Certain problems in the thermodynamics of the critical point <nekotoryye voprosy termodinamiki kriticheskoy tochki<
Taylor series expansion in powers of deviation from critical point for integral thermodynamic functions
INTEGRAL FUNCTION↗
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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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Nonsimilar solution of the multicomponent laminar boundary layer by an integral matrix method.
Nonsimilar solution to complex boundary layer problems, using matrix concept to integral relations via Taylor series expansion of parameters
MATRIX ANALYSIS↗
Improved determination of atmospheric opacity from radio astronomy measurements.
Atmospheric opacity and extraterrestrial radio source intensity related by improved Taylor series technique using least squares method
SPACE RADIATION↗
Simultaneous integration of n-bodies by analytic continuation with recursively formed derivatives.
Recursion formulae to generate Taylor series expansion for motion of n-point masses subject to gravitational attractions
Hartwell, J. G.↗
Nonsimilar solution of the multicomponent laminar boundary layer by an integral-matrix method.
Nonsimilar solution to complex laminar boundary layer problems, applying matrix concept to integral relations via Taylor series expansion of parameters
Bartlett, E. P.↗
A technique for correcting coefficient quantization errors in hybrid control systems.
Taylor series expansion used in correcting quantized digital coefficient errors in hybrid feedback control system
Chenoweth, D. L.↗
Differential approximation for radiant energy losses in nonequilibrium plasmas.
Differential approximation for radiant energy loss in nonequilibrium plasma generated from truncated Taylor series expansion of radiation source function
Harstad, K. G.↗
Error compensation for hybrid-computer solution of linear differential equations
Z-transform technique compensates for digital transport delay and digital-to-analog hold. Method determines best values for compensation constants in multi-step and Taylor series projections. Technique also provides hybrid-calculation error compared to continuous exact solution, plus system stability properties.
Kemp, N. H.↗
Mean motions and characteristics exponent at the libration points
Solar system planetary mean motions calculation from characteristic equations roots at equilibrium points of restricted three body problem, using Taylor series solution
Cochran, J. E.↗
An algorithm for integrating stepwise the restricted problem in Thiele's coordinates
Planar restricted three body problem in Thiele coordinates, developing recurrence formulas for coefficients in Taylor series expansions of solution
Estes, R. H.↗
Extension and analysis of use of derivatives for compensation of hybrid solution of linear differential equations
Hybrid computers solution of linear differential equations, analyzing Taylor series /derivatives/ use for compensation
Kemp, N. H.↗
Method for nonlinear exponential regression analysis
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Junkin, B. G.↗
A method for nonlinear exponential regression analysis
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Junkin, B. G.↗
Dynamics of a spinning space station with a counterweight connected by multiple cables.
A unique and relatively simple approach is presented for obtaining the linearized equations of motion. A conservative system consisting of two rigid bodies connected by any number of massless cables with linear axial stiffness is assumed. The cable forces and torques are expanded in a Taylor series about the equilibrium values of the system coordinates which results in a cable stiffness matrix. The method of obtaining the equilibrium values of the coordinates is discussed and results are presented. The range of validity of the linear model is determined by comparing results with a digital simulation of the nonlinear system.
Nixon, D. D.↗
Application of the adiabatic-nuclei theory to vibrational excitation.
The adiabatic-nuclei theory is shown to be quantitatively applicable to vibrational excitation of diatomic molecules by electron impact. When the dependence of the fixed-nuclei phase shifts on internuclear separation is approximated by a two-term Taylor series, the resulting formulas are transparent and easily evaluated. Application to e-H2 excitation is made, phase-shift derivatives are estimated, and the theory is found to fit experimental data.
Faisal, F. H. M.↗
Stress intensity factors for long, deep surface flaws in plates under extensional fields
Using a singular solution for a part circular crack, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50 and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the ''equivalent'' semi-elliptical flaw results was not valid for a/2c less than 0.20. Best overall agreement for the moderate (a/t approximately 0.5) to deep flaws (a/t approximatelly 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory, when compared on the basis of equivalent flaw depth and area.
Harms, A. E.↗
Design oriented structural analysis.
Recent developments in computer-aided structural design indicate a need for computerized structural analysis techniques which are efficient for the repetitive analysis of large complex structures undergoing design modifications. This paper describes such a technique based on a Taylor series approach. Results are presented for an idealized aircraft fuselage midsection to demonstrate the efficiency and accuracy of the technique. The results show that satisfactory analyses of modified structures may be obtained with the proposed technique, even for large changes in member sizes, for only a small fraction of the computational cost of a full reanalysis.
Storaasli, O. O.↗
Some approximation concepts for structural synthesis.
An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss example problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.
Schmit, L. A., Jr.↗