodology which predicts the behavior of ceramic matrix composites and has been incorporated in the computational tool CEMCAN (CEramic Matrix Composite ANalyzer). The approach combines micromechanics with a unique fiber substructuring concept. In this new concept, the conventional unit cell (the smallest representative volume element of the composite) of the micromechanics approach is modified by substructuring it into several slices and developing the micromechanics-based equations at the slice level. The methodology also takes into account nonlinear ceramic matrix composite (CMC) behavior due to temperature and the fracture initiation and progression. Important features of the approach and its effectiveness are described by using selected examples. Comparisons of predictions and limited experimental data are also provided.

Murthy, Pappu L. N.↗
NASA NTRS1992

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Swafford, Timothy W.↗
NASA NTRS1978

A triangular covariance factorization for sequential filtering algorithms

A method for propagating the square-root of the state error covariance matrix in lower triangular UDU form is described. This update method can be combined with the UDU transformation used by Bierman to obtain the equations of a square-root free triangular estimation algorithm. The method is compared with the state transition matrix time update algorithm on the basis of integration accuracy, computational efficiency and storage requirements.

Tapley, B. D.↗
NASA NTRS1991

Efficient multitasking of Choleski matrix factorization on CRAY supercomputers

A Choleski method is described and used to solve linear systems of equations that arise in large scale structural analysis. The method uses a novel variable-band storage scheme and is structured to exploit fast local memory caches while minimizing data access delays between main memory and vector registers. Several parallel implementations of this method are described for the CRAY-2 and CRAY Y-MP computers demonstrating the use of microtasking and autotasking directives. A portable parallel language, FORCE, is used for comparison with the microtasked and autotasked implementations. Results are presented comparing the matrix factorization times for three representative structural analysis problems from runs made in both dedicated and multi-user modes on both computers. CPU and wall clock timings are given for the parallel implementations and are compared to single processor timings of the same algorithm.

Overman, Andrea L.↗
NASA NTRS1989

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗
NASA NTRS1994

Sensitivity derivatives for three dimensional supersonic Euler code using incremental iterative strategy

In a recent work, an incremental strategy was proposed to iteratively solve the very large systems of linear equations that are required to obtain quasianalytical sensitivity derivatives from advanced computational fluid dynamics (CFD) codes. The technique was sucessfully demonstrated for two large two-dimensional problems: a subsonic and a transonic airfoil. The principal feature of this incremental iterative stategy is that it allows the use of the identical approximate coefficient matrix operator and algorithm to solve the nonlinear flow and the linear sensitivity equations; at convergence, the accuracy of the sensitivity derivatives is not compromised. This feature allows a comparatively straightforward extension of the methodology to three-dimensional problems; this extension is successfully demonstrated in the present study for a space-marching solution of the three-dimensional Euler equations over a Mach 2.4 blended wing-body configuration.

Korivi, Vamshi Mohan↗
NASA NTRS2007

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗
NASA NTRS1994

Pseudomaster equation for the no-count process in a continuous photodetection

The detection of cavity radiation with the detector placed outside the cavity is studied. Each leaked photon has a certain probability of propagating away without being detected. It is viewed as a continuous quantum measurement in which the density matrix is continuously revised according to the readout of the detector. The concept of pseudomaster equation for the no-count process is introduced; its solution leads to the discovery of the superoperator for the same process. It has the potential to become the key equation for continuous measurement process.

Lee, Ching-Tsung↗
NASA NTRS1976

Electric dipole moment function of the X1 Sigma/+/ state of CO - Vibration-rotation matrix elements for transitions of gas laser and astrophysical interest

The electric dipole moment function of the ground electronic state of carbon monoxide has been determined by combining numerical solutions of the radial Schrodinger equation with absolute intensity data of vibration-rotation bands. The derived dipole moment function is used to calculate matrix elements of interest to stellar astronomy and of importance in the carbon monoxide laser.

Chackerian, C., Jr.↗
NASA NTRS1990

Development of a model of space station solar array

Space structures, such as the space station solar arrays, must be extremely lightweight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a control system. The tension preload in the blanket of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomena known as grounding, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The grounding phenomena is examined in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. Various techniques are used for developing new stiffness matrices from the rigorous solutions of the differential equations, including the solution of the directed force problem. A new directed force stiffness matrix developed by the author provides all the rigid body capabilities for the beam in space.

Bosela, Paul A.↗
NASA NTRS1996

Optimization of Orifice Geometry for Cross-Flow Mixing in a Cylindrical Duct

Mixing of gaseous jets in a cross-flow has significant applications in engineering, one example of which is the dilution zone of a gas turbine combustor. Despite years of study, the design of the jet injection in combustors is largely based on practical experience. The emergence of NO(x) regulations for stationary gas turbines and the anticipation of aero-engine regulations requires an improved understanding of jet mixing as new combustor concepts are introduced. For example, the success of the staged combustor to reduce the emission of NO(x) is almost entirely dependent upon the rapid and complete dilution of the rich zone products within the mixing section. It is these mixing challenges to which the present study is directed. A series of experiments was undertaken to delineate the optimal mixer orifice geometry. A cross-flow to core-flow momentum-flux ratio of 40 and a mass flow ratio of 2.5 were selected as representative of a conventional design. An experimental test matrix was designed around three variables: the number of orifices, the orifice length-to- width ratio, and the orifice angle. A regression analysis was performed on the data to arrive at an interpolating equation that predicted the mixing performance of orifice geometry combinations within the range of the test matrix parameters. Results indicate that the best mixing orifice geometry tested involves eight orifices with a long-to-short side aspect ratio of 3.5 at a twenty-three degree inclination from the center-line of the mixing section.

Kroll, J. T.↗