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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗
NASA NTRS1976

A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response

A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN.

Everstine, G. C.↗
NASA NTRS1976

Asymptotic residual pump transmission characteristics in laser-induced stimulated Brillouin scattering

The considered asymptotic relationship is investigated and an expression is sought for the slope of the curve representing the relation between the residual fractional transmitted pump and the pump excitation in backward-traveling-wave amplification. It is found that the characteristic -2 slope of the oscillation curve is a unique property. Rapid exponential decay may very well constitute an inherent limiting factor for efficient energy conversion.

Hsu, H.↗
NASA NTRS1977

An asymptotic analysis of a general class of signal detection algorithms

For applications to the problem of radio frequency interference identification, or in the search for extraterrestrial intelligence, it is important to have a basic understanding of signal detection algorithms. A general technique for assessing the asymptotic sensitivity of a broad class of signal detection algorithms is given. In these algorithms, the decision is based on the value of X sub 1 + X sub 2...+ X sub n where the X sub 1's are obtained by sampling and preliminary processing of a physical process.

Mceliece, R. J.↗
NASA NTRS1978

Use of asymptotic methods in vibration analysis

The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.

Ashley, H.↗
NASA NTRS1979

Computer analysis of shells of revolution using asymptotic results

It is suggested that asymptotic results for the behavior of thin shells can be incorporated in a general computer code for the analysis of a complex shell structure. The advantage when compared to existing finite difference or finite element codes is a substantial reduction in computational labor with the capability of working to a specified level of accuracy. A reduction in user preparation time and dependance on user judgment is also gained, since mesh spacing can be internally generated. The general theory is described in this paper, as well as the implementation in the computer code FAST 1 (Functional Algorithm for Shell Theory) for the analysis of the general axisymmetric shell structure with axisymmetric loading.

Steele, C. R.↗
NASA NTRS1979

Asymptotic effective potentials for electron-hydrogen scattering

The asymptotic effective potential for electron- or positron-hydrogen elastic scattering is derived, correct to order x to the -7th, where x is the positron projectile coordinate, using the Feshbach optical potential as a starting point in the manner of Kleinman et al (1968). To order x to the -6th the potential agrees with the close-coupling results of Seaton and Steenman-Clark (1977) but not to order x to the -7th, where the present calculation gives the result + or - 213/2(x to the 7th) for electron and positron respectively. This coefficient differs considerably from the approximate value of Seaton and Steenman-Clark, and the discrepancy is traced to the omission of d states in their calculation.

Drachman, R. J.↗
NASA NTRS1980

Transonic swept-wing analysis using asymptotic and other numerical methods

The paper presents asymptotic methods for high-aspect-ratio wings in transonic flow developed for straight unyawed wings and for oblique wings. They show that the three-dimensional mixed-flow calculations may be reduced to solving a set of two-dimensional problems at each span station; the development of this theory and the related computational studies are reviewed. Differences between the piloted (oblique) wing, the swept-back wing, and the swept-forward-wing in the induced upwash are discussed; examples of similarity solutions are demonstrated for high subcritical and slightly supercritical component flows, and comparisons made with relaxation solutions of a full potential equation. The examples include oblique and symmetric swept wings, and the adequacy of the existing full-potential computer code is examined.

Cheng, H. K.↗
NASA NTRS1979

Asymptotic continuation method for trajectory optimization

A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.

Washburn, R. B., Jr.↗
NASA NTRS1980

Asymptotic behavior of the efficiencies in Mie scattering

Consideration is given to the asymptotic behavior of the Mie scattering and extinction efficiencies for large absorbing spheres as sphere size approaches infinity. It is shown that the method used by Chylek (1975) for evaluating the infinite sums over the Mie partial wave coefficients representing these efficiencies and proving that the extinction efficiency approaches 2 is invalid, despite the correctness of the result, and that the limiting expression for the scattering efficiency obtained by this method is also incorrect. An analytical expression is then derived from geometrical optics considerations for the scattering efficiency limit which is valid when the imaginary component of the refractive index is much less than 1.

Acquista, C.↗
NASA NTRS1980

Grid evolution in time asymptotic problems

A technique for generating systems of coordinates for solving time asymptotic problems is described which provides a simple way of moving the mesh points in physical space and reduces the error in the solution relative to that obtained using a fixed mesh. First order partial differential equations are formulated for the grid point velocity in transient problems. Local flow information and boundary motion are used to determine the interior grid point motion.

Rai, M. M.↗
NASA NTRS1980

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Peters, C.↗
NASA NTRS1981

An asymptotic unsteady lifting-line theory with energetics and optimum motion of thrust-producing lifting surfaces

A low frequency unsteady lifting-line theory is developed for a harmonically oscillating wing of large aspect ratio. The wing is assumed to be chordwise rigid but completely flexible in the span direction. The theory is developed by use of the method of matched asymptotic expansions which reduces the problem from a singular integral equation to quadrature. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. The influence of reduced frequency, aspect ratio, planform shape, and mode of oscillation on wing aerodynamics is demonstrated through numerical examples. Compared with lifting-surface theory, computation time is reduced significantly. Using the present theory, the energetic quantities associated with the propulsive performance of a finite wing oscillating in combined pitch and heave are obtained in closed form. Numerical examples are presented for an elliptic wing.

Ahmadi, A. R.↗
NASA NTRS1980

A new asymptotic method for jump phenomena

Physical phenomena involving rapid and sudden transitions, such as snap buckling of elastic shells, explosions, and earthquakes, are characterized mathematically as a small disturbance causing a large-amplitude response. Because of this, standard asymptotic and perturbation methods are ill-suited to these problems. In the present paper, a new method of analyzing jump phenomena is proposed. The principal feature of the method is the representation of the response in terms of rational functions. For illustration, the method is applied to the snap buckling of an elastic arch and to a simple combustion problem.

Reiss, E. L.↗
NASA NTRS1981

Asymptotic form of the longitudinal correlation function for isotropic homogeneous turbulence

An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.

Rosen, G.↗
NASA NTRS1980

Asymptotic solution for the reflectivity of a very rough surface

Asymptotic solutions for the reflectivity of a very rough surface are obtained in closed form up to second order in variance of slope. The zeroth-order solution gives the reflectivity of a specular surface and the sum of the higher-order terms yields the net effect of the rough surface. Within the common regions of validity of small rms slope and incident angle not close to grazing, the result agrees very well with those obtained with numerical methods.

Tsang, L.↗