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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Second-order electro-optic effect in diamond.

Observation of a second-order electrooptic effect in diamond, leading to the determination of an order of magnitude for the appropriate second-order electrooptic coefficient of diamond. A linear effect, forbidden by symmetry, is also observed and attributed to random residual strains, an average estimate of which is obtained as .00001 for the particular sample used in this experiment. Birefringence due to second-order dispersion effects is also discussed.

Anastassakis, E.↗
NASA NTRS1972

Electron paramagnetic resonance studies of a viscous nematic liquid crystal: Evidence counter to a second-order phase change

The ordering in a viscous, nematic, liquid crystal was studied using vanadyl acetyl acetonate and several nitroxides as paramagnetic probes. The ordering curve for VAAC at both K-band and X-band shows a slope discontinuity at a reduced temperature of 0.85. This discontinuity is caused by the tumbling time of the VAAC becoming comparable with the hyperfine splitting. The slope discontinuity is not present in the ordering curves of the nitroxides. The results are taken as evidence counter to the presence of a second-order phase transition.

Shutt, W. E.↗
NASA NTRS1972

Generation and application of the equations of condition for high order Runge-Kutta methods

This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition are developed for Runge-Kutta methods of order four through order nine. Once developed, these equations are used in a comparison of the local truncation errors for several sets of Runge-Kutta coefficients for methods of order three up through methods of order eight.

Haley, D. C.↗
NASA NTRS1974

Development of a second order closure model for computation of turbulent diffusion flames

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.

Varma, A. K.↗
NASA NTRS1974

A second-order theory of an artificial satellite under the influence of the oblateness of the earth

The general theory of the method of averaging is used to study the effect of the oblateness of the earth on the motion of an artificial satellite. The first-order harmonic J2 and the second-order harmonics J3 and J4 are included in the analysis. The first-order, periodic variations together with the second-order, averaged and secular variations are derived for all the six orbital elements. Alternative orbital elements and necessary relations are introduced to deal with circular orbits, orbits at critical inclination and equatorial orbits. Essential transformations and initialization procedures are also outlined.

Liu, J. J. F.↗
NASA NTRS1973

Aircraft maneuver optimization of reduced-order approximation

Review of recent work in recasting the energy type of approximation to aircraft flight in terms of singular perturbation theory and in extending this theory to three-dimensional maneuvers. Singular perturbations for differential equations arising in optimal control are first examined for a system of fairly general form but low order. The attitude dynamics for optimal flight of a rocket in vacuum is then studied as an introductory, and fairly transparent, example. The question of the choice of variables is then discussed. Finally, optimal aircraft flight in various reduced-order approximations is investigated. In particular, the problem of three-dimensional aircraft flight is formulated for singular perturbation treatment, and possibilities for decoupling into several lower-order problems are illustrated. The use of reduced-order approximation facilitates numerical computations by reducing the number of multiplier initial values that must be determined simultaneously and by improving the conditioning of the differential equations.

Kelley, H. J.↗
NASA NTRS1974

Equations of condition for high order Runge-Kutta-Nystrom formulae

Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.

Bettis, D. G.↗
NASA NTRS1974

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

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Townsend, J. C.↗
NASA NTRS1976

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗
NASA NTRS1976

A high order theory for uniform and laminated plates

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.

Lo, K. H.↗
NASA NTRS1977

Third-order solution of an artificial-satellite theory

A third-order solution was developed for the motions of artificial satellites moving in the gravitational field of the earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations were derived by the Hori perturbation method. All quantities were expanded into power series of the eccentricity, but the solution was obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth, small-eccentricity satellite with an accuracy of better than one cm over a period of one month.

Kinoshita, H.↗
NASA NTRS1977

A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume 1: The generalized method of averaging applied to the artificial satellite problem

A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.

Mcclain, W. D.↗
NASA NTRS1978

Third-order solution of an artificial-satellite theory

A third-order solution is developed for the motions of artificial satellites moving in the gravitational field of the earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations are derived by Hori's perturbations method. All quantities are expanded into power series of the eccentricity, but the solution is obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth satellite with a small eccentricity with an accuracy of better than 1 cm over 1 month.

Kinoshita, H.↗
NASA NTRS1980

Electron-optical observations of ordered FeNi in the Estherville meteorite

Electron optical studies of the ordered FeNi (taenite) phase in the Estherville meteorite are reported. A thin section of the meteorite containing a large area of continuous anisotropic taenite was studied by crossed polar reflected light microscopy, and electron probe microanalysis, transmission electron microscopy, scanning transmission electron microscopy and X-ray energy dispersive spectrometry. Results reveal the presence of preferentially ion-etched regions of clear taenite corresponding to single crystals, with superlattice reflections in the fundamental FeNi reciprocal lattice arising from long-range ordering. The presence of antiphase domain boundaries within the regions also confirms the presence of ordering. It is thus proposed that clear taenite in the Estherville meteorite contains regions of ordered FeNi phase in a disordered gamma-phase matrix.

Mehta, S.↗
NASA NTRS1980

Reduced order adaptive controller studies

The use of a reduced-order adaptive controller, can arise from a desire to reduce control complexity with a commensurate reduction in controller sensitivity or from necessity in an attempt to use a finite dimensional controller on an infinite dimensional system. An interest in developing adaptive controllers for flexible structures by application of existing lumped-parameter system (LPS) adaptive controller strategies to truncated expansion descriptions of the distributed parameter system (DPS) behavior of flexible structures has led to two qualitative descriptions of the misbehavior of reduced-order adaptive controllers. A summary is provided of these interpretations of the additional difficulties facing reduced-order adaptive controllers, which are bypassed by exact-order adaptive controllers. A test problem, which initializes attempts to quantify the qualitative insights, is also formulated.

Johnson, C. R., Jr.↗
NASA NTRS1983

Experimental determination of the particle motions associated with the low order acoustic modes in enclosures

A procedure for experimentally determining, in terms of the particle motions, the shapes of the low order acoustic modes in enclosures is described. The procedure is based on finding differentiable functions which approximate the shape functions of the low order acoustic modes when these modes are defined in terms of the acoustic pressure. The differentiable approximating functions are formed from polynomials which are fitted by a least squares procedure to experimentally determined values which define the shapes of the low order acoustic modes in terms of the acoustic pressure. These experimentally determined values are found by a conventional technique in which the transfer functions, which relate the acoustic pressures at an array of points in the enclosure to the volume velocity of a fixed point source, are measured. The gradient of the function which approximates the shape of a particular mode in terms of the acoustic pressure is evaluated to give the mode shape in terms of the particle motion. The procedure was tested by using it to experimentally determine the shapes of the low order acoustic modes in a small rectangular enclosure.

Byrne, K. P.↗
NASA NTRS1984

A simple higher-order theory for laminated composite plates

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

Reddy, J. N.↗
NASA NTRS1985

A fourth-order scheme for the unsteady compressible Navier-Stokes equations

A computational scheme is described which is second-order accurate in time and fourth-order accurate in space (2-4). This method is applied to study the stability of compressible boundary layers. The laminar compressible Navier-Stokes equations are solved with a time harmonic inflow superimposed on the steady state solution. This results in spatially unstable modes. It is shown that the second-order methods are inefficient for calculating the growth rates and phases of the unstable modes. In contrast the fourth-order method yields accurate results on relatively coarse meshes.

Bayliss, A.↗