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A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.
The paper summarizes the state-of-the-art for application of stability theory to laminar flow control using suction, wall temperature and/or favorable pressure gradient ('natural laminar flow'). Discussions include current LFC problem areas requiring stability analyses, methods of relating stability theory to transition with results from data and theory comparisons available thus far, and a summary of low disturbance data available for theory calibration on swept wings. Critical issues highlighted are problems peculiar to suction LFC on high performance transonic wings and application of the e-to-the-n-power method to both low and high speed flight data.
The discrete structural pattern in the distribution of the satellites and planets around their primaries has since its discovery been thought to hold the key to the origin and evolution of the solar system. Different attempts to rationalize this distribution are reviewed with emphasis on theories with foundation in verifiable physical processes. Foremost among these is the band structure theory, which relates the emplacement of interstellar dust and gas source material around the magnetized primarily to the critical velocity for ionization of the four major interstellar gas components. The uncertainties, that are inevitable in all reconstructions, are in this theory compensated by the support from precise manifestations of the 2/3 effect in the Saturnian ring system and in the asteroid belt, and by the reproduction of related phenomena in laboratory and space experiments.
The injection molding behavior of a concentrated suspension of Si powder in wax was studied. It was found that the injection molding behavior was a function of the processing techniques used to generate the powder. Dry ball-milled powders had the best molding behavior, while air classified and impact-milled powders demonstrated poorer injection moldability. The relative viscosity of these molding batches was studied as a function of powder properties: distribution shape, surface area, packing density, and particle morphology. The experimental behavior, in all cases, followed existing theories. The relative viscosity of an injection molding composition composed of dry ball-milled powders could be expressed using Farris' relation.
Aspects of statistical filter theory and relation to space navigation problems
Pulsed coherent radars' receiving efficiency, eta, is presently investigated as a function of range z on the basis of a theory which relates eta(z) to both the transmitted laser intensity and the point-source receiving efficiency; this efficiency is calculated by a backward method employing the back-propagated local oscillator (BPLO) approach. The theory is applied to the ideal case, in order to study system optimization when both the transmitted and the BPLO fields at the antenna are Gaussian. In the second part of this work, eta(z) is calculated for various conditions of the NOAA/ERL Wave Propagation Laboratory CO2 Doppler lidar; the sensitivity of eta(z) to transmitted laser beam quality, telescope focal setting, telescope power, scanner astigmatism, and system misalignment.
The objective of the relativity satellite mission is to perform an experiment in which a gyroscope in motion about the earth undergoes precession, presumably relativistic, with respect to the fixed stars. Performance of this experiment would clearly test the general theory of relativity and its various modifications. This is the only experiment suggested to date which would confirm the existence of motional drift as well. A mission is defined in which the measurement of the geodetic effect term to 0.2 arc sec/yr is achievable and the measurement of both geodetic and motional drift terms to an accuracy of 0.001 arc sec/yr may be possible. The design of the flying dewar satellite needed to maintain the experiment at cryogenic temperatures is discussed. The gyroscopes, magnetometer, and optical contacting method for dimensional stability of the experimental assembly are considered.
Gravity Probe B (GP-B) is a relatively gyroscope experiment begun at Stanford University in 1960 and supported by NASA since 1963. This experiment will check, for the first time, the relativistic precession of an Earth-orbiting gyroscope that was predicted by Einstein's General Theory of Relativity, to an accuracy of 1 milliarcsecond per year or better. A drag-free satellite will carry four gyroscopes in a polar orbit to observe their relativistic precession. The primary sensor for measuring the direction of gyroscope spin axis is the SQUID (superconducting quantum interference device) magnetometer. The data reduction scheme designed for the GP-B program processes the signal from the SQUID magnetometer and estimates the relativistic precession rates. We formulated the data reduction scheme and designed the Niobium bird experiment to verify the performance of the data reduction scheme experimentally with an actual SQUID magnetometer within the test loop. This paper reports the results from the first phase of the Niobium bird experiment, which used a commercially available SQUID magnetometer as its primary sensor, and adresses the issues they raised. The first phase resulted in a large, temperature-dependent bias drift in the insensitive design and a temperature regulation scheme.
The objective of this two-year project was to develop and deliver to the NASA-Glenn Research Center a two-dimensional higher-order theory, and related computer codes, for the analysis and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, brisk blades). To satisfy this objective, two-dimensional version of the higher-order theory, HOTCFGM-2D, and four computer codes based on this theory, for the analysis and design of structural components functionally graded in the radial and circumferential directions were developed in the cylindrical coordinate system r-Theta-z. This version of the higher-order theory is a significant generalization of the one-dimensional theory, HOTCFGM-1D, developed during the FY97 for the analysis and design of cylindrical structural components with radially graded microstructures. The generalized theory is applicable to thin multi-phased composite shells/cylinders subjected to steady-state thermomechanical, transient thermal and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial direction, and arbitrarily distributed in the radial and circumferential direction, thereby allowing functional grading of the internal reinforcement in the r-Theta plane. The four computer codes fgmc3dq.cylindrical.f, fgmp3dq.cylindrical.f, fgmgvips3dq.cylindrical.f, and fgmc3dq.cylindrical.transient.f are research-oriented codes for investigating the effect of functionally graded architectures, as well as the properties of the multi-phase reinforcement, in thin shells subjected to thermomechanical and inertial loading, on the internal temperature, stress and (inelastic) strain fields. The reinforcement distribution in the radial and circumferential directions is specified by the user. The thermal and inelastic properties of the individual phases can vary with temperature. The inelastic phases are presently modeled by the power-law creep model generalized to multi-directional loading (within fgmc3dq.cylindrical.f and fgmc3dq.cylindrical.transient.f for steady-state and transient thermal loading, respectively), and incremental plasticity and GVIPS unified viscoplasticity theories (within the steady-state loading versions fgmp3dq.cylindrical.f and fgmgvips3dq.cylindrical.f).
The Gravity-Probe-B relativity gyroscope experiment (GP-B) will measure the geodetic and frame-dragging precession rates of gyroscopes in a 650 km high polar orbit about the earth. The goal is to measure these two effects, which are predicted by Einstein's General Theory of Relativity, to 0.01 percent (geodetic) and 1 percent (frame-dragging). This paper presents the development progress for full-size prototype flight hardware including the gyroscopes, gyro readout and magnetic shielding system, and an integrated ground test instrument.
Space charge theory of one-dimensional, monoenergetic, unipolar and bipolar currents traversing on otherwise evacuated space between infinite plane parallel electrodes
The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.
The objective of this three-year project was to develop and deliver to NASA Lewis one-dimensional and two-dimensional higher-order theories, and related computer codes, for the analysis, optimization and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, blisk blades). To satisfy this objective, a quasi one-dimensional version of the higher-order theory, HOTCFGM-1D, and four computer codes based on this theory, for the analysis, design and optimization of cylindrical structural components functionally graded in the radial direction were developed. The theory is applicable to thin multi-phased composite shell/cylinders subjected to macroscopically axisymmetric thermomechanical and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial and circumferential directions, and arbitrarily distributed in the radial direction, thereby allowing functional grading of the internal reinforcement in this direction.
Results are presented for the loads and moments acting on the individual tail surfaces of a body-tail combination over a wide range of angles of attack and sideslip. The effects of forebody length and panel-panel interference on the characteristics are included. It is shown that large nonlinear variations in these loads and moments, which occur at some combinations of angle of attack and sideslip, cannot be predicted by low-angle theory. A relatively simple, but general, theoretical method for calculating these load and moment characteristics is described, and the results from this method are found to be in good agreement with experiment provided the initial positions of the forebody vortices are known. It is shown that a simple application of slender-body theory can be used to predict the side loads due to sideslip that are contributed by a vertical tail on a wide variety of wing-body-tail combinations at low angles of attack. For several configurations, changes are indicated which reduced the vertical-tail loads per unit yawing moment of each complete configuration at large angles of attack. Some results are presented on the effect of high angle of attack on the induced-flow field and tail loads due to a wing at supersonic speed.
A personal computer application (CXWIN4G) has been written which greatly simplifies the task of extracting skin friction measurements from interferograms of oil flows on the surface of wind tunnel models. Images are first calibrated, using a novel approach to one-camera photogrammetry, to obtain accurate spatial information on surfaces with curvature. As part of the image calibration process, an auxiliary file containing the wind tunnel model geometry is used in conjunction with a two-dimensional direct linear transformation to relate the image plane to the physical (model) coordinates. The application then applies a nonlinear regression model to accurately determine the fringe spacing from interferometric intensity records as required by the Fringe Imaging Skin Friction (FISF) technique. The skin friction is found through application of a simple expression that makes use of lubrication theory to relate fringe spacing to skin friction.
The present state of empirical knowledge about neutron-star masses is reviewed. It is shown how the mass function of a pulsar-containing binary system can be inferred from measurements of the pulsation period and the projected semimajor axis of the pulsar orbit plus independent information concerning the inclination of the orbital plane, the mass of the companion star, or both. Relevant observational properties, the type of information used to constrain the pulsar mass, and the range of allowable pulsar masses are summarized for the binary systems 3U 0900-40, Cen X-3, SMC X-1, Her X-1, and PSR 1913+16. It is found that as long as the general theory of relativity is correct, neutron-star masses should range from about 1.4 to 1.9 solar masses if the companion is a normal white dwarf or should be less than about 1.9 solar masses if the companion is some other object. It is concluded that these mass estimates are entirely consistent with the predictions of nuclear physics theory.
Broadband Fan Noise Prediction System (BFaNS) is a computer program that, as its name indicates, predicts the broadband noise generated by the fan stage of a turbofan engine. This noise is the sum of (1) turbulent-inflow noise, which is caused by turbulence impinging on leading edges of the fan and the fan exit guide vane and (2) self noise, which is caused by turbulence convecting past the corresponding trailing edges. The user provides input data on the fan-blade, vane, and flow-path geometries and on the mean and turbulent components of the flow field. BFaNS then calculates the turbulent-inflow noise by use of D. B. Hanson's theory, which relates sound power to the inflow turbulence characteristics and the cascade geometry. Hanson s program, BBCASCADE, is incorporated into BFaNS, wherein it is applied to the rotor and stator in a stripwise manner. The spectra of upstream and downstream sound powers radiated by each strip are summed to obtain the total upstream and downstream sound-power spectra. The self-noise contributions are calculated by S. A. L. Glegg's theory, which is also applied in a stripwise manner. The current version of BFaNS is limited to fans with subsonic tip speeds.
The values of the key atmospheric turbulence parameters (structure constants) for temperature and water vapor, that is, C(exp 2)(sub T), and C(exp 2)(sub Q), are highly dependent upon the vertical height within the atmosphere thus making it necessary to specify profiles of these values along the atmospheric propagation path. The remote sensing method suggested and described in this work makes use of a rapidly integrating microwave profiling radiometer to capture profiles of temperature and humidity through the atmosphere. The integration times of currently available profiling radiometers are such that they are approaching the temporal intervals over which one can possibly make meaningful assessments of these key atmospheric parameters. These integration times, coupled with the boundary effects of the Earth’s surface are, however, unconventional for turbulence characterization; the classical Kolmogorov turbulence theory and related 2/3 law for structure functions prevalent in the inertial subrange are no longer appropriate. An alternative to this classical approach is derived from first principles to account for the nuances of turbulent mechanics met with using radiometer sensing, that is, the large-scale turbulence driven by the various possible boundary conditions within the buoyancy subrange. Analytical expressions connecting the measured structure functions to the corresponding structure parameters are obtained. The theory is then applied to an experimental scenario involving radiometric profile measurements of temperature and shows very good results.