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NASA NTRS1986

Stress on the surface of Venus: Analysis of data provided by Venera-15 and Venera-16

There are no large-scale sedimentation and erosion processes on Venus, therefore the observed deformation must be formed on the surface or close to it, and in the ellipsoids of stresses one of the main axes must be perpendicular to the surface. According to the deformation visible on photography from Venera-15, 16, the orientations of the ellipsoids of stresses are established in the different sections of the Montes Maxwell and the northern parquet. A geological model is established, according to which the Montes Maxwell is an arched vault and the region to the south a conjugate bend, separated by a shift zone.

Ronka, L. B.↗

NASA NTRS1987

Shapes of small satellites

The accurate measurement of limb coordinates on small satellite is the major technique for evaluating their sizes and shapes in the absence of good stereoscopic image coverage. The shapes of satellites may be clues to their internal structure if they are relaxed into ellipsoids. The distinction between irregular and ellipsoidal satellites can now be made quantitatively with the availability of many accurate limb profiles of satellites. The residuals from these fit ellipses provide a convenient and quantitative measure of the topography on the satellites. Departures from gravitational (and tidal) equipotentials would be greater, but on the average this is a good measure of the relaxed or nonrelaxed nature of the shape of the objects. The limb topography is also related to specific forms on the objects, and a systematic survey of these forms on small and larger objects is underway.

Thomas, P.↗

NASA NTRS1986

Breakdown characteristics of an isolated conducting object in a uniform electric field

A laboratory experiment was conducted to determine the physical processes involved in the electrical breakdown of a particular spark gap arrangement. The gap consists of an isolated conducting ellipsoid located midway between two large flat electrodes. Gradual increase of the applied electric field, E, in the gap produces corona on the ellipsoid tips followed by flashover in a leader-arc sequence. The leader phase consists of the abrupt formation of ionized channels which partially bridge the gap and then decay prior to the arc. Measurements of dE/dt and of current were made, and photographs were taken with an image converter. Experimental parameters are listed.

Grothaus, M. G.↗

NASA NTRS1984

Simulation and analysis of airborne antenna radiation patterns

The objective is to develop an accurate and efficient analytic solution for predicting high frequency radiation patterns of fuselage-mounted airborne antennas. This is an analytic study of airborne antenna patterns using the Uniform Geometrical Theory of Diffraction (UTD). The aircraft is modeled in its most basic form so that the solution is applicable to general-type aircraft. The fuselage is modeled as a perfectly conducting composite ellipsoid; whereas, the wings, stabilizers, nose, fuel tanks, and engines, are simulated as perfectly conducting flat plates that can be attached to the fuselage and/or to each other. The composite-ellipsoid fuselage model is necessary to successfully simulate the wide variety of real world fuselage shapes. Since the antenna is mounted on the fuselage, it has a dominant effect on the resulting radiation pattern so it must be simulated accurately, especially near the antenna. Various radiation patterns are calculated for commercial, private, and military aircraft, and the Space Shuttle Orbiter. The application of this solution to numerous practical airborne antenna problems illustrates its versatility and design capability. In most cases, the solution accuracy is verified by the comparisons between the calculated and measured data.

Kim, J. J.↗

NASA NTRS1988

The shape and internal structure of Mimas

The present effort to determine the shape of Mimas proceeds on the basis of limb profiles from six Voyager images; the fitting of ellipses to the limbs indicates that the shape is a triaxial ellipsoid. The satellite mass determined by Kozai (1957), in conjunction with a second-order theory for the ellipsoidal figure of equilibrium, leads to a satellite mean radius determination of 198.8 + or - 0.6 km, and a mean density of 1.137 + or - 0.018 g/cu cm. It is suggested that Mimas is probably differentiated, with a rocky core and a water-ice crust; alternatively, Mimas has a cosmic composition of ice and rock and is undifferentiated.

Dermott, Stanley F.↗

NASA NTRS1988

Radii, shapes, and topography of the satellites of Uranus from limb coordinates

The present use of limb coordinates to ascertain radii, shape and local topographic characteristics for the five large Uranian satellites directly measured satellite ellipsoidal shapes, determining radii with subpixel accuracy. While Umbriel, Titania, and Oberon are spherical, Miranda and Ariel are noted to be ellipsoids whose equatorial bulges agree with previously determined mean densities. Miranda's topography exhibits substantial deformation of cratered terrain and the younger coronae, as well as uplift and complex faulting at coronae margins.

Thomas, P. C.↗

NASA NTRS1988

Effective permittivity of dielectric mixtures

General mixing formulas are derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasi-static analysis, assuming the diameter of the inclusion particles to be much smaller than one wavelength. The results are applicable to general multiphase mixtures, and the scattering ellipsoids of the different phases can have different sizes and arbitrary ellipticity distribution and axis orientation, i.e., the mixture may be isotropic or anisotropic. The resulting mixing formula is nonlinear and is suitable for iterative solutions. The formula contains a quantity called the apparent permittivity, and with different choices of this quantity, the result leads to the generalized Lorentz-Lorenz formula, the generalized Polder-van Santen formula, and the generalized coherent potential-quasicrystalline approximation formula. The results are applied to calculating the complex effective permittivity of dry and wet snow, and sea ice.

Sihvola, Ari H.↗

NASA NTRS1988

Origin of petrofabrics and magnetic anisotropy in ordinary chondrites

Three-dimensional finite strain and magnetic susceptibility anisotropy have been determined for 15 ordinary chondrites. The axes of strain and magnetic ellipsoids roughly correlate in both magnitude and orientation. The shapes of these ellipsoids are generally oblate spheroids that define a dominant foliation and a weak lineation. These characteristics suggest deformation involving uniaxial compaction. The degree of uniaxial deformation correlates with intensity of shock, as indicated by optical, TEM and chemical criteria. These data, plus the lack of a relationship between foliation and metamorphic history, indicate that dynamic processes, i.e., impacts, produced planar deformation fabrics in chondrites.

Sneyd, Deana S.↗

NASA NTRS1988

Speckle interferometry of asteroids

By studying the image two-dimensional power spectra or autocorrelations projected by an asteroid as it rotates, it is possible to locate its rotational pole and derive its three axes dimensions through speckle interferometry under certain assumptions of uniform, geometric scattering, and triaxial ellipsoid shape. However, in cases where images can be reconstructed, the need for making the assumptions is obviated. Furthermore, the ultimate goal for speckle interferometry of image reconstruction will lead to mapping albedo features (if they exist) as impact areas or geological units. The first glimpses of the surface of an asteroid were obtained from images of 4 Vesta reconstructed from speckle interferometric observations. These images reveal that Vesta is quite Moon-like in having large hemispheric-scale albedo features. All of its lightcurves can be produced from a simple model developed from the images. Although undoubtedly more intricate than the model, Vesta's lightcurves can be matched by a model with three dark and four bright spots. The dark areas so dominate one hemisphere that a lightcurve minimum occurs when the maximum cross-section area is visible. The triaxial ellipsoid shape derived for Vesta is not consistent with the notion that the asteroid has an equilibrium shape in spite of its having apparently been differentiated.

Drummond, Jack↗

NASA NTRS1988

Photometric geodesy of main-belt asteroids. II - Analysis of lightcurves for poles, periods, and shapes

The assumption that asteroids can be modeled as smooth, featureless, triaxial ellipsoids that rotate about their shortest axes is presently used to study all but one of the 26 asteroids treated in the Weidenschilling et al. (1987) 'photometric geodesy' program. Rotational poles derived from three independent methods are used to determine each asteroid's sidereal period and triaxial ellipsoid axial ratios, together with their associated photometric parameters. The asteroids appear to have rotational poles that do not lie along their orbital planes.

Drummond, J. D.↗

NASA NTRS1989

Dual redundant arm configuration optimization with task-oriented dual arm manipulability

It is shown that the required motion and force trajectories of a given task can be abstracted by a series of desired manipulability ellipsoids, and that a task-oriented dual-arm manipulability measure (TODAMM) can be mathematically defined by quantifying how the manipulability of one arm affects the other and measuring the geometrical closeness between the desired and the actual manipulability ellipsoids. TODAMM can be used in the optimization of dual-arm joint configurations. The task-oriented manipulability measure developed can also be used in the joint configuration optimization of a single arm, providing efficient joint configurations in terms of joint motions and joint torques for the required Cartesian motions and static forces. The dual-arm joint configuration optimization based on TODAMM can be applied to a variety of tasks which require dual-arm cooperation.

Lee, Sukhan↗

NASA NTRS1988

Task-oriented dual-arm manipulability and its application to configuration optimization

A measure of static manipulability is derived for a dual-redundant-arm (DRA) system engaged in cooperative task execution. Considering the kinematic interaction between the two cooperating arms, the dual-arm (DA) manipulability is defined as the intersection between the two manipulability ellipsoids from individual arms. A task-oriented DA manipulability measure is defined as the measure of geometrical similarity between the desired and the actual DA manipulability ellipsoids at the selected task points. Mathematical formulas are developed to define task-oriented DRA static manipulability, and their application to the optimization of DRA joint and grasp configurations is demonstrated.

Lee, Sukhan↗

NASA NTRS1989

Problems in determining the surface density of the Galactic disk

A new method is presented for determining the local surface density of the Galactic disk from distance and velocity measurements of stars toward the Galactic poles. The procedure is fully three-dimensional, approximating the Galactic potential by a potential of Staeckel form and using the analytic third integral to treat the tilt and the change of shape of the velocity ellipsoid consistently. Applying the procedure to artificial data superficially resembling the K dwarf sample of Kuijken and Gilmore (1988, 1989), it is shown that the current best estimates of local disk surface density are uncertain by at least 30 percent. Of this, about 25 percent is due to the size of the velocity sample, about 15 percent comes from uncertainties in the rotation curve and the solar galactocentric distance, and about 10 percent from ignorance of the shape of the velocity distribution above z = 1 kpc, the errors adding in quadrature. Increasing the sample size by a factor of 3 will reduce the error to 20 percent. To achieve 10 percent accuracy, observations will be needed along other lines of sight to constrain the shape of the velocity ellipsoid.

Statler, Thomas S.↗

NASA NTRS1989

Coordination of two redundant robots

A solution is presented for the optimal force distributions of two redundant coordinating robots. Two robots whose end-effectors firmly grasp a common inertial load form a closed-chain structure, and thus the robots must observe a set of constraint conditions on (1) the end-effector positions, orientations, linear and angular velocities and (2) the forces and torques inserted onto the end-effectors by the load. To achieve the maximum load capability, the optimal force distribution under the known posture is developed. If the robots are redundant, joint solutions may be obtained if some optimization criterion such as manipulability is imposed. The singularity, manipulability, and force ellipsoids are investigated in terms of the two manipulator Jacobian matrices. The manipulability is shown to correspond to the cascade structure, while the force ellipsoid corresponds to the parallel structure in terms of the manipulator Jacobian matrices.

Tao, Jian M.↗

NASA NTRS1989

Infrared backscattering

All particles in the atmosphere are not spherical. Moreover, the scattering properties of randomly oriented nonspherical particles are not equivalent to those of spherical particles no matter how the term equivalent is defined. This is especially true for scattering in the backward direction and at the infrared wavelengths at which some atmospheric particles have strong absorption bands. Thus calculations based on Mie theory of infrared backscattering by dry or insoluble atmospheric particles are suspect. To support this assertion, it was noted that peaks in laboratory-measured infrared backscattering spectra show appreciable shifts compared with those calculated using Mie theory. One example is ammonium sulfate. Some success was had in modeling backscattering spectra of ammonium sulfate particles using a simple statistical theory called the continuous distribution of ellipsoids (CDE) theory. In this theory, the scattering properties of an ensemble are calculated. Recently a modified version of this theory was applied to measured spectra of scattering by kaolin particles. The particles were platelike, so the probability distribution of ellipsoidal shapes was chosen to reflect this. As with ammonium sulfate, the wavelength of measured peak backscattering is shifted longward of that predicted by Mie theory.

Bohren, Craig F.↗

NASA NTRS1990

Variable magnification variable dispersion glancing incidence imaging x ray spectroscopic telescope

A variable magnification variable dispersion glancing incidence x ray spectroscopic telescope capable of multiple high spatial revolution imaging at precise spectral lines of solar and stellar x ray and extreme ultraviolet radiation sources includes a primary optical system which focuses the incoming radiation to a primary focus. Two or more rotatable carriers each providing a different magnification are positioned behind the primary focus at an inclination to the optical axis, each carrier carrying a series of ellipsoidal diffraction grating mirrors each having a concave surface on which the gratings are ruled and coated with a multilayer coating to reflect by diffraction a different desired wavelength. The diffraction grating mirrors of both carriers are segments of ellipsoids having a common first focus coincident with the primary focus. A contoured detector such as an x ray sensitive photographic film is positioned at the second respective focus of each diffraction grating so that each grating may reflect the image at the first focus to the detector at the second focus. The carriers are selectively rotated to position a selected mirror for receiving radiation from the primary optical system, and at least the first carrier may be withdrawn from the path of the radiation to permit a selected grating on the second carrier to receive radiation.

Hoover, Richard↗

NASA NTRS1990

Task-dependent color discrimination

When color video displays are used in time-critical applications (e.g., head-up displays, video control panels), the observer must discriminate among briefly presented targets seen within a complex spatial scene. Color-discrimination threshold are compared by using two tasks. In one task the observer makes color matches between two halves of a continuously displayed bipartite field. In a second task the observer detects a color target in a set of briefly presented objects. The data from both tasks are well summarized by ellipsoidal isosensitivity contours. The fitted ellipsoids differ both in their size, which indicates an absolute sensitivity difference, and orientation, which indicates a relative sensitivity difference.

Poirson, Allen B.↗

NASA NTRS1990

Surface characterizations of color threshold

The paper evaluates how well three different parametric shapes, ellipsoids, rectangles, and parallelograms, serve as models of three-dimentional detection contours. The constraints of the procedures for deriving the best-fitting shapes on inferences about the theoretical visual detection mechanisms are described. Results of two statistical tests show that only the parallelogram fits the data with more precision than the variance in repeated threshold measurements, and thus provides a slightly better fit than the other two shapes. Nevertheless it does not serve as a better guide than the ellipsoidal model for interpolating from the measurements to thresholds in novel color directions.

Poirson, Allen B.↗