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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33
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NASA NTRS1975

Accuracy of site coordinates obtainable by a mobile lunar laser station

The accuracy with which a mobile lunar laser station can be located was the subject of a modeling study. The influence of the number and accuracy of fixed lunar ranging stations, the uncertainty in polar motion, and data loss due to weather and similar factors were considered, and the results are given in a cartographic form. In general, all three coordinates (for coordinates to latitude + or - 60 deg) were determined to better than the pole uncertainty, given three or more fixed sites and reasonable weather. This result indicates that one or more mobile stations would be suitable for the study of geotectonics.

Loumos, G. L.↗
NASA NTRS1975

Transonic airfoil flowfield analysis using Cartesian coordinates

A numerical technique for analyzing transonic airfoils is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that Cartesian coordinates are used rather than a grid which fits the airfoil, such as the conformal circle-plane or 'sheared parabolic' coordinates which were used previously. Comparison with previous results shows that it is not necessary to match the computational grid to the airfoil surface, and that accurate results can be obtained with a Cartesian grid for lifting supercritical airfoils.

Carlson, L. A.↗
NASA NTRS1975

On the use of a coordinate transformation for the solution of the Navier-Stokes equations

The equations of fluid motion have been formulated in a generalized noncartesian, nonorthogonal coordinate system. A particular coordinate transformation, which transforms a domain with an irregular lower boundary into a cube, has been constructed. The transformed system, unlike the original one, has flat boundaries and homogeneous boundary conditions. Where the topography is flat, the original and transformed system are identical, and extra terms do not appear. A finite difference scheme for solving the transformed equations has been constructed and will be described later.

Gal-Chen, T.↗
NASA NTRS1975

Surface coordinates and cartography of Mercury

A control net of Mercury has been established photogrammetrically by using the Mariner 10 pictures; coordinates of 1328 points are given. The Mariner 10 coordinate system uses a system of longitudes in which the twentieth meridian passes through the center of the small crater Hun Kal and the spin axis is assumed normal to the orbital plane. A reference mosaic of Mercury has been published, and a series of 1:5,000,000 maps is now being produced.

Davies, M. E.↗
NASA NTRS1975

Averaged initial Cartesian coordinates for long lifetime satellite studies

A set of initial Cartesian coordinates, which are free of ambiguities and resonance singularities, is developed to study satellite mission requirements and dispersions over long lifetimes. The method outlined herein possesses two distinct advantages over most other averaging procedures. First, the averaging is carried out numerically using Gaussian quadratures, thus avoiding tedious expansions and the resulting resonances for critical inclinations, etc. Secondly, by using the initial rectangular Cartesian coordinates, conventional, existing acceleration perturbation routines can be absorbed into the program without further modifications, thus making the method easily adaptable to the addition of new perturbation effects. The averaged nonlinear differential equations are integrated by means of a Runge Kutta method. A typical step size of several orbits permits rapid integration of long lifetime orbits in a short computing time.

Pines, S.↗
NASA NTRS1976

Extending the Lorentz transformation by characteristic coordinates

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in a restricted region near the axis of the motion. In such coordinates the velocity of light remains invariant even for observers moving with variable velocity. By a particular choice of the scale relation the restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of constant velocity and locally in the case of variable velocity.

Jones, R. T.↗
NASA NTRS1976

Space telescope coordinate systems, symbols, and nomenclature definitions

The major coordinate systems as well as the transformations and transformation angles between them, for the Space Telescope are defined. The coordinate systems were primarily developed for use in pointing and control system analysis and simulation. Additional useful information (on nomenclature, symbols, quaternion operations, etc.) is also contained.

Kennel, H. F.↗
NASA NTRS1975

Computer-developed construction of analytic expressions for the coordinates and partial derivatives of Jupiter's Galilean satellites

A method for improving Sampson's (1910, 1912, 1921) original work in developing series expressions for accurate coordinates of the Galilean satellites is discussed. The method, which utilizes computer-based algebraic manipulation software, was developed to reconstruct Sampson's theory, remove existing errors, introduce neglected effects, and provide analytic expressions for the coordinates as well as for the partial derivatives with respect to orbital parameters, Jupiter's mass and oblateness, the satellite masses, and Jupiter's pole and rotation period. The software system, capable of handling Poisson series with up to 73 polynomial variables and 28 trigonometric arguments, is described. The preliminary solution is presented, and procedures are outlined for calculating perturbations and eliminating auxiliary parameters.

Lieske, J. H.↗
NASA NTRS1975

Station coordinates in the Standard Earth III system derived by using camera data from ISAGEX

Simultaneous and individual camera observations of Geos 1, Geos 2, Pageos, and Midas 4 obtained during the International Satellite Geodesy Experiment are used to determine station coordinates. The Smithsonian Astrophysical Observatory Standard Earth III system of coordinates is utilized to tie the geometrical network to a geocentric system and as a reference for calculating satellite orbits. The normal systems for geometrical and dynamical solutions are combined.

Gaposchkin, E. M.↗
NASA NTRS1975

Coordinate transformation and truncation for rotating spacecraft with flexible appendages

The analytical structures of alternative coordinate transformations for the variables that characterize the deformations of finite element models of flexible appendages on rotating spacecraft are examined. Particular emphasis is given to the truncation operations that are essential for efficient numerical simulations of flexible spacecraft, due to the necessarily large number of coordinates employed in a finite element description. A theorem is developed which establishes necessary conditions for the commutativity of the required truncation and inversion operations. The recommended alternative for the rotating elastic appendage is a complex transformation with previously published orthogonality properties, which permit the derivation in this paper of a relatively simple explicit set of transformed and truncated equations of modal vibration in real variables.

Likins, P.↗
NASA NTRS1976

Numerical solutions for laminar and turbulent viscous flow over single and multi-element airfoils using body-fitted coordinate systems

The technique of body-fitted coordinate systems is applied in numerical solutions of the complete time-dependent compressible and incompressible Navier-Stokes equations for laminar flow and to the time-dependent mean turbulent equations closed by modified Kolmogorov hypotheses for turbulent flow. Coordinate lines are automatically concentrated near to the bodies at higher Reynolds number so that accurate resolution of the large gradients near the solid boundaries is achieved. Two-dimensional bodies of arbitrary shapes are treated, the body contour(s) being simply input to the program. The complication of the body shape is thus removed from the problem.

Thompson, J. F.↗
NASA NTRS1977

Computer transformation of partial differential equations into any coordinate system

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Sullivan, R. D.↗
NASA NTRS1977

Coordinated rocket and satellite measurements of an auroral event. I - Satellite observations and analysis

Results of a coordinated auroral experiment involving the Atmosphere Explorer C satellite and a sounding rocket are reported. Auroral primary electron fluxes and neutral gas densities measured by instruments on the satellite are used in a model calculation of the thermospheric manifestation of the aurora. There is encouraging agreement between the calculated and measured electron density, electron temperature, secondary electron flux, and O I emissions at 5577 and 6300 A. A discrepancy between the calculated and the rocket-measured 3914-A emission profile is discussed in terms of experiment geometry and auroral physics. The coordinated measurements are used to infer vertical fluxes of ionization and of electron thermal energy at high altitudes

Rees, M. H.↗
NASA NTRS1977

Numerical solutions for viscous and potential flow about arbitrary two-dimensional bodies using body-fitted coordinate systems

A procedure for numerical solution of the time-dependent, incompressible Navier-Stokes equations for the flow about arbitrarily shaped two-dimensional bodies is given. This solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having a coordinate line coincident with the body contour regardless of its shape. The implicit solution utilizes the vorticity-stream function formulation with a false-position iterative adjustment of the surface vorticity in satisfaction of the no-slip boundary condition. Excellent agreement with the Blasius boundary layer solution is obtained for a semi-infinite flat plate. Results are presented for Reynolds numbers up to 2000 for several airfoils and a cambered rock.

Thames, F. C.↗
NASA NTRS1978

Body-fitted coordinates systems transformations

Two computer programs generate two-dimensional body-fitted coordinate systems and coordinate transformation. Programs are useful in fields requiring accurate numerical representation of boundary conditions and accurate numerical solutions of partial differential equations.

Mastin, C. W.↗
NASA NTRS1978

Applications of the hybrid coordinate method to the TOPS autopilot

Preliminary results are presented from the application of the hybrid coordinate method to modeling TOPS (thermoelectric outer planet spacecraft) structural dynamics. Computer simulated responses of the vehicle are included which illustrate the interaction of relatively flexible appendages with an autopilot control system. Comparisons were made between simplified single-axis models of the control loop, with spacecraft flexibility represented by hinged rigid bodies, and a very detailed three-axis spacecraft model whose flexible portions are described by modal coordinates. While single-axis system, root loci provided reasonable qualitative indications of stability margins in this case, they were quantitatively optimistic when matched against responses of the detailed model.

Fleischer, G. E.↗
NASA NTRS1978

/U,B,K/ coordinates - A natural system for studying magnetospheric convection

The formulation of the magnetospheric convection problem involves a coordinate system consisting of the electric potential, the magnetic field intensity, and the modified longitudinal invariant. The mapping is extended to include all particles and not just those mirroring in the magnetic equator. Equations of motion for the particle mirror points in this representation are presented. The analysis results in a natural division of the magnetosphere into accelerator and dynamo regions and use of the coordinate system permits trajectory-dependent effects to be distinguished from source- or sink-dependent effects. The representation is illustrated by application to the analysis of the nose structure protons observed by Smith and Hoffman (1974).

Whipple, E. C., Jr.↗
NASA NTRS1979

The Look-point Aircraft Coordinate Estimator (LACE) and potential applications

A look-point aircraft coordinate estimator (LACE) consisting of a windshield runway symbol projector, pilot input controls, microprocessor, and eye-alignment device is described. The estimator is used by a pilot to determine his aircraft's position relative to a runway or other visible terrain or target. The pilot initially superimposes and then corrects the superposition of the runway symbol over the runway during approach during periods when the runway is visible. Using the pilot's inputs the microprocessor calculates the position of the aircraft in terms of runway coordinates, then generates an approach trajectory and issues instructions to an autopilot. The microprocessor contains a model of the aircraft's dynamics and calculates a theoretical aircraft trajectory. The theoretical position of the aircraft is then used to drive the runway symbol, with the pilot's input being additive. The system thus acts as an aid in making low visibility approaches and landings when only an occasional glimpse of the runway is possible and no ground referenced landing systems are available. The system can also be used as an independent landing monitor for ground referenced landing systems.

Anderson, W. W.↗