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NASA NTRS1972

Recent satellite measurements of the morphology and dynamics of the plasmasphere.

The characteristic morphology and dynamics of the plasmasphere vary with local time and with geomagnetic conditions. On the nightside the plasmapause position changes predictably with changing magnetic activity. Once established at a specific L-shell value, the steep density gradient on the nightside corotates into the dayside, where filling from the ionosphere takes place. In the duskside bulge region the characteristic density profile inside the plasmapause displays a smooth decrease proportional to 1/R to the fourth power where R is radial distance. Plasmasphere morphology and dynamics can be understood in terms of a time-varying convection electric-field model of the magnetosphere that includes the bulge region as part of the main circulation pattern of the plasmasphere.

Chappell, C. R.↗

NASA NTRS1972

Thermal ions in the magnetosphere.

The distribution and dynamics of thermal (approximately 1 eV) plasma are of fundamental importance for understanding many magnetospheric processes. Above the ionosphere the bulk of the thermal plasma is found in the plasmasphere, which displays varying characteristics in the different LT regions. These different characteristics are reviewed with specific interest placed on the H(+) ion density profiles, since the H(+) ions are the main component of the plasmasphere. Plasmasphere dynamics and morphology can be explained in terms of a time-varying convection model of the magnetosphere which incorporates the bulge region as part of the main flow pattern of the plasmasphere.

Chappell, C. R.↗

NASA NTRS1972

Coronal survey in X-rays of O VII and Ne IX.

Results of a rocket experiment flown on Apr. 29, 1971, in which a survey of the solar corona was carried out with a pair of collimated Bragg spectrometers to study the resonance, intersystem, and forbidden line emission from the helium-like ions O vii (22 A) and Ne ix (13 A). The observed X-ray emission came from the general corona, seven plage regions, and one dynamic feature - the late stage of a small flare. From the intensity of the O vii and Ne ix resonance lines the electron temperature and emission measure of the individual emitting regions are derived on the basis of two models, one in which the region is assumed to be isothermal and another in which the emission measure decreases exponentially with increasing temperature. The latter model, which is the most adequate of the two, yields for the electron temperature of the time-varying feature 2,000,000 to 3,000,000 K, for the other active regions 1,500,000 to 2,500,000 K, and for the general corona 1,300,000 to 1,700,000 K. The Ne ix emitting regions are about 1.5 times as hot as the O vii regions.

Acton, L. W.↗

NASA NTRS1972

Invariance and stability for bounded uncertain systems.

The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.

Peng, T. K. C.↗

NASA NTRS1973

A sequence solution to the Fokker-Planck equation.

In this paper a new approach to nonlinear system analysis based on the Fokker-Planck equation is developed. The development begins as a modification of the parametrix method of partial differential equation theory and provides a sequence solution to the multidimensional time-varying Fokker-Planck equation. This sequence is simplified for the case where only a steady-state solution or a solution for the variance of a particular combination of states is desired. Equations are presented in a form suitable for obtaining numerical results using a digital computer.

Mayfield, W. W.↗

NASA NTRS1973

Transient characteristics of simple systems to modulated random noise.

Discussed are the mean-square response exceedance characteristics of a single-tuned system to amplitude modulated noise. The results bear on the accuracy of spectral estimates of nonstationary data, and subsequently, relate directly to the design, analysis, and testing of structural systems in environments as gusts, earthquakes, and ignition transients. For noise correlated as an exponentially damped cosine, the nonstationary response may exceed its stationary value by a factor in excess of two. A time-varying shaping filter explanation is offered for this behavior. For white noise, such exceedances do not occur.

Barnoski, R. L.↗

NASA NTRS1973

Evaluation of glide paths for landing a VTOL airplane using linear regulator theory.

A method of evaluating certain characteristics of approach paths for VTOL airplanes is presented which is based on the solution of the matrix Riccati equation to obtain an optimal state variable feedback controller. The longitudinal equations of motion of the airplane are linearized about a preselected path and the resulting system of equations is treated as a linear, time-varying regulator. The controller which minimizes a quadratic cost function is applied to the linearized system to determine the airplane's ability to return to the prescribed path given a specified initial error in altitude. The procedure is applied to the XC-142A, tilt-wing, V/STOL airplane, under decelerating approach conditions with a glide path consisting of two segments, the first having a smaller angle of descent than the second.

Reid, G. F.↗

NASA NTRS1973

Time variation in the reaction-zone structure of two-phase spray detonations.

A detailed theoretical analysis of the time-varying detonation structure in a monodisperse spray is presented. The theory identifies experimentally observed reaction-zone overpressures as deriving from blast waves formed therein by the explosive ignition of the spray droplets, and follows in time the motion, change in strength, and interactions of these blast waves with one another, and with the leading shock. The results are compared with experimental data by modeling the motion of a finite-size circular pressure transducer through the theoretical data field in an x-t space.

Pierce, T. H.↗

NASA NTRS1973

Heat flow experiment

The heat flow experiment conducted during the Apollo 17 flight in the Taurus-Littrow area of the moon is discussed. The concept of the experiment is based on the direct measurement of the vertical flow of heat through the regolith. The measurement is made far enough below the surface so that the time-varying heat flow resulting from the very large diurnal variations of the surface temperature is small as compared with the flow from the interior. The equipment used for the experiment is described and illustrated. Graphs are developed to present the results of heat flow and surface temperature measurements.

Langseth, M. G., Jr.↗

NASA NTRS1973

Lunar surface magnetometers

Discussion of the properties of both the stationary and portable magnetometers used in the Apollo program to measure static and dynamic fields on the lunar surface. A stationary magnetometer is described in which the three orthogonal vector components of the magnetic field are measured by three fluxgate sensors which are located at the ends of three orthogonal booms and contain ferromagnetic cores driven to saturation by means of a periodic current. In the Apollo 16 magnetometer special high-stability ring-core sensors were used which provided an output voltage to the analog-to-digital converter which is proportional to the magnetic field. A portable magnetometer is described which consists of a set of three orthogonal fluxgate sensors mounted on top of a tripod connected to an electronics box by a ribbon cable. The above-mentioned stationary magnetometer simultaneously measured the time-varying components of the field which were later subtracted from the portable magnetometer measurements to give the desired resultant steady field values caused by the magnetized crustal material.

Dyal, P.↗

NASA NTRS1973

Mariner 9 photometric observations of Mars from November 1971 through March 1972

The large quantity of Mariner 9 television pictures taken at phase angles ranging up to twice those accessible from earth has been used to describe integrated photometric properties of Mars. Although frame-to-frame variations emphasize the shortcomings of vidicon cameras when used in a photometric mode, statistical trends have yielded data comparable with earth-based observations. Analysis of atmospheric parameters over a period of changing opacity - November 1971 through March 1972 - has provided time-varying optical depths and light-scattering information. Linear function characterization of the Mars reflectance is clearly discrepant at large incidence or emission angles and at phase angles greater than 40 deg.

Thorpe, T. E.↗

NASA NTRS1973

Effects of changing canopy directional reflectance on feature selection

The use of a Monte Carlo model for generating sample directional reflectance data for two simplified target canopies at two different solar positions is reported. Successive iterations through the model permit the calculation of a mean vector and covariance matrix for canopy reflectance for varied sensor view angles. These data may then be used to calculate the divergence between the target distributions for various wavelength combinations and for these view angles. Results of a feature selection analysis indicate that different sets of wavelengths are optimum for target discrimination depending on sensor view angle and that the targets may be more easily discriminated for some scan angles than others. The time-varying behavior of these results is also pointed out.

Smith, J. A.↗

NASA NTRS1973

Dynamic response and stability of a gas-lubricated Rayleigh-step pad

The quasi-static, pressure characteristics of a gas-lubricated thrust bearing with shrouded, Rayleigh-step pads are determined for a time-varying film thickness. The axial response of the thrust bearing to an axial forcing function or an axial rotor disturbance is investigated by treating the gas film as a spring having nonlinear restoring and damping forces. These forces are related to the film thickness by a power relation. The nonlinear equation of motion in the axial mode is solved by the Ritz-Galerkin method as well as the direct, numerical integration. Results of the nonlinear response by both methods are compared with the response based on the linearized equation. Further, the gas-film instability of an infinitely wide Rayleigh step thrust pad is determined by solving the transient Reynolds equation coupled with the equation of the motion of the pad. Results show that the Rayleigh-step geometry is very stable for bearing number A up to 50. The stability threshold is shown to exist only for ultrahigh values of Lambda equal to or greater than 100, where the stability can be achieved by making the mass heavier than the critical mass.

Cheng, C.↗

NASA NTRS1961

Analytical Investigation of an Adaptive Flight-Control System Using a Sinusoidal Test Signal

An analytical study was made of an adaptive flight-control system which measures vehicle response to small-amplitude control-surface deflections produced by a sinusoidal test signal. Changes in the response to this signal are related to environmental changes,, and the system is continuously altered to maintain this response equal to a preselected value. The system is suitable for use in high-performance aircraft and missiles and requires only the addition of a signal generator and a logic circuit consisting of a filter-rectifier network and a comparator-integrator network to a basic command-control system. Thus, it presents a relatively simple approach to the problem. The effects on system performance of variation in flight condition, system-gain level, test-signal frequency, and sensor location are included in the analysis. Longitudinal control of a high-performance research aircraft over flight conditions ranging from landing approach to a Mach number of 5.8 at an altitude of 150,000 feet, and longitudinal control of a four-stage solid-fuel missile including the first bending mode over the atmospheric portion of a launch trajectory constituted the basis for the analytical study. Results of an analog-computer study using time-varying coefficients are presented to compare the control obtained with the adaptive system with-that obtained with a fixed-gain system during the atmospheric portion of a missile launch trajectory. The system has demonstrated an ability to maintain satisfactory vehicle control-system stability over wide ranges of environmental change.

Harris, Jack E.↗

NASA NTRS1961

Analytical Method of Approximating the Motion of a Spinning Vehicle with Variable Mass and Inertia Properties Acted Upon by Several Disturbing Parameters

An analytical method has been developed which approximates the dispersion of a spinning symmetrical body in a vacuum, with time-varying mass and inertia characteristics, under the action of several external disturbances-initial pitching rate, thrust misalignment, and dynamic unbalance. The ratio of the roll inertia to the pitch or yaw inertia is assumed constant. Spin was found to be very effective in reducing the dispersion due to an initial pitch rate or thrust misalignment, but was completely Ineffective in reducing the dispersion of a dynamically unbalanced body.

Buglia, James J.↗

NASA NTRS1961

An Explicit Linear Filtering Solution for the Optimization of Guidance Systems with Statistical Inputs

The determination of optimum filtering characteristics for guidance system design is generally a tedious process which cannot usually be carried out in general terms. In this report a simple explicit solution is given which is applicable to many different types of problems. It is shown to be applicable to problems which involve optimization of constant-coefficient guidance systems and time-varying homing type systems for several stationary and nonstationary inputs. The solution is also applicable to off-design performance, that is, the evaluation of system performance for inputs for which the system was not specifically optimized. The solution is given in generalized form in terms of the minimum theoretical error, the optimum transfer functions, and the optimum transient response. The effects of input signal, contaminating noise, and limitations on the response are included. From the results given, it is possible in an interception problem, for example, to rapidly assess the effects on minimum theoretical error of such factors as target noise and missile acceleration. It is also possible to answer important questions regarding the effect of type of target maneuver on optimum performance.

Stewart, Elwood C.↗

NASA NTRS1962

The Theory of Pulsating Flow in Conical Nozzles

A knowledge of the dynamic characteristics of nozzles and orifices is important in many control and stability analyses of engineering devices. It is usual to assume that the instantaneous flow-rate, for a given set of inlet conditions and outlet pressure, is the same as the nontransient value for the same operating conditions. Recently, in connection with the stability analysis of an externally pressurized thrust bearing, the validity of this assumption was questioned. The analysis presented in this paper was undertaken to provide an answer. The present analysis applies to any fluid, liquid, or gas flowing into a simple conical nozzle. The amplitude and phase of the mass-flux response to a sinusoidally time-varying pressure fluctuation at the nozzle exit are determined. An approximate formula is given for these quantities in terms of the nozzle throat area, the solid angle subtended by the cone, the velocity of the fluid at the nozzle throat, the acoustic velocity at the throat, and the frequency of the pressure fluctuation.

Elrod, H. G., Jr.↗

NASA NTRS1961

Method for Approximating the Vacuum Motions of Spinning Symmetrical Bodies with Nonconstant Spin Rates

The analysis includes non-constant spin rates and inertias and considers the effects of time-varying thrust misalignments, mass unbalance, and jet damping. The method was developed for bodies having small trans verse angular velocities. Results are presented in the form of equations for space-referenced Euler angles, flight-path angles, body-referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. Also, equations for maximum wobble have been derived for certain input conditions. Comparisons with numerical solutions are included for two sample problems.

Martz, C. William↗