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Charged particle calibrations based on differenced range versus integrated Doppler (DRVID) are smoothed and fitted with a polynomial prior to its application in the orbit determination process. A description is given of the results of the tests performed on the computer program performing these calculations to determine its characteristics and to evaluate the acceptability of its computations. This program, called MEDIA, is described.
Fundamental characterization of the constant-amplitude fatigue crack propagation is achieved by an analysis of the rate of change of crack length with change in number of applied loading cycles, defining the rate values such that they are consistent with the basic assumption of smoothness and continuity in the fatigue crack growth process. The technique used to satisfy the analytical conditions and minimize the effects of local material anomalies and experimental errors is that of fitting a smooth curve to the entire set of basic data by least square regression. This yields a well-behaved function relating the number of cycles to the crack length. By taking the first derivative of the function, the crack growth rate is obtained for each point. The class of curve fitting functions used in the analysis is the polynomial of degree n.
A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.
The experimental measures and techniques are described which are used to obtain the strength tensor components, including cubic terms. Based on a considerable number of biaxial pressure tests together with specimens subjected to a constant torque and internal pressure, a modified form of the plane stress tensor polynomial failure equation was obtained that was capable of predicting ultimate strength results well. Preliminary data were obtained to determine the effect of varying post cure times and ambient temperatures (-80 F to 250 F) on the change in two tensor strength terms, F sub 2 and F sub 22. Other laminate configurations yield corresponding variations for the remaining strength parameters.
Algebraic criteria are proposed for testing stability properties of multivariable polynomials. The tests are recursive and can be executed in a finite number of steps.
Frequently a photograph received from a spacecraft will be smeared by some process, e.g., by camera motion. Algebraically such smearing can be represented as p = sigma f, where sigma is the true picture, p is the received picture, and f is the smearing function. (p, sigma, and f are polynomials in two variables x and y.) Thus, in principle, sigma can be recovered by multiplying p by 1/f. However, there are problems involved in computing 1/f. Some of these problems are investigated.
Higher order numerical methods derived from polynomial spline interpolation or Hermitian differencing are applied to a separating laminar boundary layer, i.e., the Howarth problem, and the turbulent flat plate boundary layer flow. Preliminary results are presented. It is found that accuracy equal to that of conventional second order accurate finite difference methods is achieved with many fewer mesh points and with reduced computer storage and time requirements.
It is shown that a closer reexamination of Yun's 1976 paper reveals the reducibility of SQFR to GCD. The natural question that follows is whether GCD is reducible to SQFR. That is answered affirmatively and the derivation actually suggests an algorithm for computing GCD's when input polynomials are already represented by their SQFR form.
Equations are presented which attempt to fit least squares polynomials to tables of date. It is concluded that much data are needed to reduce the measurement error standard deviation by a significant amount, however at certain points great accuracy is attained.
This paper presents a FORTRAN program written to solve for the kernel of a matrix of polynomials with real coefficients. It is an implementation of Sain's free modular algorithm for solving the minimal design problem of linear multivariable systems. The structure of the program is discussed, together with some features as they relate to questions of implementing the above method. An example of the use of the program to solve a design problem is included.
A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of a composite limina subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion. Environmental effects including ambient temperature, exposure to vacuum, length of post-cure time, and rate of cool down were also investigated. Behavior changes associated with polymer (epoxy) matrix composites were determined in terms of variations in stiffness and tensile strength.
An efficient algorithm for selecting the degree of a polynomial that defines a curve that best approximates a data set was presented. This algorithm was applied to both oscillatory and nonoscillatory data without loss of generality.
This paper describes a complete case study of the application of the theory of minimal design to multivariable control of jet engines. The minimal-design problem is approached from the viewpoint of polynomial modules, and computational experience with PL/I and FORMAC-PL/I software is discussed. The complete minimal-design solution exhibits flexibilities not apparent in early industry studies, and a matrix approach to pole assignment can be used to advantage in this situation.
A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of laminated composite structures subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion.
The report has examined the claim that grazing incidence telescopes having surfaces described by generalized equations have image characteristics superior to those of the paraboloid-hyperboloid and Wolter-Schwarzschild configurations. With emphasis on specific applications in solar and cosmic X-ray/EUV astronomy, raytracing has shown that in many cases there is no advantage in the polynomial design, and in those cases where advantages are theoretically to be expected, the advantages are outweighed by practical considerations.
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
The effectiveness of the algorithm of polynomial striction of the data is examined, and the selection of an algorithm is carried out, according to the results of measurements of the components of the permanent magnetic field in communication sequences from the Venera-9 space vehicle, where the shock waves were recorded. It is shown that the most effective algorithm, according to the coefficient of striction, is the algorithm of the zero order interpolator. Also examined is the increase in effectiveness with the introduction of a variable threshold of comparison. The root-mean-square deviation of the error of regeneration of the data with various thresholds is calculated, and qualitative analysis of the distortions is carried out, having shown a considerable change in the form of the small discontinuities, which may be interpreted as potential interplanetary shock waves.
A comparative failure analysis is presented based on the application of quadratic and cubic forms of the tensor polynomial lamina strength criterion to various composite structural configurations in a plane stress state. Failure loads have been predicted for off-angle laminates under simple loading conditions and for symmetric-balanced laminates subject to varying degrees of biaxial tension, including configurations subject to multimode failures. Some experimental data are also provided to support these calculations. From these results, the necessity of employing a cubic strength criterion to accurately predict the failure of composite laminae is demonstrated.