High-precision Chebyshev series approximation to the exponential integral
Calculating exponential integral using Chebyshev series expansion of associated functions
Lee, K. L.↗
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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.
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How to assemble a Keplerian processor
Computer program for two body problem literal series expansions using Kepler functions with Bessel and Poisson series operation
Broucke, R.↗
On the Laplace relation among the satellites of Uranus
Three of Uranus' satellites are involved in an interaction similar to the Laplace relation among the Galilean satellites of Jupiter. However, there are no pair-wise commensurabilities in the Uranus system as there are among the Galilean satellites. Thus analysis by Fourier expansion of disturbing functions becomes too unwieldy for practical calculation. Instead, the unexpanded perturbations are numerically averaged over a time scale short compared to the important variations in the Laplace relation. Perturbations of Miranda's orbit are estimated to be of observable magnitude for reasonable masses of Ariel and Umbriel.
Greenberg, R.↗
An Atmospheric Cloud Physics Laboratory for the Space Laboratory
Results of research and engineering analyses to date show that it is feasible to develop and fly on the first Spacelab mission a multipurpose laboratory in which experiments can be performed on the microphysical processes in atmospheric clouds. The paper presents a series of tables on the Atmospheric Cloud Physics Laboratory, with attention given to experiment classes, the preliminary equipment list (particle generators, optical and imaging devices, particle detectors and characterizers, etc.), initial equipment (scientific equipment subsystems and flight support subsystems), and scientific functional requirements (the expansion chamber, the continuous flow diffusion chamber, the static diffusion chamber, the humidifier, and particle generators).
Smith, R.↗
Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain
A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.
Klein, V.↗
Prediction of composite thermal behavior made simple
A convenient procedure is described to determine the thermal behavior (thermal expansion coefficients and thermal stresses) of angleplied fiber composites using a pocket calculator. The procedure consists of equations and appropriate graphs for various ( + or - theta) ply combinations. These graphs present reduced stiffness and thermal expansion coefficients as functions of (+ or - theta) in order to simplify and expedite the use of the equations. The procedure is applicable to all types of balanced, symmetric fiber composites including interply and intraply hybrids. The versatility and generality of the procedure is illustrated using several step-by-step numerical examples.
Chamis, C. C.↗
NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model
A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.
Source record↗
Prediction of composite hygral behavior made simple
A convenient procedure is described to determine the hygral behavior (moisture expansion coefficients and moisture stresses) of angleplied fiber composites using a pocket calculator. The procedure consists of equations and appropriate graphs for various (+ or - theta) ply combinations. These graphs present reduced stiffness and moisture expansion coefficients as functions of (+ or - theta) in order to simplify and expedite the use of the equations. The procedure is applicable to all types of balanced, symmetric fiber composites including interply and intraply hybrids. The versatility and generality of the procedure is illustrated using several step-by-step numerical examples.
Chamis, C. C.↗
The effects of microcracking on the thermal expansion of graphite-epoxy composites
A study of the effects of thermal environment and microcracking in graphite epoxy composites was made. Research indicates that microcracking does affect the thermal expansion of composite laminates. The amount of reduction in thermal expansion was a function of the crack density. A maximum reduction of approximately 25% occurred in a quasi-isotropic specimen with a crack density of 2.05 mm 1 in the 90 deg plies. Laminate analysis with appropriate reductions in E sub 2 and Alpha sub 2 of the damaged plies appears to be capable of modeling the observed
Bowles, D. E.↗
The axisymmetric elasticity problem for a laminated plate containing a circular hole
The elasticity problem for a laminated thick plate which consists of two bonded dissimilar layers and which contains a circular hole is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface by using the Love strain function. Through the expansion of the boundary conditions into Fourier series the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented and the stress intensity factors are calculated.
Delale, F.↗
A new numerical method for the simulation of three dimensional flow in a pipe
A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction.
Leonard, A.↗
Tropical cyclone track and genesis forecasting using satellite microwave sounder data
Although many dynamical and statistical prediction schemes are available to forecasters, tropical cyclone track errors are still large. One primary difficulty is that tropical cyclones exist over the data-sparse tropical oceans. Satellite sounders, however, routinely provide numerous data over these areas. Mean layer temperatures from the Scanning Microwave Spectrometer on board the Nimbus 6 satellite are decomposed using empirical orthogonal functions, and the expansion coefficients are related to deviations from the persistence forecast location, to speed change, to direction change and to intensity change. The significance of the regression equations is tested by a null hypothesis of zero correlation coefficient. It appears that significant information about tropical cyclone motion exists in the satellite-estimated mean layer temperatures, especially at upper levels. A physical interpretation of the statistical results is offered, and a one-storm-out independent test is used to test the stability of the equations. Finally, some further work is suggested.
Kidder, S. Q.↗
Prediction of composite hygral behavior made simple
A convenient procedure is described to determine the hygral behavior (moisture expansion coefficients and moisture stresses) of angleplied fiber composites using a pocket calculator. The procedure consists of equations and appropriate graphs for various (+ or - theta) ply combinations. These graphs present reduced stiffness and moisture expansion coefficients as functions of (+ or - theta) in order to simplify and expedite the use of the equations. The procedure is applicable to all types of balanced, symmetric fiber composites including interply and intraply hybrids. The versatility and generality of the procedure is illustrated using several step-by-step numerical examples. Previously announced in STAR as N82-16181
Chamis, C. C.↗
A new numerical method for the simulation of three-dimensional flow in a pipe
A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction. Previously announced in STAR as N82-31644
Leonard, A.↗
On the potential use of satellite sounder data in forecasting tropical cyclone motion
Although many prediction schemes are available, tropical cyclone track forecast errors are still unacceptably large. A primary difficulty is that tropical cyclones and their environments are poorly observed by conventional data networks. Satellite sounders, however, routinely provide numerous observations near these storms. Mean layer temperatures from the Scanning Microwave Spectrometer (SCAMS) on board the Nimbus-6 satellite are decomposed using empirical orthogonal functions, and the expansion coefficients are related to deviations from persistence track forecasts. Based on multiple correlation coefficients it appears that upper-level (250-100 mb) temperatures contain significant information about the right-angle error of the persistence forecast location. Temperatures from the 1000-500 mb layer seemed to contain little forecast information. Implications of these results for further work are offered.
Kidder, S. Q.↗
Dispersion characteristics for wide slotlines on low-permittivity substrates
A spectral-domain Galerkin method is used to calculate the dispersion characteristics of wide slotlines on low-permittivity substrates that are electrically thin. The range of parameters covered are d/lambda sub 0 = 0.006-0.06, W/lambda sub 0 = 0.005-2.0, and epsilon sub r = 2.22, 3.0, 3.8, and 9.8. The choice of expansion and testing functions makes possible the extraction of the asymptotic form of the infinite integrals, resulting in a computationally efficient solution. The agreement between calculated and measured slot wavelengths on narrow and wide slots is generally within 2.0 percent over 2-6 GHz.
Janaswamy, R.↗
Does the geoid drift west?
In 1970 Hide and Malin noted a correlation of about 0.8 between the geoid and the geomagnetic potential at the Earth's surface when the latter is rotated eastward in longitude by about 160 degrees and the spherical harmonic expansions of both functions are truncated at degree 4. From a century of magnetic observatory data, Hide and Malin inferred an average magnetic westward drift rate of about 0.27 degrees/year. They attributed the magnetic-gravitational correlation to a core event at about 1350 A.D. which impressed the mantle's gravity pattern at long wavelengths onto the core motion and the resulting magnetic field. The impressed pattern was then carried westward 160 degrees by the nsuing magnetic westward drift. An alternative possibility is some sort of steady physical coupling between the magnetic and gravitational fields (perhaps migration of Hide's bumps on the core-mantle interface). This model predicts that the geoid will drift west at the magnetic rate. On a rigid earth, the resulting changes in sea level would be easily observed, but they could be masked by adjustment of the mantle if it has a shell with viscosity considerably less than 10 to the 21 poise. However, steady westward drift of the geoid also predicts secular changes in g, the local acceleration of gravity, at land stations. These changes are now ruled out by recent independent high-accuracy absolute measurements of g made by several workers at various locations in the Northern Hemisphere.
Backus, G. E.↗
Temperature effects on the universal equation of state of solids
Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P=0) isothermal bulk modulus; (2)it P=0 pressure derivative; (3) the P=0 volume; and (4) the P=0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.
Vinet, P.↗