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At least 523 records · Page 29

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NASA NTRS1975

Lagged low order control systems with powered controls

With powered controls, a high order control system can be changed to a lower order control system with a lag, which is better suited to our position control skills and strategies. Separate groups of untrained men were trained on an acceleration control system, or on a rate control system with an exponential lag of either .5, 2, or 4 sec. Acquisition time was reliably shorter with all the lagged rate control systems than with the unlagged acceleration control system.

Poulton, E. C.↗

NASA NTRS1975

Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt's numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

Su, S. F.↗

NASA NTRS1975

15th order resonance terms using the decaying orbit of TETR-3

Fifteenth-order commensurability of the orbit of TETR-3 (1971-83B) is studied. The study is designed to obtain good discrimination of 15th-order resonances through a better range of inclinations. The first low inclination orbit, 33 deg, is used for this purpose; it is very sensitive to the high degree terms which were rather poorly represented by previously analyzed orbits.

Wagner, C. A.↗

NASA NTRS1975

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-

Rubin, S. G.↗

NASA NTRS1975

Thirteenth-order orbital resonance on a Diademe 2 fragment

A strong thirteenth-order resonance has been observed in an analysis which is based on U.S. Navy tracking data regarding the slowly decaying orbit of a Diademe 2 fragment. The exact commensurability for the orbit occurred in late 1973. The major changes due to the resonance were over by late 1974. Approaches for a significant improvement of thirteenth-order geopotential terms are discussed.

Wagner, C. A.↗

NASA NTRS1975

Second-order small-disturbance solutions for hypersonic flow over power-law bodies

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.

Townsend, J. C.↗

NASA NTRS1975

Second-order non-iterative ADI solution of non-linear partial differential equations

A new method for the solution of non-linear partial differential equations by an ADI procedure is described. Although the method is second order accurate in time, it does not require either iterations or predictor corrector methods to overcome the nonlinearity of the equations. Thus the computational effort required for the solution of the non-linear problem becomes similar to that required for the linear case. The method is applied to a two-dimensional 'extended Burgers equation'. Linear stability is studied, and some numerical solutions obtained. The improved accuracy obtained by the 2nd order truncation error is clearly manifested.

Wolfshtein, M.↗

NASA NTRS1976

A higher order panel method for linearized supersonic flow

A higher order panel method using linearly varying source and quadratically varying doublet distributions for computing linearized supersonic flow over arbitrary wings and bodies is described. With tangential mass flux boundary conditions on circular cones at angles of attack, the source panel method gave pressure distributions which are in excellent agreement with exact nonlinear theory. The numerical source panel method was demonstrated to be very stable by randomly panelling an axially symmetric body. For wings with thickness and camber, both the source and doublet panel methods yield excellent agreement with exact linearized solutions. Computational experiments indicate that the use of exact surface paneling in lieu of linearized boundary conditions for wings provides better agreement with higher order theory and with experiment.

Ehlers, F. E.↗

NASA NTRS1976

Higher-order effects of initial deformation on the vibrations of crystal plates

A system of plate equations for the thickness-shear and flexural vibrations superposed on large initial deflection due to bending is derived; in the stress-strain relations, the terms associated with the fourth-order elastic stiffness coefficients are retained. An explicit formula for the change in the fundamental cut-off thickness shear frequency is obtained, and the effects of the terms associated with the fourth-order constants appear to be significant for large gradients of the rotation angles.

Markenscoff, X.↗

NASA NTRS1976

On the optimal minimum order observer-based compensator and the limited state variable feedback controller

Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.

Llorens-Ortiz, B.↗

NASA NTRS1976

A source array for generating higher order acoustic modes in circular ducts

A unique source array has been developed for the generation of both spinning and non-spinning higher order modes in a circular duct. The array consists of two concentric rings of sources. Through individual control of the response of each element, the array provided phase and amplitude control in the radial as well as circumferential directions. Radial modes shapes were measured in a 12-inch diameter anechoically-terminated hollow duct. These modes could be generated at their cut-off frequency and throughout a frequency range extending to the cut-off frequency for the next higher order radial mode. Comparisons are given between theory and experiment for the generation of specific modes. The radial dependence of the measured mode shapes was enhanced considerably by the design of this array. The results indicate a significant improvement over previous mode generation mechanisms. The contamination of the generated mode by additional spurious modes is also considered for variations between individual elements within the source array.

Wyerman, B. R.↗

NASA NTRS1977

Third-order nonlinearities in molecular hydrogen - Two-photon resonance enhanced third-harmonic generation and Raman scattering

Effects of quantum mechanical interferences on third-order susceptibilities in molecules are studied. First principle calculations for molecular hydrogen are presented and shown to agree with results derived from experimental stimulated Raman gain and spontaneous Raman cross-section data. 10 percent third-harmonic conversion efficiency in H2 at 1 atm without phase matching should require a 150 MW per sq cm at 4.81 microns. As little as 5.9-MW power is sufficient when the beam is properly focused. Resonance Raman scattering (RRS) is proposed for experimentally investigating the interference effects, which tend to reduce the strength of third-order nonlinear susceptibilities.

Pan, C.-L.↗

NASA NTRS1977

Characteristics of first order shock induced magnetic transitions in iron and discrimination from TRM

Reflected light microscopy provides information on first-order shock transitions in iron and iron-nickel and permits discrimination of microstructures due to shock transitions from those imparted by thermal transitions. In addition, thin-foil electron microscopy is used to characterize magnetic transitions in fine-particle iron. First-order magnetic phase changes, such as that from the antiferromagnetic face centered cubic state to the ferromagnetic body centered cubic state, are studied with the aim of calibrating the shock and thermal mechanisms of magnetization in iron with a particle size range between 250 and 1200 A. The efficiency of remanence due to shock transition is also estimated.

Wasilewski, P.↗

NASA NTRS1978

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

Mcclelland, J.↗

NASA NTRS1978

Minimal order observers for linear functions of the state vector

The problem of estimating linear functions of a state vector in a multi-input/output system is considered. A simple lower bound on the observer order with arbitrary eigenvalues is established. Algorithms to construct minimal-order stable (or arbitrary dynamics) observers are also outlined.

Srinathkumar, S.↗

NASA NTRS1978

Fourth-order acoustic torque in intense sound fields

The observation of a fourth-order acoustic torque in intense sound fields is reported. The torque was determined by measuring the acoustically induced angular deflection of a polished cylinder suspended by a torsion fiber. This torque was measured in a sound field of amplitude greater than that in which first-order acoustic torque has been observed.

Wang, T. G.↗

NASA NTRS1977

Using model order tests to determine sensory inputs in a motion study

In the study of motion effects on tracking performance, a problem of interest is the determination of what sensory inputs a human uses in controlling his tracking task. In the approach presented here a simple canonical model (FID or a proportional, integral, derivative structure) is used to model the human's input-output time series. A study of significant changes in reduction of the output error loss functional is conducted as different permutations of parameters are considered. Since this canonical model includes parameters which are related to inputs to the human (such as the error signal, its derivatives and integration), the study of model order is equivalent to the study of which sensory inputs are being used by the tracker. The parameters are obtained which have the greatest effect on reducing the loss function significantly. In this manner the identification procedure converts the problem of testing for model order into the problem of determining sensory inputs.

Repperger, D. W.↗

NASA NTRS1979

Analysis and design of a second-order digital phase-locked loop

A specific second-order digital phase-locked loop (DPLL) was modeled as a first-order Markov chain with alternatives. From the matrix of transition probabilities of the Markov chain, the steady-state phase error of the DPLL was determined. In a similar manner the loop's response was calculated for a fading input. Additionally, a hardware DPLL was constructed and tested to provide a comparison to the results obtained from the Markov chain model. In all cases tested, good agreement was found between the theoretical predictions and the experimental data.

Blasche, P. R.↗