SEARCH · Engineering Papers

Results for “linear equations”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29

All sources NASA NTRS DOE OSTI

NASA NTRS1986

Decoupling control synthesis for an oblique-wing aircraft

Interest in oblique-wing aircraft has surfaced periodically since the 1940's. This concept offers some substantial aerodynamic performance advantages but also has significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. This paper presents a technique for synthesizing a decoupling controller while providing the desired stability augmentation. The proposed synthesis procedure uses the concept of a real model-following control system. Feedforward gains are selected on the assumption that perfect model-following conditions are satisfied. The feedback gains are obtained by using eigensystem assignment, and the aircraft is stabilized by using partial state feedback. The effectiveness of the control laws developed in achieving the desired decoupling is illustrated by application to linearized equations of motion of an oblique-wing aircraft for a given flight condition.

Alag, G. S.↗

NASA NTRS1985

Gravity wave vertical energy flux at 95 km

A three-field photometer (3FP) located at Mt. Torrens near Adelaide, is capable of monitoring different airglow emissions from three spaced fields in the sky. A wheel containing up to six different narrow bandpass interference filters can be rotated, allowing each of the filters to be sequentially placed into each of the three fields. The airglow emission of interest is the 557.7 nm line which has an intensity maximum at 95 km. Each circular field of view is located at the apexes of an equilateral triangle centered on zenith with diameters of 5 km and field separations of 13 km when projected to the 95-km level. The sampling period was 30 seconds and typical data lengths were between 7 and 8 hours. The analysis and results from the interaction of gravity waves on the 557.7 nm emission layer are derived using an atmospheric model similar to that proposed by Hines (1960) where the atmosphere is assumed isothermal and perturbations caused by gravity waves are small and adiabatic, therefore, resulting in linearized equations of motion. In the absence of waves, the atmosphere is also considered stationary. Thirteen nights of quality data from January 1983 to October 1984, covering all seasons, are used in this analysis.

Jacob, P. G.↗

NASA NTRS1986

Model-following control for an oblique-wing aircraft

A variable-skew oblique wing offers a substantial aerodynamic performance advantage for aircraft missions that require both high efficiency in subsonic flight and supersonic dash or cruise. The most obvious characteristic of the oblique-wing concept is the asymmetry associated with wing-skew angle which results in significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. A technique for synthesizing a decoupling controller while providing the desired stability augmentation. The proposed synthesis procedure uses the cncept of explicit model following. Linear quadratic optimization techniques are used to design the linear feedback system. The effectiveness of the control laws developed in achieving the desired decoupling is illustrated for a given flight condition by application to linearized equations of motion, and also to the nonlinear equations of six degrees of freedom of motion with nonlinear aerodynamic data.

Alag, G. S.↗

NASA NTRS1985

Energy partitioning in the Io plasma torus

The Io plasma torus, which emits substantial amounts of EUV radiation from multiply ionized oxygen and sulfur, represents one of the significant discoveries of the Voyager 1 mission. The present study is concerned with the effects of various physical processes on the density and energy partitioning of the Io plasma torus. For the ions the dominant effects, which have different relative importance in different parameter regimes, are electron impact ionization, charge exchange, electron-ion collisions, and confinement time loss. Attention is given to a physical model, the solution of the quasi-linear equations, the obtained results, and an interpretation of observations in relation to the model results.

Smith, R. A.↗

NASA NTRS1985

Accretion disk oscillations - A local analysis in a disk of finite thickness

Two types of oscillations are observed to occur in dwarf novae: 'coherent' and 'quasi-periodic' oscillations. These may be associated with the pulsation of the white dwarf or the accretion disk components of the dwarf nova. Here a local (short-wavelength) analysis is utilized to study the oscillation of a self-consistent, two-dimensional model of an accretion disk. The linearized equations describing adiabatic, inviscid, nonaxisymmetric oscillations are used to derive a fifth-order algebraic equation for the (complex) pulsation frequency of the disk. The solutions of this equation for various values of the wavevector k reveal that the disk is capable of supporting (1) a pair of high-frequency acoustic modes (p-modes); (2) a pair of intermediate-frequency modes which may share the characteristics of internal gravity waves (g-modes) and inertial waves; and (3) a mode associated with a dynamical instability (purely imaginary frequency). The role played by the shear in determining the stability or instability of these modes is also considered. Finally, the global oscillation frequencies of the disk are discussed.

Carroll, B. W.↗

NASA NTRS1986

The cosmic-ray source composition

The cosmic-ray source composition is shown to be related to the observed cosmic-ray abundances by a set of linear equations which are valid for either ad hoc path length distributions or quantitative solutions of galactic propagation models. In the limit of no ionization energy loss, this method is exact for all path length distributions and can replace more detailed numerical integrations; it provides a simple way to calculate directly the source composition implied by a particular set of cross sections, observed abundances, and propagation model. This method is used to determine the source abundances of the galactic cosmic rays in a model-independent manner. Compared to a simple exponential, the path length distribution required by observations is deficient in the contributions from short (not greater than 0.5 g/sq cm) paths at energies of a few GeV per nucleon.

Margolis, S. H.↗

NASA NTRS1986

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

King, H. F.↗

NASA NTRS1986

Model-following control for an oblique-wing aircraft

A variable-skew oblique wing offers a substantial aerodynamic performance advantage for aircraft missions that require both high efficiency in subsonic flight and supersonic dash or cruise. The most obvious characteristic of the oblique-wing concept is the asymmetry associated with wing-skew angle which results in significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. This paper presents a technique for synthesizing a decoupling controller while providing the desired stability augmentation. The proposed synthesis procedure uses the concept of explicit model following. Linear quadratic optimization techniques are used to design the linear feedback system. The effectiveness of the control laws developed in achieving the desired decoupling is illustrated for a given flight condition by application to linearized equations of motion, and also to the nonlinear equations of six degrees of freedom of motion with nonlinear aerodynamic data.

Alag, G. S.↗

NASA NTRS1986

Tilt-rotor flutter control in cruise flight

Tilt-rotor flutter control under cruising operation is analyzed. The rotor model consists of a straight fixed wing, a pylon attached to the wingtip, and a three-blade rotor. The wing is cantilevered to the fuselage and is allowed to bend forward and upward. It also has a torsional degree of freedom about the elastic axis. Each rotor blade has two bending degrees of freedom. Feedback of wingtip velocity and acceleration to cyclic pitch is investigated for flutter control, using strip theory and linearized equations of motion. To determine the feedback gain, an eigenvalue analysis is performed. A second, independent, timewise calculation is conducted to evaluate the control law while employing more sophisticated aerodynamics. The effectiveness of flutter control by cyclic pitch change was confirmed.

Nasu, Ken-Ichi↗

NASA NTRS1987

Radial orbit error reduction and sea surface topography determination using satellite altimetry

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Engelis, Theodossios↗

NASA NTRS1987

Automated problem scheduling and reduction of synchronization delay effects

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs.

Saltz, Joel H.↗

NASA NTRS1987

The growth of Goertler vortices in compressible boundary layers

The linear instability of Goertler vortices in compressible boundary layers is considered. Using asymptotic methods in the high wavenumber regime, it is shown that a growth rate estimate can be found by solving a sequence of linear equations. The growth rate obtained in this way takes non-parallel effects into account and can be found much more easily than by ordinary differential equation eigenvalue calculations associated with parallel flow theories.

Hall, Philip↗

NASA NTRS1987

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Badavi, F. F.↗

NASA NTRS1986

Decoupling control synthesis for an oblique-wing aircraft

Alag, G. S.↗

NASA NTRS1986

On the Lagrangian turbulence in continua

Lagrangian turbulence in continua is introduced as a failure of Euclidian metric of a material system of coordinates, and it is shown that the Ricci tensor of such a system of coordinates may be used as a measure of L-turbulence. The conditions which are sufficient, though not necessary, for instability of an initially infinitesimal disturbance of this tensor are determined for fluid, elastic, and viscoelastic bodies. The results are obtained from the linearized equations, and therefore the growth of unstable solutions may be bounded.

Zak, M.↗

NASA NTRS1986

Automated tuning of airframe vibration by structural optimization

Numerical optimization techniques are used to modify the dynamic response at a specified point(s) of a helicopter airframe structure due to a steady state narrow band excitation. Calculation of steady state vibration amplitude is reduced to the solution of linear equations with complex coefficients. The sensitivity of the dynamic amplitudes with respect to the structural parameter perturbations can be computed with the same technique as the one used in the static displacement sensitivity without requiring eigenvector sensitivity. Approximate models for critical structural responses are created based on the sensitivity data to reduce the amount of computational effort and to enable the design of structures of practical scale and complexity. This approach is general in that it accommodates static, dynamic, and frequency constraints simultaneously as long as their computational models are available. It can be used in optimizing mass distribution as well as stiffness modifications of practical structures.

Miura, H.↗

NASA NTRS1985

Finite difference methods for the solution of unsteady potential flows

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

Caradonna, F. X.↗

NASA NTRS1986

Magnetospheric equilibrium configurations and slow adiabatic convection

This review paper demonstrates how the magnetohydrostatic equilibrium (MHE) theory can be used to describe the large-scale magnetic field configuration of the magnetosphere and its time evolution under the influence of magnetospheric convection. The equilibrium problem is reviewed, and levels of B-field modelling are examined for vacuum models, quasi-static equilibrium models, and MHD models. Results from two-dimensional MHE theory as they apply to the Grad-Shafranov equation, linear equilibria, the asymptotic theory, magnetospheric convection and the substorm mechanism, and plasma anisotropies are addressed. Results from three-dimensional MHE theory are considered as they apply to an intermediate analytical magnetospheric model, magnetotail configurations, and magnetopause boundary conditions and the influence of the IMF.

Voigt, Gerd-Hannes↗