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At least 163 records · Page 9

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NASA NTRS1975

Coordinate systems in lunar ranging

Three distinct coordinate systems are required in the interpretation of the lunar range observations: a celestial frame and two-body-fixed frames. However, there is no coordinate system that is uniquely, or even preferentially, related to the observations themselves. Effectively, one specifies the coordinate systems by the procedures used in data reduction and parameter improvement. Each of the three systems affects the others in some way, and internal inconsistencies are quite possible. The discussion examines some of the more important aspects of this problem.

Mulholland, J. D.↗

NASA NTRS1975

On the periodic coordination of linear stochastic systems

The decentralized stochastic control of a linear dynamic system consisting of several subsystems is considered. A two-level approach is used by the introduction of a coordinator who collects measurements from the local controllers periodically and in return transmits coordinating parameters. Two types of coordination are considered: open-loop feedback and closed loop. The resulting control laws are found to be intuitively attractive.

Chong, C.-Y.↗

NASA NTRS1976

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.↗

NASA NTRS1977

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.↗

NASA NTRS1979

Application of a numerical orthogonal coordinate generator to axisymmetric blunt bodies

An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about axisymmetric blunt bodies is presented. This technique can generate orthogonal meshes which have unequally spaced points in two directions. Relations are given for the numerical generation of the metric coefficients. Body shapes ranging from simple analytical bodies to complex reverse curvature bodies are presented together with their orthogonal coordinate systems. The relatively good accuracy of the technique is shown in tabular data describing coordinate line slopes and metric coefficients. The predictor-corrector numerical method used to generate these results is both simple in concept and easy to program, so that the application of the technique should be broader than the results presented.

Graves, R. A., Jr.↗

NASA NTRS1979

Determination of station coordinates from Lageos

Laser tracking of Lageos by the NASA and SAO laser tracking systems from its launch in May 1976 until December 1976 has been used to derive the coordinates of the tracking stations. The NASA tracking data from four systems in the United States had a precision of 10 to 15 cm and the SAO stations in North America, South America and Australia had precisions between 0.8 meters and 1.3 meters. Nearly 90,000 observations of Lageos were used in this analysis. Thirty-one orbital arcs, each five days in length, were derived which had orbital fits of 25 cm for the NASA data and at about 1 meter level for the SAO data. The coordinates of all eight stations were derived from this data set and the preliminary estimate of the overall accuracy of 50 cm in each coordinate. These results are in general agreement at about the 30 cm level with other results obtained from laser tracking of Beacon Explorer C.

Smith, D. E.↗

NASA NTRS1980

A new coordinate transformation for turbulent boundary layer flows

The transformation permits a uniform mesh to be used in the computational coordinate which extends across the layer. This coordinate transformation uses the local value of the skin friction coefficient to scale the thickness of the wall layer region, and the local maximum value of turbulent viscosity to scale the boundary-layer thickness. Results are presented for two dimensional boundary layers in both positive and negative pressure gradients and comparisons are made with experimental data and conventional variable-grid results for low speed turbulent boundary-layers. The cases chosen illustrate the capability of this new transformation to capture the boundary layer growth over the full extent of laminar, transitional, and turbulent flow with no grid adjustment as well as its ability to consistently enlarge the wall layer region for accurate shear stress representation. Results of mesh refinement studies using the new coordinate transformation are presented.

Carter, J. E.↗

NASA NTRS1980

Generation of orthogonal boundary-fitted coordinate systems

A method is presented for computing orthogonal boundary fitted coordinate systems for geometries with coordinate distributions specified on all boundaries. The system which has found most extensive use in generating boundary fitted grids is made up of Poisson equations, of which the functions P and Q provide a means for controlling the spacing and density of grid lines in the coordinate system. While questions remain concerning the existence and uniqueness of orthogonal systems, the generating method presented adds to the available, useful techniques for constructing these systems.

Coleman, R. M.↗

NASA NTRS1982

A global model of the neutral thermosphere in magnetic coordinates based on OGO 6 data

Data from the OGO 6 satellite have been analyzed in magnetic latitude and magnetic local time coordinates for various seasons and magnetic activity levels. These measurements show considerable detail, particularly in the auroral regions where the energy inputs are well organized in this coordinate system. This detail is not readily observed in models based on geographic coordinates. Atomic oxygen and helium densities and a parameter related to the molecular nitrogen density were analyzed. The long-term averages of these quantities are presented in graphical form and as analytic functions to provide models of these thermospheric parameters. The atomic oxygen and helium densities show minima at high latitudes in the postmidnight sector for nearly all seasons and magnetic activity levels. The exospheric temperature inferred from the N2 density increases toward high latitudes for all seasons and all magnetic activity levels. This inferred temperature is about 300 deg K higher at the summer magnetic pole than at the winter magnetic pole.

Stehle, C. G.↗

NASA NTRS1982

The origin and evolution of the coordinated data analysis workshop process

During the planning stage for the International Magnetospheric Study (IMS), it was stressed that coordinated observations among various satellites and among satellite, ground-based, balloon, and rocket (GBR) experiments were essential in obtaining the required observational data base. In the course of operating the Satellite Situation Center (SSC), it was found to be desirable to assemble a problem-oriented digital data base, consisting of a large number of physical parameters obtained from satellite and GBR sensors, in a computer system which would permit a large number of scientists to manipulate, display, discuss, study and analyze the data together in a coordinated manner. It was felt that such a process might shorten the time required to gain full scientific understanding of the observations. This approach was called the Coordinated Data Analysis Workshop (CDAW) process. Attention is given to the preliminary concept, the the initial implementation of the CDAW process, and aspects of subsequent evolution.

Vette, J. I.↗

NASA NTRS1983

Coordinate systems

Jovian coordinate systems are different from those employed in the case of the earth. Latitude and longitude coordinates are usually established relative to some solid surface. Because Jupiter does not have a solid surface (at least none which is visible through the clouds), arbitrary, but convenient, coordinate grids have been prescribed. A spin equator is made out from observations of cloud motion, and the direction of the planetary spin axis is, therefore, determined with relatively good accuracy. The problem in establishing a Jupiter longitude system is that the mean rotation period of the clouds is a function of latitude. The solution selected was to define two separate longitude grids. A third longitude system became necessary with the detection of radio signals which gave evidence for a rotating planetary magnetic field. Attention is also given to orbital phase angle and longitude conventions for satellites, and two latitude systems for Jupiter

Dessler, A. J.↗

NASA NTRS1982

Coordinate generation with precise controls over mesh properties

Powerful local controls have been developed for mesh generation with the class of multisurface coordinate transformations. The controls come from local piecewise linear interpolants, and the resulting coordinates have continuous first derivatives. At the boundaries, the mesh controls provide the capability of joining distinct coordinate systems together with continuous derivatives. Away from boundaries, a local region can be given a particular mesh form to model internal objects or to simplify a problem. Applications of the controls are illustrated with a sequence of two-dimensional examples. For simplicity, each is generated about a NACA0012 airfoil which is of unit length and with leading edge pointed in a negative x-direction.

Eiseman, P. R.↗

NASA NTRS1982

High level continuity for coordinate generation with precise controls

Coordinate generation techniques with precise local controls have been derived and analyzed for continuity requirements up to both the first and second derivatives, and have been projected to higher level continuity requirements from the established pattern. The desired local control precision was obtained when a family of coordinate surfaces could be uniformly distributed without a consequent creation of flat spots on the coordinate curves transverse to the family. Relative to the uniform distribution, the family could be redistributed from an a priori distribution function or from a solution adaptive approach, both without distortion from the underlying transformation which may be independently chosen to fit a nontrivial geometry and topology.

Eiseman, P. R.↗

NASA NTRS1982

General curvilinear coordinate systems

The basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial differential equations are discussed. With such coordinate systems, all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries. A number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given. The material of this paper is applicable to all types of coordinate system generation.

Thompson, J. P.↗

NASA NTRS1982

Error induced by coordinate systems

It is pointed out that the choice of a curvilinear coordinate system can have a substantial effect on the error in the numerical solution of a partial differential equation. The truncation error is dependent not only on the higher order derivatives of the solution and the local grid spacing, but also on the rate-of-change of the grid spacing and on the departure of the grid from orthogonality. In connection with the present investigation, an analysis is conducted of the local truncation error in the approximation of first and second order derivatives on a curvilinear grid. Attention is given to a number of examples which illustrate the two fundamental sources of truncation error in the numerical solution of partial differential equations on curvilinear coordinate systems. The first is the grid spacing and changes in grid spacing which is measured by the first and second order derivatives of the functions defining the coordinate system. The second source is the higher order derivatives of the solution itself.

Mastin, C. W.↗

NASA NTRS1982

Reference coordinate systems for Earth dynamics: A preview

Geodynamics is the subject of intensive international research during last decade. A common requirement for all investigations is the necessity of a well defined coordinate system attached to the Earth in some prescribed way. In addition, a well defined inertial coordinate system is also needed in which the motions of the terrestrial system can be monitored. The problems encountered when establishing such coordinate systems and the transformations between them are presented. In addition, problems related to the modeling of the deformable Earth are discussed. Finally, action items are listed which are necessary to assure that the reference system issue is resolved early and that uniformity is assured by means of international agreements.

Mueller, I. I.↗

NASA NTRS1983

Evaluating multiple coordinated windows for programming workstations

Programmers might benefit from larger screens with multiple windows or multiple screens, especially if convenient coordination among screens are arranged. Uses for multiple coordinated displays in a programmers workstation are explored. Initial efforts focus on the potential applications, a command language for coordinating the displays, and the psychological basis for effective utilization so as to avoid information overload. Subsequent efforts will be devoted to implementing the concepts and performing controlled psychologically oriented experiments to validate the hypotheses.

Shneiderman, B.↗

NASA NTRS1984

Coordination of Fe, Ga and Ge in high pressure glasses by Moessbauer, Raman and X-ray absorption spectroscopy, and geological implications

For some time, it has been recognized that the structure of silicate liquids has a great bearing on such magma properties as viscosity, diffusivity, and thermal expansion and on the extrapolation of thermodynamic quantities outside of the experimentally measurable range. In this connection it is vital to know if pressure imposes changes in melt structure similar to the pressure-induced reconstructive transformations in crystals. In the present study on 1 bar and high pressure glasses, an investigation is conducted regarding the coordination of Fe(3+) in Fe silicate glasses by Moessbauer spectroscopy. Raman spectroscopy is employed to explore the coordinations of Ge(4+) in GeO2 glasses and of Ga(3+) in NaGa silicate glasses, while the coordination of Ga(3+) in NaGaSiO4 glasses is studied with the aid of methods of X-ray absorption spectroscopy.

Fleet, M. E.↗