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NASA NTRSDate not supplied

Linearized Frequency-Domain Gust Analysis and Adjoint-Based Sensitivities

Gust analysis is added to a linearized frequency-domain method in FUN3D, a NASA computational fluid dynamics solver. The method linearizes about a nonlinear static equilibrium condition and is therefore appropriate for problems with small perturbations such as transonic stochastic gust analysis. In addition to the gust analysis, adjoint-based sensitivities of stochastic gust constraints are implemented for multidisciplinary design optimization. The linearized frequency-domain gust model and adjoint-based sensitivities are described and verified. The method is applied to an optimization for mass minimization of the AGARD 445.6 wing subject to a stochastic gust constraint limiting the displacement of the wing tip.

Aeroelasticity↗
NASA NTRS1996

The General Necessary Condition for the Validity of Dirac's Transition Perturbation Theory

For the first time, from the natural requirements for the successive approximation the general necessary condition of validity of the Dirac's method is explicitly established. It is proved that the conception of 'the transition probability per unit time' is not valid. The 'super-platinium rules' for calculating the transition probability are derived for the arbitrarily strong time-independent perturbation case.

Quang, Nguyen Vinh↗
NASA NTRS1971

Lunar gravity derived from long-period satellite motion, a proposed method

A method was devised to determine the spherical harmonic coefficients of the lunar gravity field. The method consists of a two-step data reduction and estimation process. Pseudo-Doppler data were generated simulating two different lunar orbits. The analysis included the perturbing effects of the L1 lunar gravity field, the earth, the sun, and solar radiation pressure. Orbit determinations were performed on these data and long-period orbital elements were obtained. The Kepler element rates from these solutions were used to recover L1 lunar gravity coefficients. Overall results of the experiment show that lunar gravity coefficients can be accurately determined and that the method is dynamically consistent with long-period perturbation theory.

Ferrari, A. J.↗
NASA NTRS1979

Analytical method for the effects of the asteroid belt on planetary orbits

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant-density asteroid belt. The derivations include extensions and adaptations of Plakhov's (1968) analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness, and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus. The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained by using the analytic expressions and those obtained by numerical integration are discussed. The effects of the asteroid belt on earth-based ranging to Mars are also demonstrated.

Mayo, A. P.↗
NASA NTRS1985

Hydrodynamic stability problem formulated by numerical solutions of the Navier-Stokes equations

The problem of hydrodynamic stability and the transition from laminar to turbulent flows are reformulated by seeking numerical solutions of the full, unapproximated Navier-Stokes equations. This method differs significantly from the well known Orr-Sommerfeld equation approach. The oncoming laminar flow is disturbed by forced, time dependent perturbations. The magnitudes of these perturbations are arbitrary. Then, the ensuing spatial and temporal development of the imposed perturbations on the basic flow is calculated by direct numerical solutions of the time dependent Navier-Stokes equations. One of the main advantages of this method is its ability to simulate nonlinear processes. As a specific application of this technique to SSME (Space Shuttle Main Engine) flow configurations, computer programs have been written for the two dimensional flow over a backward facing step. This numerical code will be tested for operational use as part of a continued research collaboration effort with the NASA/MSFC counterparts.

Hyun, J. M.↗
NASA NTRS1973

Magnetic testing

Magnetic techniques are described for the nondestructive evaluation of defects in materials. The physical principles, and the magnetic-particle method are discussed along with magnetic-hysteresis measurements and electric current perturbations.

Pasley, R. L.↗
NASA NTRS1974

Viscous-fluid reaction to a torsionally oscillating spheroid Linearized steady-state weak-separation solution

For both the linearized prolate and oblate problems, perturbation series for all orders of eccentricity are obtained. The 'weak separation' method of solving partial-differential-equation boundary-value problems assumes that each linearly independent solution is a sum of products of single-variable functions. The method is applied to a hierarchy of partial differential equations. The weak-separation solutions are constructed by generalizing only the Bessel functions of the homogeneous solution.

Tompkins, D. R., Jr.↗
NASA NTRS1974

Secondary vorticity in axial compressor blade rows

A theoretical investigation of secondary flow in compressor blade rows is presented. Formulas for calculating secondary flows in annular cascade blade passages are derived. The influence of the relative rotation vector on secondary velocity perturbations, using recent developments in shear-flow theory, is examined. A method of calculating the flow through successive blade rows is given and a comparison is made with experimental results.

Dixon, S. L.↗
NASA NTRS1976

A limiting analysis for edge effects in angle-ply laminates

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

Hsu, P. W.↗
NASA NTRS1984

Orientation and shape-control of an orbiting flexible beam under the influence of solar radiation pressure

In this paper, the uncontrolled and controlled dynamics of a thin flexible beam in orbit and in the presence of solar radiation disturbance are analyzed. A beam nominally oriented along (i) the local horizontal and carrying a gimballed rigid dumbbell for gravity stabilization, and (ii) a beam nominally oriented along the local vertical are considered. The uncontrolled dynamics of the beam in the presence of the solar radiation pressure disturbance shows the excitation of the rigid pitch mode. The control laws previously designed for the case where the environmental effects were neglected, are found to be inadequate to control the shape and orientation of very flexible beams that are exposed to solar radiation disturbances. The control laws and the gain parameters are reevaluated for both cases of nominal beam orientations; this results, in general, in increased robustness of the closed-loop system. Methods of obtaining a robust control system in the presence of environmental perturbations are discussed.

Krishna, R.↗
NASA NTRS1986

Theoretical study of the X 2Pi and A 2Sigma(+) states of CuO and CuS

Theoretical spectroscopic constants and dipole moments are determined for the X 2Pi and A 2Sigma(+) states of CuO and CuS, using extended Gaussian basis sets and incorporating correlation using both configuration interaction (CI) and coupled pair (CPF) methods. Relativistic corrections (Darwin plus mass velocity), included using first-order perturbation theory, are found to be relatively small. At the CPF level, significant configuration mixing with the 3d(9)4s(1) occupation occurs for both states, resulting in some bond shortening and a significant increase in the dissociation energy. The best spectroscopic parameters are in excellent agreement with experiment for both CuO and CuS. In analogy with CuO, CuS is predicted to have a yet unobserved 2Sigma(+) state near 10,000 per cm.

Langhoff, S. R.↗
NASA NTRS1986

Theoretical study of the low-lying electronic states of ZnO and ZnS

Theoretical spectroscopic constants and dipole moments are determined for the 1 Sigma(+), 1,3 Pi, and 3 Sigma(+) states of ZnO and ZnS, using extended Gaussian basis sets and incorporating correlation using both configuration-interaction and coupled pair (CPF) methods. Relativistic corrections (Darwin plus mass velocity), included using first-order perturbation theory, are relatively small. At the CPF level, both ZnO and ZnS have 1 Sigma(+) ground states, with the 3 Pi state lying 209 and 2075/cm higher, respectively. The 3 Sigma(+) state lies about 1.5 eV higher in ZnO and 2.1 eV higher in ZnS. The 1,3 Pi states are relatively close together since the exchange splitting is small with the sigma electron localized on Zn and the pi electron on oxygen (or sulfur).

Bauschlicher, C. W., Jr.↗
NASA NTRS1991

Jacobi-Integral Method For Two-Body Problem

Jacobi-integral method enables efficient, accurate computation of trajectory of natural satellite or spacecraft perturbed by component of gravitational potential depending explicitly on both position and time. Instead of total energy, Jacobi integral, which is energylike constant of motion in this case, embedded in Newtonian differential equations of motion. Trajectories computed in fewer steps. With modifications, applicable to such terrestrial problems as motions of rotors and of beams of electrically charged particles in changing electrical and magnetic fields.

Bond, Victor R.↗