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NASA NTRS1974

Research study on stabilization and control: Modern sampled-data control theory. Continuous and discrete describing function analysis of the LST system

The dynamics of the Large Space Telescope (LST) control system were studied in order to arrive at a simplified model for computer simulation without loss of accuracy. The frictional nonlinearity of the Control Moment Gyroscope (CMG) Control Loop was analyzed in a model to obtain data for the following: (1) a continuous describing function for the gimbal friction nonlinearity; (2) a describing function of the CMG nonlinearity using an analytical torque equation; and (3) the discrete describing function and function plots for CMG functional linearity. Preliminary computer simulations are shown for the simplified LST system, first without, and then with analytical torque expressions. Transfer functions of the sampled-data LST system are also described. A final computer simulation is presented which uses elements of the simplified sampled-data LST system with analytical CMG frictional torque expressions.

Kuo, B. C.↗

NASA NTRS1974

The saturation spectrum of parametric instabilities

Recent calculations on the nonlinear saturation spectrum of the parametric decay instability are described. The initial calculations did not use the correct expression for the spontaneous emission term and were aimed at obtaining the distribution of spectral energy in the unstable part of wave vector space. Results of those initial calculations are combined here with the correct expression for the spontaneous emission term to obtain the distribution of spectral energy in the stable part of wave vector space. These latter calculations are believed to be relevant to the interpretation of the so called plasma line spectra obtained in ionospheric heating experiments at Arecibo, Puerto Rico.

Fejer, J. A.↗

NASA NTRS1973

A new criterion for failure of materials by environment-induced cracking

A new criterion has been developed for predicting failure of materials by environment-induced cracking. The criterion has been developed by the use of fracture mechanics concepts and assumes that the relationship between crack-growth rate and stress intensity can be described by three separable regions of behavior as first suggested by Wiederhorn. The analytical form of the criterion relates failure time to the initial crack length and the critical crack length or alternatively, to the initial stress intensity and the fracture toughness for various conditions of stress and the environmental variables. The analytical expression is examined by the use of some experimental data on the hydrogen-induced cracking of Ti-5Al-2.5 Sn, and it is demonstrated that the expression predicts the general expected form of the relationship between the normalized stress intensity parameter and the failure time.

Williams, D. P.↗

NASA NTRS1973

Correction of sunspot intensities for scattered light

Correction of sunspot intensities for scattered light usually involves fitting theoretical curves to observed aureoles (Zwaan, 1965; Staveland, 1970, 1972). In this paper we examine the inaccuracies in the determination of scattered light by this method. Earlier analyses are extended to examine uncertainties due to the choice of the expression for limb darkening. For the spread function, we consider Lorentzians and Gaussians for which analytic expressions for the aureole can be written down. Lorentzians lead to divergence and normalization difficulties, and should not be used in scattered light determinations. Gaussian functions are more suitable.

Mullan, D. J.↗

NASA NTRS1973

Interaction terms in gas-solid two-phase flows

From both experimental data and theoretical results of the two-phase flow, the complete expression of the interaction force between a gas and solid particles at low Reynolds number flow is obtained. The interaction force contains two terms: one is proportional to the difference between the velocities of the gas and the solid particle with a coefficient as a function of volume fraction Z and the other is proportional to the product of the total pressure of the mixture and the gradient of solid volume fraction. The second term is new. When Z tends to 0, the completion expression of interaction force reduces to the well-known Stokes formula.

Pai, S. I.↗

NASA NTRS1973

Multivariable system synthesis with step disturbance rejection

The primary objective of this paper is to present a constructive procedure for the synthesis of linear multivariable systems whose entire internal state and output are corrupted by unknown step disturbances. It is assumed that the dynamical behavior of the system is expressed in any one of three equivalent ways - i.e., the state space representation, the controllable and observable differential operator representation, and the transfer matrix representation. In terms of the transfer matrix representation, T(s), the synthesis procedure is shown to be capable of producing any stable, desired closed loop transfer matrix, Td(s), which can be expressed as the product of T(s) and any proper rational matrix, Tc(s), while simultaneously eliminating the steady-state effect of step disturbances at the output of the system. Furthermore, the synthesis scheme outlined employes only the known, directly measurable input and output signals.

Wolovich, W. A.↗

NASA NTRS1974

A simple formulation of oxygen absorption at centimeter wavelengths

Carefully performed experiments by a number of investigators have supported the Van Vleck line shape theory for oxygen absorption in the lower-frequency wing (0-50 GHz). In view of the frequent need to compute oxygen absorption at centimeter wavelengths and lower a computationally simple four-line absorption model based on the Van Vleck theory is offered. The approximation yields computational accuracy better than 1% over the entire range of atmospheric pressures and temperatures for frequencies less than 30 GHz when it is compared with the Van Vleck 45-line expression. The versatility of the model in adapting to various line-broadening expressions is also shown. Instead of refining the present theories, this communication is mainly intended to propose a more convenient formulation to compute oxygen absorption.

Claassen, J. P.↗

NASA NTRS1973

Acoustic propagation in ducts with varying cross sections

The method of multiple scales is used to derive the equations that describe the spatial and temporal variation of the amplitudes and phases of a wave packet propagating in slowly varying hard-walled or lined ducts. The analysis is carried out for rectangular as well as circular ducts. These equations are statements of the conservation of energy. For large admittance or high-frequency modes, an approximate expression is obtained for the attenuation. This expression shows that all possible acoustic modes are attenuating. The results also show that decreasing the cross sectional area can lead to elimination of some of the acoustic modes.

Nayfeh, A. H.↗

NASA NTRS1973

Effect of the acoustic boundary layer on the wave propagation in ducts

An analysis is presented for the wave propagation in two-dimensional and circular lined ducts taking into account the effects of viscosity in both the mean and the acoustic problems. The method of composite expansions is used to express each acoustic flow quantity as the sum of an inviscid part and a boundary layer part insignificant outside a thin layer next to the wall. The problem is reduced to solving a second-order ordinary differential equation for the pressure perturbation as in the inviscid acoustic case but with a modified specific wall admittance. An analytic expression is presented for the variation of the modified admittance with the wall and flow parameters, such as the acoustic boundary layer thickness, the mean velocity and temperature gradients at the wall, the frequency of oscillation, and the wavelength.

Nayfeh, A. H.↗

NASA NTRS1974

The nondominant poles of a distributed-active low-pass network

In extending Howe's (1969) work on design equations for active distributed RC networks, expressions relating the nondominant pole locations of a distributed-active low-pass network to the dominant pole locations are derived, along with expressions relating the Q of the nondominant poles to the Q of the dominant poles. It is shown that, in general, the effect of the nondominant poles is very small.

Huelsman, L. P.↗

NASA NTRS1973

Constitutive relations associated with the Mott-Smith distribution function

It is shown that the distribution function assumed by Mott-Smith determines a unique relation between heat flux, stress, and fluid velocity given by q = (3/2) tau u - i.e., it provides a constitutive relation for heat flux, and it also determines a simple expression for the ratio of third-order central moments. These expressions allow the equation of transfer for (C sub x) squared to be cast in a form that yields a nonlinear constitutive relation for stress. The results obtained from the Mott-Smith ansatz are compared with the theory of Baganoff and Nathenson (1970) and results from a numerical solution of the Boltzmann equation for shock-wave structure obtained by Hicks et al. (1972).

Nathenson, M.↗

NASA NTRS1974

Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/

The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.

Phillips, D. H.↗

NASA NTRS1974

A method of revitalizing Sampson's theory of the Galilean satellites

A method is developed by which Sampson's theory of motion of Jupiter's Galilean satellites can be revitalized by use of algebraic manipulation software on a digital computer. The technique seeks (1) to remove algebraic errors existing in the current Sampson theory, (2) to introduce some neglected effects due to solar interactions and the 3-7 commensurability between the outer two satellites, (3) to allow for nonzero amplitude and phase of the libration, (4) to allow future revision of the arbitrary constants of integration, (5) to express the final results as analytic functions of variations in the numerous arbitrary constants of integration and arbitrary parameters, and (6) to provide analytic partial derivatives by means of which the numerical values of coefficients in the expressions for the coordinates can be adjusted. The level of precision desired is one arc second (Jovicentric) for the coordinates (2, 3.3, 5.2, and 9.1 km, respectively, for satellites I through IV).

Lieske, J. H.↗

NASA NTRS1974

Lunar perturbations of artificial satellites of the earth

The disturbing function for the lunar perturbations of an artificial satellite are derived, using ecliptic elements for the moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the earth. The results can then be applied to numerical integration by using coordinates of the moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the moon's motion represented by a precessing and rotating elliptical orbit.

Giacaglia, G. E. O.↗

NASA NTRS1974

Phase-bunching and other non-linear processes occurring in gyroresonant wave-particle interactions

Consideration of the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. Simple expressions are derived which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle, and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region.

Gendrin, R.↗

NASA NTRS1974

The recovery of polarized apparent temperature distributions of flat scenes from antenna temperature measurements

The reception theory for quasi-monochromatic partially polarized emissions is employed to describe the antenna temperature when observing a flat scene from within or above an absorbing/emitting atmosphere. When the polarization aspects of the antenna and scene are carefully observed, the resulting integral expression for the antenna temperature differs significantly from that reported for polarization invariant temperature distributions. It is observed that the antenna couples to both emitted surface polarizations, and the phase character of the antenna introduces a term involving the product of the polarized and cross-polarized antenna patterns. A matrix approximation of the integral expression is suggested and developed as a means for inverting polarized antenna temperature observations for the underlying partially polarized apparent temperature distributions.

Claassen, J. P.↗

NASA NTRS1974

Diffraction theory techniques applied to aperture antennas on finite circular and square ground planes

Expressions which represent the elevation-plane patterns of a large TEM mode coax aperture and a TM-01 mode circular aperture on finite circular and square ground planes have been derived using geometrical theory of diffraction; design curves for the coax case are presented. The expressions for the field pattern were obtained by superposing the infinite ground plane solutions, the first-order diffracted field solutions, and the axial caustic solutions in their respective regions of validity. The pattern analyses for the coax and circular apertures are verified experimentally.

Cockrell, C. R.↗

NASA NTRS1974

Absorption of infrared radiation by electrons in the field of a neutral hydrogen atom

An analytical expression for the absorption coefficient is developed from a relationship between the cross-section for inverse bremsstrahlung absorption and the cross-section for electron-atom momentum transfer; it is accurate for those photon frequencies v and temperatures such that hv/kT is small. The determination of the absorption of infrared radiation by free-free transitions of the negative hydrogen ion has been extended to higher temperatures. A simple analytical expression for the absorption coefficient has been derived.

Stallcop, J. R.↗