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At least 163 records · Page 9

Static shape forming for an electrostatically controlled membrane mirror

A design concept is described permitting the static construction of a flexible membrane reflector for use in a radiometer spacecraft. The scheme utilizes electrostatic forces to actively shape the membrane toward a specified reflector surface with a required degree of precision. The formulations of the required electrostatic attractive forces, and stress and strain distributed in the membrane are presented in this paper in terms of curvilinear coordinates. An example is given to illustrate a variety of spherical membrane characteristics associated with different boundary conditions.

Juang, J. N.

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.

Examination of Multiple Lithologies Within the Primitive Ordinary Chondrite NWA 5717

Northwest Africa 5717 is a primitive (subtype 3.05) ungrouped ordinary chondrite which contains two apparently distinct lithologies. In large cut meteorite slabs, the darker of these, lithology A, looks to host the second, much lighter in color, lithology B (upper left, Fig. 1). The nature of the boundary between the two is uncertain, ranging from abrupt to gradational and not always following particle boundaries. The distinction between the lithologies, beyond the obvious color differences, has been supported by a discrepancy in oxygen isotopes and an incongruity in the magnesium contents of chondrule olivine. Here, quantitative textural analysis and mineralogical methods have been used to investigate the two apparent lithologies within NWA 5717. Olivine grains contained in a thin section from NWA 7402, thought to be paired to 5717, were also measured to re-examine the distinct compositional range among the light and dark areas. Procedure: Particles from a high-resolution mosaic image of a roughly 13x15cm slice of NWA 5717 were traced in Adobe Photoshop. Due to the large size of the sample, visually representative regions of each lithology were chosen to be analyzed. The resulting layers of digitized particles were imported into ImageJ, which was used to measure their area, along with the axes, the angle from horizontal, and the centroid coordinates of ellipses fitted to each particle following the approach. Resulting 2D pixel areas were converted to spherical diameters employing the unfolding algorithm, which outputs a 3D particle size distribution based on digitized 2D size frequency data. Spatstat was used to create kernel density plots of the centroid coordinates for each region. X-ray compositional maps, microprobe analyses, and Mossbauer spectroscopy was conducted on a thin section of NWA 7402, tentatively paired to NWA 5717.

Cato, M. J.

Magnetospheric and ionospheric signals in magnetic observatory monthly means: Electrical conductivity of the deep mantle

First differences of magnetic observatory monthly means for 1963-1982 were analyzed using techniques of spherical harmonics analysis and power spectral analysis. The external source signal is shown to be primarily zonal in geomagnetic coordinates. Prominent peaks are present in the power spectrum at frequencies of 1.0 cycle/yr and 2.0 cycles/yr. The annual signal is largest on the degree 2 external zonal spherical harmonic, while the semiannual signal is largest on the degree 1 and degree 3 external zonal spherical harmonics. The presence of the semiannual signal on odd-degree spherical harmonics and of the annual signal on even-degree spherical harmonics was predicted from symmetry considerations and the annual cycle of solar inclination. These signals are all modulated by the sunspot frequency and its harmonics. The degree 1 term is believed to be due mainly to magnetopause and ring currents while the degree 2 and degree 3 terms are believed to be due mainly to ionospheric currents. The degree 1 external zonal harmonic has a continuous spectrum in addition to the semiannual spectral peak. A corresponding degree 1 internal term is due to electromagnetic induction. The degree 1 continuous spectrum is useful for study of the electrical conductivity of the deep mantle. A global geomagnetic response function consistent with a mantle conductivity of about 10 S/m at the core-mantle boundary has been derived.

Mcleod, Malcolm G.

Gravitational analog of the canonical acoustic black hole in Einstein-scalar-Gauss-Bonnet theory

In this work, in the context of modified gravity, a curved spacetime analogous to the 'canonical acoustic black hole (CABH)' is constructed. The source is a self-interacting scalar field which is non-minimally coupled to gravity through the Gauss–Bonnet invariant. The scalar-Gauss–Bonnet coupling function is characterized by three positive parameters: σ with units of (length), μ with units of (length)4, and a dimensionless parameter s, thus defining a three-parameter model for which the line element of CABH is a solution. The spacetime is equipped with spherical and static symmetry and has a single horizon determined in Schwarzschild coordinates by the region r = μ^(1/4). The solution admits a photon sphere at r = (3μ)^(1/4), and it is shown that in the region (3μ)^(1/4) ⩽ r < ∞ the scalar field satisfies the null, weak, and strong energy conditions. Nonetheless, the model with s = 1 has major physical relevance since for this case the scalar field is well defined in the entire region r ⩾ μ^(1/4), while for s ≠ 1 the scalar field blows up on the horizon.

Pedro Cañate

Improved gravity field and station-coordinate estimates from laser tracking data

Knowledge of the long-wavelength features of the geopotential and the geocentric coordinates of satellite-tracking stations is significantly improved by the use of precision satellite tracking with lasers. Tracking data on nine satellites are combined with terrestrial gravimetry to obtain a spherical-harmonics representation of the geopotential complete through degree and order 24. Laser tracking data are used to determine the coordinates of tracking stations. This coordinate system is referred to an inertial reference frame by use of camera observations and observations of deep-space probes. Resulting geodetic parameters provide better satellite ephemerides and a reference for analyzing satellite-to-sea-surface altimetry.

Gaposchkin, E. M.

Variations of three-dimensional anisotropy of cosmic rays during Forbush decreases.

Variations of three-dimensional anisotropy of cosmic rays during Forbush decreases are examined by a spherical harmonic method and by constructing successive isointensity contour maps in the solar ecliptic coordinate system. The east-west and north-south anisotropies are studied statistically and for several individual events; the data are based on cosmic ray records from about 24 stations for the 3-year period from 1966 to 1968. For the individual events, the high anisotropies of about 4% are examined in terms of the convective, diffusive and density gradient components of the differential streaming as well as the interplanetary magnetic field and solar wind. In each case, vector gradients are derived that lead to the observed anisotropies, and the magnitude of these gradients is typically 10-20 times that of the quiet time interplanetary gradient.

Yoshida, S.

The second-order gravitational red shift

The direct measurement of the nonlinear term of the gravitational field equations by using very stable clocks is discussed along with measuring the perhelion advance of a planet or satellite. These are considered measurements of the second-order gravitational red shift. The exact expression for the frequency shift of light in a gravitational field is derived. Other topics discussed include: The Doppler-cancelling technique; the second-order red shift in a spherically symmetric gravitational field; finite signal transit time; and the reality and interpretation of coordinates in the second-order red shift experiment.

Jaffe, J.

Solution of Aeroacoustic Problems by a Nonlinear, Hybrid Method

Category 1, problem 3 (scattering of sound by a sphere) and category 2, problem 1 (spherical source in a cylindrical duct subject to uniform flow) are solved in generalized coordinates using the nonlinear Euler equations together with nonreflecting boundary conditions. A temporally and spatially fourth-order accurate finite-difference, Runge-Kutta time-marching technique is employed for the near-field calculations and a Kirchhoff method is employed for the prediction of far-field sound. Computations are all performed on parallel processors using the data-parallel paradigm.

Oezyoeruek, Yusuf

Orbital Debris Shape Effect Investigations for Mitigating Risk

NASA’s Orbital Debris Program Office (ODPO) and Hypervelocity Impact Technology (HVIT) team have coordinated to better understand the risks to upper stages and spacecraft from non-spherical orbital debris. It is well understood that fragmentation (collision or explosion) events in orbit produce fragments of various materials, sizes, and shapes. To further characterize these parameters, the ODPO is developing the next-generation Orbital Debris Engineering Model (ORDEM) version 4.0 to include orbital debris shape distributions. Ground-based assets, such as radar and optical sensors, can provide size estimates and some insight into material based on radar return or optical filter photometry/spectroscopy, respectively. Characterizing an object’s shape requires more laboratory analyses to infer how shape affects these measurements. More importantly, in addition to size and material/density, the shape of fragments in orbit will alter the ballistic limit equations used in orbital debris risk assessments with NASA’s Bumper Code. The ODPO plans to release ORDEM 4.0 in the coming years. Performing ground-based laboratory impact tests on high-fidelity spacecraft mockups provides the means to directly measure size, mass, material/density, and shape of fragments, all key parameters needed to characterize real-world break up events. The DebriSat test, the results of which are provided, showcases the details of this type of experiment. The goal of this collaborative research between the ODPO and the HVIT team is to include a shape parameter in the environmental and breakup models used to assess risk for various space structures. This paper examines ground-based laboratory impact tests and the associated fragment shape categories. Provided these defined shapes, the approach is simplified by assuming a right circular cylinder (RCC) approximation with varying length-to-diameter ratios. Highlights of impact tests conducted by the HVIT team using non-spherical projectiles based on the RCC approximation are presented. Hydrocode simulations have also been performed to expand on the complexity of variations with non-spherical projectiles. Lastly, ray-tracing simulations of various RCCs of known material are provided to support the ongoing research on optical reflectance distributions with known shapes and to highlight how this may modify the current optical size estimation model. The status and plan forward are outlined for NASA's orbital debris shape effect investigation using a multidisciplinary approach by the ODPO and the HVIT team.

Heather Cowardin

Orbital Debris Shape Effect Investigations for Mitigating Risk

NASA’s Orbital Debris Program Office (ODPO) and Hypervelocity Impact Technology (HVIT) team have coordinated to better understand the risks to upper stages and spacecraft from non-spherical orbital debris. It is well understood that fragmentation (collision or explosion) events in orbit produce fragments of various materials, sizes, and shapes. To further characterize these parameters, the ODPO is developing the next-generation Orbital Debris Engineering Model (ORDEM) version 4.0 to include orbital debris shape distributions. Ground-based assets, such as radar and optical sensors, can provide size estimates and some insight into material based on radar return or optical filter photometry/spectroscopy, respectively. Characterizing an object’s shape requires more laboratory analyses to infer how shape affects these measurements. More importantly, in addition to size and material/density, the shape of fragments in orbit will alter the ballistic limit equations used in orbital debris risk assessments with NASA’s Bumper Code. The ODPO plans to release ORDEM 4.0 in the coming years. Performing ground-based laboratory impact tests on high-fidelity spacecraft mockups provides the means to directly measure size, mass, material/density, and shape of fragments, all key parameters needed to characterize real-world break up events. The DebriSat test, the results of which are provided, showcases the details of this type of experiment. The goal of this collaborative research between the ODPO and the HVIT team is to include a shape parameter in the environmental and breakup models used to assess risk for various space structures. This paper examines ground-based laboratory impact tests and the associated fragment shape categories. Provided these defined shapes, the approach is simplified by assuming a right circular cylinder (RCC) approximation with varying length-to-diameter ratios. Highlights of impact tests conducted by the HVIT team using non-spherical projectiles based on the RCC approximation are presented. Hydrocode simulations have also been performed to expand on the complexity of variations with non-spherical projectiles. Lastly, ray-tracing simulations of various RCCs of known material are provided to support the ongoing research on optical reflectance distributions with known shapes and to highlight how this may modify the current optical size estimation model. The status and plan forward are outlined for NASA's orbital debris shape effect investigation using a multidisciplinary approach by the ODPO and the HVIT team.

Heather Cowardin

Map Projection Induced Variations in Locations of Polygon Geofence Edges

This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.

Neeley, Paula

Measured pressure distributions, aerodynamic coefficients and shock shapes on blunt bodies at incidence in hypersonic air and CF4

Pressure distributions, aerodynamic coefficients, and shock shapes were measured on blunt bodies of revolution in Mach 6 CF4 and in Mach 6 and Mach 10 air. The angle of attack was varied from 0 deg to 20 deg in 4 deg increments. Configurations tested were a hyperboloid with an asymptotic angle of 45 deg, a sonic-corner paraboloid, a paraboloid with an angle of 27.6 deg at the base, a Viking aeroshell generated in a generalized orthogonal coordinate system, and a family of cones having a 45 deg half-angle with spherical, flattened, concave, and cusp nose shapes. Real-gas effects were simulated for the hperboloid and paraboloid models at Mach 6 by testing at a normal-shock density ratio of 5.3 in air and 12 CF4. Predictions from simple theories and numerical flow field programs are compared with measurement. It is anticipated that the data presented in this report will be useful for verification of analytical methods for predicting hypersonic flow fields about blunt bodies at incidence.

Miller, C. G., III

Two-integral distribution functions for axisymmetric galaxies

The new method presented for finding distribution functions, which depend only on the classical integrals of energy and angular momentum for stellar systems with known axisymmetric densities, is the analog for the axisymmetric case of Eddington's classical solution for the isotropic distribution function, depending only on energy, of a known spherical density. It is required that density be expressed as a function of the potential and of a radial coordinate. Our solution is also an integral which is derived directly from the density, and hence can be used with complicated densities. A numerical quadrature is generally required to evaluate this solution, but contour integrals can be computed accurately by numerical quadrature; this is preferable to an explicit evaluation if the latter is an infinite series, such as is obtained using Fricke's method. We give several examples, including some for which our distribution functions are new. Our method can be extended simply to the related problems of finding anisotropic distribution functions for spherical or disk systems.

Hunter, C.

Vertical Distribution of Aersols and Water Vapor Using CRISM Limb Observations

Near-infrared spectra taken in a limb-viewing geometry by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on-board the Mars Reconnaissance Orbiter (MRO) provide a useful tool for probing atmospheric structure. Specifically, the observed radiance as a function of wavelength and height above the limb allows the vertical distribution of both dust and ice aerosols to be retrieved. These data serve as an important supplement to the aerosol profiling provided by the MRO/MCS instrument allowing independent validation and giving additional information on particle physical and scattering properties through multi-wavelength studies. A total of at least ten CRISM limb observations have been taken so far covering a full Martian year. Each set of limb observations nominally contains about four dozen scans across the limb giving pole-to-pole coverage for two orbits at roughly 100 and 290 W longitude over the Tharsis and Syrtis/Hellas regions, respectively. At each longitude, limb scans are spaced roughly 10 degrees apart in latitude, with a vertical spatial resolution on the limb of roughly 800 m. Radiative transfer modeling is used to model the observations. We compute synthetic CRISM limb spectra using a discrete-ordinates radiative transfer code that accounts for multiple scattering from aerosols and accounts for spherical geometry of the limb observations by integrating the source functions along curved paths in that coordinate system. Retrieved are 14-point vertical profiles for dust and water ice aerosols with resolution of 0.4 scale heights between one and six scale heights above the surface. After the aerosol retrieval is completed, the abundances of C02 (or surface pressure) and H20 gas are retrieved by matching the depth of absorption bands at 2000 nm for carbon dioxide and at 2600 run for water vapor. In addition to the column abundance of water vapor, limited information on its vertical structure can also be retrieved depending on the signal available from aerosol scattering.

Smith, Michael D.

Tunable-Bandwidth Filter System

A tunable-bandwidth filter system (TBFS), now undergoing development, is intended to be part of a remote sensing multispectral imaging system that will operate in the visible and near infrared spectral region (wavelengths from 400 to 900 nm). Attributes of the TBFS include rapid tunability of the pass band over a wide wavelength range and high transmission efficiency. The TBFS is based on a unique integration of two pairs of broadband Raman reflection holographic filters with two rotating spherical lenses. In experiments, a prototype of the TBFS, was shown to be capable of spectral sampling of images in the visible range over a 200 nm spectral range with a spectral resolution of 30 nm. The figure depicts the optical layout of a prototype of the TBFS as part of a laboratory multispectral imaging system for the spectral sampling of color test images in two orthogonal polarizations. Each pair of broadband Raman reflection holographic filters is mounted at an equatorial plane between two halves of a spherical lens. The two filters in each pair are characterized by steep spectral slopes (equivalently, narrow spectral edges), no ripple or side lobes in their pass bands, and a few nanometers of non-overlapping wavelength range between their pass bands. Each spherical lens and thus the filter pair within it is rotated in order to rapidly tune its pass band. The rotations of are effected by electronically controlled, programmable, high-precision rotation stages. The rotations are coordinated by electronic circuits operating under overall supervision of a personal computer in order to obtain the desired variation of the overall pass bands with time. Embedding the filters inside the spherical lenses increases the range of the hologram incidence angles, making it possible to continuously tune the pass and stop bands of the filters over a wider wavelength range. In addition, each spherical lens also serves as part of the imaging optics: The telephoto lens focuses incoming light to a field stop that is also a focal point of each spherical lens. A correcting lens in front of the field stop compensates for the spherical aberration of the spherical lenses. The front surface of each spherical lens collimates the light coming from the field stop. After the collimated light passes through the filter in the spherical lens, the rear surface of the lens focuses the light onto a charge-coupled-device image detector.

Bailey, John W.

A generalized orthogonal coordinate system for describing families of axisymmetric and two-dimensional bodies

A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.

Gnoffo, P. A.