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NASA NTRS2011

Geopotential Field Anomaly Continuation with Multi-Altitude Observations

Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with multi-altitude boundary conditions in Cartesian and spherical coordinates and investigates the advantages and limitations of these applications. Continuations by EPS (Equivalent Point Source) inversion and the FT (Fourier Transform), as well as by SCHA (Spherical Cap Harmonic Analysis) are considered. These methods were selected because they are especially well suited for analyzing multi-altitude data over finite patches of the earth such as covered by the ADMAP database. In general, continuations constrained by multi-altitude data surfaces are invariably superior to those constrained by a single altitude data surface due to anomaly measurement errors and the non-uniqueness of continuation.

Kim, Jeong Woo↗

NASA NTRS2012

Geopotential Field Anomaly Continuation with Multi-Altitude Observations

Kim, Jeong Woo↗

NASA NTRS1977

Liquid jet impingement normal to a disk in zero gravity

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

Labus, T. L.↗

NASA NTRS1980

Analytical satellite theory in extended phase space

It is noted that a satellite theory, based on extended phase space and on the true anomaly, was introduced by Scheifele (1970). In the present paper a simple canonical transformation is shown that makes the transition from the classical Delaunay elements to the Scheifele variables. It is stressed that neither spherical coordinates nor Hamilton-Jacobi theory is used. Finally, attention is given to the meaning of the new variables, especially the use of the true anomaly as one of the variables.

Bond, V.↗

NASA NTRS1987

Loran-C approach guidance project current status

There are four areas of work in the Loran-C flight test project. Current results provide performance data on the effects of Signal Noise Ratio (SNR) on the dynamic performance of the receiver filters for Loran-C data, and data on Loran-C grid deformation at a microscale of 100 meters. The Loran-C receiver provides a line of position (LOP) Master and Slave transmitter at an angle 0 to magnetic north. No transformation to latitude-longitude reference frame is required since this is the major source of Loran-C navigation errors. A local coordinate frame is established centered at touchdown point on the runway with directions along and across the runway. A Loran-C data collection system was set up. The Loran-C data are sent directly to an Apple II computer with a 12 inch monitor. The effect of SNR on Loran-C precision is shown for two receiver filters of different frequency response. A set of ground level static readings of touchdown was taken around Hanscom Field and transferred to an accurate detailed layout drawing; this showed local distortions of the average touchdown values.

Elias, A. L.↗

NASA NTRS1992

A deconvolution technique for Hubble Space Telescope FGS fringe analysis

A technique has been developed for directly transforming interferometer fringe visibility functions ('S curves') from the Hubble Space Telescope (HST) fine guidance sensors (FGSs) into intensity profiles of the program object. In a process analogous to Fourier transform image deconvolution, an S curve from a double star yields a pair of narrow profiles containing information on the separation (in one coordinate), and relative brightness of the two stars. The procedure has yielded high internal precision for the separation and relative brightness in tests with HST data. Simulations indicate that it can also deconvolve S curves from multiple stars or continuous intensity distributions such as resolvable stellar or extragalactic objects. Similar deconvolution analyses may be useful in other types of interferometry.

Hershey, John L.↗

NASA NTRS1995

A FFT Method for the Quasiclassical Selection of Initial Ro-Vibrational States of Triatomic Molecules

This paper describes the use of an exact fast Fourier transform (FFT) method to prepare specified vibrational-rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating-rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational-rotational state selected. For example, in the case of the ground vibrational state of a non-rotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001 h(bar) of the specified quantization values and energies within 5 cm(sup -1) of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However for states for which the fundamental frequencies become commensurate (resonance states), there are additional complications. In these cases it is necessary to determine a new set of "fundamental" frequencies and to modify the quantization conditions. Once these adjustments are made, good results are obtained for resonance states. The major problems are in labelling the large number of Fourier coefficients and the presence of regions of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the ro-vibrational states of H2O.

Eaker, Charles W.↗

NASA NTRS2018

Action Pathways for Transforming Cities

Transformation is required for cities to fulfil their leadership potential on climate change. Five action pathways can guide them: integrate mitigation and adaptation; coordinate risk reduction and climate adaptation; cogenerate risk information; focus on disadvantaged populations; and improve governance and knowledge networks.

Civil engineering↗

NASA NTRS1980

A simple numerical orthogonal coordinate generator for fluid dynamic applications

An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about two dimensional and axisymmetric bodies is presented. The technique is based on a predictor corrector numerical method. It can be used to generate orthogonal meshes which have unequally spaced points in two directions. These orthogonal meshes in their transformed computational plane are, however, equally spaced so that the differencing for the metric coefficients and the fluid dynamic equation terms can be easily determined using equally spaced central finite differences. Solutions to the Navier-Stokes equations for flow over blunt bodies with reverse curvature are presented. The coupling of the time dependent fluid dynamic equations and the coordinate generator worked well with no undesirable effects noted.

Graves, R. A., Jr.↗

NASA NTRS1974

The long-term prediction of artificial satellite orbits

Survey of averaging and multirevolution methods for long-term orbit prediction. A technical approach with the following features is recommended: (1) averaged variation-of-parameter equations, (2) analytical expressions for oblateness and third-body effects, (3) definite integrals for atmospheric drag and lunar effects (for long-period orbits), (4) nonsingular equinoctial element formulation, (5) multistep numerical integration processes, and (6) precise osculating-to-mean element transformation. Several orbital predictions illustrate the contribution of this technical approach to overall accuracy and efficiency. Future development of the analytical averaging method in nonsingular coordinates by automated manipulation of literal series is discussed.

Cefola, P. J.↗

NASA NTRS1976

High-beta turbulence in two-dimensional magnetohydrodynamics

Equations of ideal magnetohydrodynamics are used to study incompressible turbulent flows in a specified geometry where all the field quantities vary with only two spatial dimensions. The procedures adopted are basically those of Kraichnan (1967), in which classical equilibrium ensembles are built around constants of the motion identified from the Fourier-transformed equations of motion. Once the constants of the motion are identified, the statistical formulation of the problem is presented in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients. Canonical ensembles are constructed in this phase space by classical arguments. The theory developed permits isolation of some qualitatively new gross physical effects which have so far not been calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long-wavelength, self-generated, magnetic fields for a wide range of initial parameters.

Fyfe, D.↗

NASA NTRS1978

Development of a three-dimensional Navier-Stokes code on CDC star-100 computer

A three-dimensional code in body-fitted coordinates was developed using MacCormack's algorithm. The code is structured to be compatible with any general configuration, provided that the metric coefficients for the transformation are available. The governing equations are developed in primitive variables in order to facilitate the incorporation of physical boundary conditions and turbulence-closure models. MacCormack's two-step, unsplit, time-marching algorithm is used to solve the unsteady Navier-Stokes equations until steady-state solution is achieved. Cases discussed include (1) flat plate in supersonic free stream; (2) supersonic flow along an axial corner; (3) subsonic flow in an axial corner at M infinity = 0.95; and (4) supersonic flow in an axial corner at M infinity 1.5.

Vatsa, V. N.↗

NASA NTRS1989

A numerically exact full wave packet approach to molecule-surface scattering

A numerically exact spectral method for solving the time-dependent Schroedinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a two-dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2 scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the close-coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.

Mowrey, R. C.↗

NASA NTRS1976

The development of the Poincare-similar elements with true anomaly as the independent variable

In reference 1, the Hamiltonian of the unperturbed two-body problem in extended phase space is established. Depending on the type of time transformation, eight canonical elements were developed with the true anomaly or the eccentric anomaly as the independent variable. These two new sets, DS(phi) and DS(u), however contain singularities for small eccentricities and inclinations. In reference 2, these singularities are removed by a transformation from DS(u) to eight canonical PS(u) elements. In reference 3, the DS(phi) variables are transformed to the PS(phi) elements to remove the singularities. However, no direct relation was established between the eight canonical PS(phi) elements and the Cartesian coordinates. It is the purpose of this report to establish those relations and to develop the perturbed equations of motion in the PS(phi) space. This report also demonstrates the accuracy of this new set when it is applied to numerical orbit prediction problems.

Mueller, A.↗

NASA NTRS1984

Elimination of uncontrollable rigid body mode, appendix C

The planar system model is examined which reveals two rigid body modes. One is due to the pure translation of the whole experiment assembly and is uncontrollable because the only control input is a torque at the gimbal. The other rigid body mode is due to the pointing of the gimbal and is the one for which control is sort. The problem arises from the Vector V2 which relates the control input to the modal coordinates. Since its fifth and sixth elements are both nonzero, neither body mode can be thrown away as is. The two rigid body modes must be transformed so that one is unaffected by the control input and one is left controllable. The uncontrollable mode can then be eliminated from the model for design purposes. A process is described to accomplish the elimination of the uncontrollable rigid body mode.

Source record↗

NASA NTRS2013

The GLAS Standard Data Products Specification--Level 2, Version 9

The Geoscience Laser Altimeter System (GLAS) is the primary instrument for the ICESat (Ice, Cloud and Land Elevation Satellite) laser altimetry mission. ICESat was the benchmark Earth Observing System (EOS) mission for measuring ice sheet mass balance, cloud and aerosol heights, as well as land topography and vegetation characteristics. From 2003 to 2009, the ICESat mission provided multi-year elevation data needed to determine ice sheet mass balance as well as cloud property information, especially for stratospheric clouds common over polar areas. It also provided topography and vegetation data around the globe, in addition to the polar-specific coverage over the Greenland and Antarctic ice sheets.This document defines the Level-2 GLAS standard data products. This document addresses the data flow, interfaces, record and data formats associated with the GLAS Level 2 standard data products. The term standard data products refers to those EOS instrument data that are routinely generated for public distribution. The National Snow and Ice Data Center (NSDIC) distribute these products. Each data product has a unique Product Identification code assigned by the Senior Project Scientist. The Level 2 Standard Data Products specifically include those derived geophysical data values (i.e., ice sheet elevation, cloud height, vegetation height, etc.). Additionally, the appropriate correction elements used to transform the Level 1A and Level 1B Data Products into Level 2 Data Products are included. The data are packaged with time tags, precision orbit location coordinates, and data quality and usage flags.

Lee, Jeffrey E.↗

NASA NTRS1975

Nature of the requirements for reference coordinate systems /Review paper/

The current need for more precisely defined reference coordinate systems arises for geodynamics because the earth can certainly not be treated as a rigid body when measurement uncertainties reach the few-centimeter scale or its angular equivalent. At least two coordinate systems seem to be required. The first is a system defined in space relative to appropriate astronomical objects, suitable for ultimately expressing the dynamical equations of motion for the earth. The second coordinate system must be associated with the nonrigid earth in some well defined way so that the rotational motions of the whole earth are represented by the transformation parameters relating the earth system to the space-inertial system. The earth system should be defined so that the dynamical equations for relative motions of the various internal mechanical components of the earth and accurate measurements of these motions are conveniently expressed in this system.

Lundquist, C. A.↗

NASA NTRS1992

Development of a residual acceleration data reduction and dissemination plan

A major obstacle in evaluating the residual acceleration environment in an orbiting space laboratory is the amount of data collected during a given mission: gigabytes of data will be available as SAMS units begin to fly regularly. Investigators taking advantage of the reduced gravity conditions of space should not be overwhelmed by the accelerometer data which describe these conditions. We are therefore developing a data reduction and analysis plan that will allow principal investigators of low-g experiments to create experiment-specific residual acceleration data bases for post-flight analysis. The basic aspects of the plan can also be used to characterize the acceleration environment of earth orbiting laboratories. Our development of the reduction plan is based on the following program of research: the identification of experiment sensitivities by order of magnitude estimates and numerical modelling; evaluation of various signal processing techniques appropriate for the reduction, supplementation, and dissemination of residual acceleration data; and testing and implementation of the plan on existing acceleration data bases. The orientation of the residual acceleration vector with respect to some set of coordinate axes is important for experiments with known directional sensitivity. Orientation information can be obtained from the evaluation of direction cosines. Fourier analysis is commonly used to transform time history data into the frequency domain. Common spectral representations are the amplitude spectrum which gives the average of the components of the time series at each frequency and the power spectral density which indicates the power or energy present in the series per unit frequency interval. The data reduction and analysis scheme developed involves a two tiered structure to: (1) identify experiment characteristics and mission events that can be used to limit the amount of accelerator data an investigator should be interested in; and (2) process the data in a way that will be meaningful to the experiment objectives. A general outline of the plan is given.

Rogers, Melissa J. B.↗