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NASA NTRS2010

Planetary Image Geometry Library

The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A Java wrapper around the library allows parts of it to be used from Java code (via a native JNI interface). Future conversions of all or part of the library to Java are contemplated.

Deen, Robert C.↗

NASA NTRS1993

Mathematical Relationships Between Two Sets of Laser Anemometer Measurements for Resolving the Total Velocity Vector

The mathematical relations between the measured velocity fields for the same compressor rotor flow field resolved by two fringe type laser anemometers at different observational locations are developed in this report. The relations allow the two sets of velocity measurements to be combined to produce a total velocity vector field for the compressor rotor. This report presents the derivation of the mathematical relations, beginning with the specification of the coordinate systems and the velocity projections in those coordinate systems. The vector projections are then transformed into a common coordinate system. The transformed vector coordinates are then combined to determine the total velocity vector. A numerical example showing the solution procedure is included.

Owen, Albert K.↗

NASA NTRS1989

Nonlinear finite element formulation for the large displacement analysis in multibody system dynamics

A total Lagrangian finite element formulation for the deformable bodies in multibody mechanical systems that undergo finite relative rotations is developed. The deformable bodies are discretized using finite element methods. The shape functions that are used to describe the displacement field are required to include the rigid body modes that describe only large translational displacements. This does not impose any limitations on the technique because most commonly used shape functions satisfy this requirement. The configuration of an element is defined using four sets of coordinate systems: Body, Element, Intermediate element, Global. The body coordinate system serves as a unique standard for the assembly of the elements forming the deformable body. The element coordinate system is rigidly attached to the element and therefore it translates and rotates with the element. The intermediate element coordinate system, whose axes are initially parallel to the element axes, has an origin which is rigidly attached to the origin of the body coordinate system and is used to conveniently describe the configuration of the element in undeformed state with respect to the body coordinate system.

Rismantab-Sany, J.↗

NASA NTRS2007

International Space Station Remote Sensing Pointing Analysis

This paper analyzes the geometric and disturbance aspects of utilizing the International Space Station for remote sensing of earth targets. The proposed instrument (in prototype development) is SHORE (Station High-Performance Ocean Research Experiment), a multiband optical spectrometer with 15 m pixel resolution. The analysis investigates the contribution of the error effects to the quality of data collected by the instrument. This analysis supported the preliminary studies to determine feasibility of utilizing the International Space Station as an observing platform for a SHORE type of instrument. Rigorous analyses will be performed if a SHORE flight program is initiated. The analysis begins with the discussion of the coordinate systems involved and then conversion from the target coordinate system to the instrument coordinate system. Next the geometry of remote observations from the Space Station is investigated including the effects of the instrument location in Space Station and the effects of the line of sight to the target. The disturbance and error environment on Space Station is discussed covering factors contributing to drift and jitter, accuracy of pointing data and target and instrument accuracies.

Jacobson, Craig A.↗

NASA NTRS1986

Solution of separated flows using a simultaneous iteration technique

Generalization and improvement of an earlier work developed for studying separated flows using boundary layer type equations are presented. The improvements include extensions to a general coordinate system and use of a more general zonal technique for solving the coupled equations. In order to be able to consider arbitrary geometries, second order accurate (in space) conservative differences are generated by considering the integral formulation of the governing equations in a general coordinate system. The general coordinate system is handled in as general a manner as possible to allow for the use of either analytically or numerically generated coordinate systems. A marching procedure was used for solving the Partially Parabolized Navier-Stokes (PPNS) equations in the viscous region coupled in a fully implicit manner with the elliptic inviscid equation. To test the algorithm and compare to other solutions, solutions for flow over a flat plate and flow past the symmetrical 12 percent thick Joukowski airfoil (J012) at zero angle of attack were presented.

Source record↗

NASA NTRS1987

A global marching technique for the prediction of separated flows over arbitrary airfoils

The flow over arbitrary airfoils is analyzed using a boundary-layer-type solver developed for studying separated flows. The scheme includes extension to a general coordinate system and use of a more general zonal technique for solving the coupled equations. In order to be able to consider arbitrary geometries, second order accurate (in space) conservative differences are generated by considering the integral formulation of the governing equations in a general coordinate system. The general coordinate system is handled in as general a manner as possible to allow for the use of either analytically or numerically generated coordinate system. Different C type grids (orthogonal and nonorthogonal) were generated using different grid generation techniques to analyze the flow over arbitrary airfoils (J012, J025, NACA0012). A comparison with the experiment is demonstrated.

Halim, Ahmad A. M.↗

NASA NTRS1985

Users manual for coordinate generation code CRDSRA

Generation of a viable coordinate system represents an important component of an isolated airfoil Navier-Stokes calculation. The manual describes a computer code for generation of such a coordinate system. The coordinate system is a general nonorthogonal one in which high resolution normal to the airfoil is obtained in the vicinity of the airfoil surface, and high resolution along the airfoil surface is obtained in the vicinity of the airfoil leading edge. The method of generation is a constructive technique which leads to a C type coordinate grid. The method of construction as well as input and output definitions are contained herein. The computer code itself as well as a sample output is being submitted to COSMIC.

Shamroth, S. J.↗

NASA NTRS1991

The display of spatial information and visually guided behavior

The basic informational elements of spatial orientation are attitude and position within a coordinate system. The problem that faces aeronautical designers is that a pilot must deal with several coordinate systems, sometimes simultaneously. The display must depict unambiguously not only position and attitude, but also designate the relevant coordinate system. If this is not done accurately, spatial disorientation can occur. The different coordinate systems used in aeronautical tasks and the problems that occur in the display of spatial information are explained.

Bennett, C. Thomas↗

NASA NTRS1987

Numerical simulation of transonic propeller flow using a 3-dimensional small disturbance code employing novel helical coordinates

The numerical simulation of three-dimensional transonic flow about propeller blades is discussed. The equations for the unsteady potential flow about propellers is given for an arbitrary coordinate system. From this the small disturbance form of the equation is derived for a new helical coordinate system. The new coordinate system is suited to propeller flow and allows cascade boundary conditions to be applied straightforward. A numerical scheme is employed which solves the steady flow as an asymptotic limit of unsteady flow. Solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an eight bladed cascade. Both high and low advance ratio cases are given which include a lifting case as well as nonlifting cases. The nonlifting cases are compared to solutions from a Euler code.

Snyder, Aaron↗

NASA NTRS1987

Numerical simulation of transonic propeller flow using a three-dimensional small disturbance code employing novel helical coordinates

Snyder, Aaron↗

NASA NTRS1986

Relativistic effects in astronomical timing measurements

In this paper the relativistic transformations that are necessary to transform the results of earth-based astronomical timing observations from the terrestrial frame in which the observations are made to the proper frame of the astronomical object being observed are derived. Two coordinate systems are considered, the first being the parametrized post-Newtonian coordinate system and the second being a coordinate system based on the use of temps dynamique barycentrique as a time coordinate. Effects due to propagation of signals through curved spacetime and due to the relativistic gravitational time dilation for the earth are derived in each system. The results are then applied to three modern accurate data types spacecraft ranging, pulsar timing, and VLBI. A new effect is found in the analysis of VLBI data, amounting to a rescaling of VLBI-determined baselines produced by the curvature of space in the neighborhood of the sun.

Hellings, R. W.↗

NASA NTRS1971

Applications of laser ranging and VLBI observations for selenodetic control

The observation equations necessary to utilize lunar laser ranging and very long baseline interferometry measurements were developed for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The observation equations derived are based on a general model in which the unknown parameters included: the selenodetic Cartesian coordinates, the geocentric coordinates of earth stations, parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system, the parameters of the orientation of the average terrestrial coordinate system with respect to a fixed celestial coordinate system, and the geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris.

Fajemirokun, F. A.↗

NASA NTRS1972

Geos 1 Secor observations in the Pacific /Solution SP 7/.

Secor observations have defined a geodetic network extending through the Pacific Ocean from Japan, with three stations on the Japanese datum, to the west coast of the United States. Thus this network was connected to major datums on both ends. However, observations on Geos 1 were taken only in the middle of the network, from Truk Island to Maui, so that the network determined by Geos 1 observations alone is not directly attached to any major geodetic datum. A little-known procedure called 'inner adjustment' was found to be the appropriate method to define a coordinate system for the adjustment of the isolated network and to determine the inner consistency of the observations. The network was indirectly tied to the North American datum by the use of (1) satellite observing stations of other observing systems whose coordinates were previously determined, (2) relative positions of these and nearby Secor stations, as determined by local surveys, and (3) geodetic heights composed of leveled (orthometric) heights plus geoid heights obtained from a geoid map.

Mueller, I. I.↗

NASA NTRS1981

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

Smith, R. E.↗

NASA NTRS1982

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

Hah, C.↗

NASA NTRS1985

A canonical form for nonlinear systems

The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form.

Su, R.↗

NASA NTRS1986

A canonical form for nonlinear systems

The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.

Su, R.↗

NASA NTRS1987

A hierarchically distributed architecture for fault isolation expert systems on the space station

The Space Station Axiomatic Fault Isolating Expert Systems (SAFTIES) system deals with the hierarchical distribution of control and knowledge among independent expert systems doing fault isolation and scheduling of Space Station subsystems. On its lower level, fault isolation is performed on individual subsystems. These fault isolation expert systems contain knowledge about the performance requirements of their particular subsystem and corrective procedures which may be involved in repsonse to certain performance errors. They can control the functions of equipment in their system and coordinate system task schedules. On a higher level, the Executive contains knowledge of all resources, task schedules for all systems, and the relative priority of all resources and tasks. The executive can override any subsystem task schedule in order to resolve use conflicts or resolve errors that require resources from multiple subsystems. Interprocessor communication is implemented using the SAFTIES Communications Interface (SCI). The SCI is an application layer protocol which supports the SAFTIES distributed multi-level architecture.

Miksell, Steve↗