On integration of Hamilton-Jacobi partial differential equation.
Hamilton-Jacobi partial differential equation integration method, using variational principle and transversality condition
Ghaffari, A.↗
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Effects on the motion of a body attracted by a rotating source, part 2 Progress report
Iterative method determining variation of any order of planned circular orbit about rotating gravitational source
Knothe, H.↗
Large strain, elasto-plastic finite element analysis
Two dimensional structures large strain elastoplastic analysis by finite element method, using variational principles to derive equilibrium equations
Evensen, D. A.↗
A modified linear membrane theory for the pressurized toroid
Pressurized toroid modified linear membrane theory, presenting approximate solutions for derived boundary value problem by variational calculus methods
Clark, S. K.↗
Computer experiments on the structure and dynamics of spiral galaxies
The evolution of an initially balanced rotating disk of stars with an initial velocity dispersion given by Toomre's local criterion was investigated by means of a computer model for isolated disks of stars. It was found that the disk is unstable against very large scale modes. A stable axisymmetric disk with a velocity dispersion much larger than that given by Toomre's criterion was generated. The final mass distribution for the disk gives a high density central core and a disk population of stars that is closely approximated by an exponential variation. Various methods and rates of cooling the hot axisymmetric disks were investigated. It was found that the cooling resulted in the development of two-arm spiral structures which persisted as long as cooling continued. An experiment was performed to induce spiral structure in a galaxy by means of the close passage of a companion galaxy. Parameters similar to those expected for M51 and its companion were used. It was found that because of the high velocity dispersion of the disturbed disk galaxy, only a weak two-arm spiral structure appeared. The evolution of a uniformly rotating disk galaxy which is a stationary solution of the collisionless Boltzmann equation was investigated for various values of the initial rms velocity dispersion. It was found that the disk becomes stable at a value of the velocity dispersion predicted by theory.
Hohl, F.↗
Subsonic annular wing theory with application to flow about nacelles
A method has recently been developed for calculating the flow over a subsonic nacelle at zero angle of attack. The method makes use of annular wing theory and boundary-layer theory and has shown good agreement with both experimental data and more complex theoretical solutions. The method permits variation of the mass flow by changing the size of a center body.
Mann, M. J.↗
Project SOLWIND: Space radiation exposure
A special orbital radiation study was conducted for the SOLWIND project to evaluate mission-encountered energetic particle fluxes. Magnetic field calculations were performed with a current field model, extrapolated to the tentative spacecraft launch epoch with linear time terms. Orbital flux integrations for circular flight paths were performed with the latest proton and electron environment models, using new improved computational methods. Temporal variations in the ambient electron environment are considered and partially accounted for. Estimates of average energetic solar proton fluences are given for a one year mission duration at selected integral energies ranging from E greater than 10 to E greater than 100 MeV; the predicted annual fluence is found to relate to the period of maximum solar activity during the next solar cycle. The results are presented in graphical and tabular form; they are analyzed, explained, and discussed.
Stassinopoulos, E. G.↗
Elementary introduction to the Green's function
A technique, using the method of variation of parameters for solving differential equations, is developed for introducing Green's functions early in an undergraduate curriculum. Various examples are presented.
Whitten, R. C.↗
A practical method for correcting bidirectional reflectance variations
The purpose of the investigation was to analyze angular bidirectional reflectance variations and to test the hypothesis that first order variations could be described from a consideration of shadows created by surface perturbations. The results demonstrate the validity of this approach, and while it is not suitable for calculating absolute spectral reflectance characteristics, the development of such a model was not the objective of the investigation. Instead, a model was needed which can make relative angular corrections to bidirectional reflectance measurements independent of the details of surface geometry.
Egbert, D. D.↗
A statistical method for time-continuous assimilation of remote sounding temperatures
A time-continuous statistical method is presented for the four-dimensional assimilation of remote sounding temperatures based on radiometric measurements from polar-orbiting satellites. This method is applied to DST-6 data from the NOAA-4 and Nimbus-6 satellites. Experiments are reported in which the state of the atmosphere throughout the test period was determined using a varying amount of satellite data and in which different methods were used for their assimilation. Data from the NOAA-4 satellite only, from Nimbus-6 only, and from both satellites together were used; the methods tested include different variations of the statistical method as well as more traditional methods. The conclusions are that: (1) satellite-derived temperature data can have a modest, but statistically significant positive impact on numerical weather prediction in the two-to-three day range; (2) this impact is highly sensitive to the quantity of data available; and (3) the assimilation method plays a major role in the magnitude of the impact for the same data.
Ghil, M.↗
A summary of spectral synthesis procedures for multivariable systems
A new approach to the eigensystem assignment problem is presented. The approach utilizes a null-space formulation of the eigenvalue/eigenvector assignment problem to simultaneously realize arbitrary eigenvalue specifications, approximate desired modal behavior, and achieve low eigensystem sensitivity with respect to plant parameter variations. The methods are applied to the design of regulator and integral plus proportional servo control systems.
Liberty, S. R.↗
Note on the eigensolution of a homogeneous equation with semi-infinite domain
The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.
Wadia, A. R.↗
Some experiments on the effect of remote sounding temperatures upon weather forecasting
A time-continuous statistical method is presented for the four dimensional assimilation of remote sounding temperatures based on radiance measurements from polar orbiting satellites. This method is applied to DST 6 data from the NOAA 4 and Nimbus 6 satellites. The state of the atmosphere throughout the test period was determined using a varying amount of satellite data from the NOAA 4 satellite only, from Nimbus 6 only, and from both satellites together. The methods tested included different variations of the statistical method, as well as more traditional methods. It is concluded that satellite derived temperature data can have a modest, but statistically significant positive impact on numerical weather prediction in the two to three day range, and that this impact is highly sensitive to the quantity of data available and to the assimilation method used.
Halem, M.↗
A four dimensional variational analysis experiment
A demonstration that the four dimensional variational analysis method using the governing equations as exact constraints can be successfully employed for a perfect model and for a simple, but nonlinear, system is presented. The method is stable in an assimilation cycle. The method reconstructs the unobservable variables; in the case demonstrated, no velocity data was observed. The analysis errors are much smaller than the observing system errors.
Hoffman, R.↗
Nondestructive evaluation of residual stress in low-carbon steel, introduction
The degree of insensitivity of the temperature dependence method to variations in preferred orientations in A508 low carbon steel specimens was determined. A pulsed phase locked loop was used to measure ultrasonic velocity in these specimens in the temperature range of 50 C below and above room temperature. Results are given in tables and indicate that the temperature dependence of ultrasonic longitudinal velocity in four specimens cut at different angles remains unchanged as a function of orientation within + or -2%. The variation of temperature dependence of ultrasonic shear velocity in the A508 steel as a function of applied stresses was also measured. Results show that values at zero stress are equal regardless of whether the polarization direction is parallel or perpendicular to the direction in which the stress is applied.
Source record↗
Background noise measurements from jet exit vanes designed to reduced flow pulsations in an open-jet wind tunnel
Many open jet wind tunnels experience pulsations of the flow which are typically characterized by periodic low frequency velocity and pressure variations. One method of reducing these fluctuations is to install vanes around the perimeter of the jet exit to protrude into the flow. Although these vanes were shown to be effective in reducing the fluctuation content, they can also increase the test section background noise level. The results of an experimental acoustic program in the Langley 4- by 7-Meter Tunnel is presented which evaluates the effect on tunnel background noise of such modifications to the jet exit nozzle. Noise levels for the baseline tunnel configuration are compared with those for three jet exit nozzle modifications, including an enhanced noise reduction configuration that minimizes the effect of the vanes on the background noise. Although the noise levels for this modified vane configuration were comparable to baseline tunnel background noise levels in this facility, installation of these modified vanes in an acoustic tunnel may be of concern because the noise levels for the vanes could be well above background noise levels in a quiet facility.
Hoad, D. R.↗
Comparison of experimental and analytical predictions of rotor blade-vortex interactions using model scale acoustic data
Helicopter blade-vortex interaction (BVI) noise is studied using a model scale rotor acoustic data base and an analytical rotor wake prediction method. The variation of BVI acoustic levels with vehicle flight conditions (forward speed and disk attitude) is presented. Calculations of probable BVI locations on the rotor disk are made for a range of operating conditions using the measured acoustic signals and an acoustic ray tracing technique. Analytical predictions of possible BVI locations on the rotor disk are made using a generalized distorted wake analysis program. Comparisons of the interaction locations are made with the results of both the analytic approach and the acoustic ray tracing technique.
Martin, R. M.↗
SASS wind ambiguity removal by direct minimization. II - Use of smoothness and dynamical constraints
A variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. The VAM yields the best fit to the data by minimizing an objective function S which is a measure of the lack of fit. The SASS data are described and the function S and the analysis procedure are defined. Analyses of a single ship report which are analogous to Green's functions are presented. The analysis procedure is tuned and its sensitivity is described using the QE II storm. The procedure is then applied to a case study of September 6, 1978, south of Japan.
Hoffman, R. N.↗