A program for computer gridding of satellite photographs for mesoscale research
Computer program for gridding of satellite photographs using coordinate transformations of Fujita graphical method
COMPUTER PROGRAM↗
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Initial alignment of a strapdown inertial reference and navigation system.
Strapdown inertial reference and navigation system initial alignment utilizing coordinate- transformation matrix computer
SPACE NAVIGATION↗
ACCELERATING FRAMES OF REFERENCE AND THE CLOCK PARADOX
Coordinate transformation between inertial reference system and noninertial acceleration system - clock paradox
INERTIAL REFERENCE SYSTEM↗
A rapid method for obtaining frequency-response functions for multiple input photogrammetric data
A two-digital-camera photogrammetric technique for measuring the motion of a vibrating spacecraft structure or wing surface and an applicable data-reduction algorithm are presented. The 3D frequency-response functions are obtained by coordinate transformation from averaged cross and autopower spectra derived from the 4D camera coordinates by Fourier transformation. Error sources are investigated analytically, and sample results are shown in graphs.
Kroen, M. L.↗
Integration of vestibular and head movement signals in the vestibular nuclei during whole-body rotation
Single-unit recordings were obtained from 107 horizontal semicircular canal-related central vestibular neurons in three alert squirrel monkeys during passive sinusoidal whole-body rotation (WBR) while the head was free to move in the yaw plane (2.3 Hz, 20 degrees /s). Most of the units were identified as secondary vestibular neurons by electrical stimulation of the ipsilateral vestibular nerve (61/80 tested). Both non-eye-movement (n = 52) and eye-movement-related (n = 55) units were studied. Unit responses recorded when the head was free to move were compared with responses recorded when the head was restrained from moving. WBR in the absence of a visual target evoked a compensatory vestibulocollic reflex (VCR) that effectively reduced the head velocity in space by an average of 33 +/- 14%. In 73 units, the compensatory head movements were sufficiently large to permit the effect of the VCR on vestibular signal processing to be assessed quantitatively. The VCR affected the rotational responses of different vestibular neurons in different ways. Approximately one-half of the units (34/73, 47%) had responses that decreased as head velocity decreased. However, the responses of many other units (24/73) showed little change. These cells had signals that were better correlated with trunk velocity than with head velocity. The remaining units had responses that were significantly larger (15/73, 21%) when the VCR produced a decrease in head velocity. Eye-movement-related units tended to have rotational responses that were correlated with head velocity. On the other hand, non-eye-movement units tended to have rotational responses that were better correlated with trunk velocity. We conclude that sensory vestibular signals are transformed from head-in-space coordinates to trunk-in-space coordinates on many secondary vestibular neurons in the vestibular nuclei by the addition of inputs related to head rotation on the trunk. This coordinate transformation is presumably important for controlling postural reflexes and constructing a central percept of body orientation and movement in space.
Non-NASA Center↗
Computer derivations of equations of motion in a general orthogonal curvilinear coordinate system using the Formac language
Non-numeric digital computer program using coordinate transformation in deriving equations of motion for particles in general orthogonal curvilinear system
DIGITAL COMPUTER↗
Mars Science Laboratory Frame Manager for Centralized Frame Tree Database and Target Pointing
The FM (Frame Manager) flight software module is responsible for maintaining the frame tree database containing coordinate transforms between frames. The frame tree is a proper tree structure of directed links, consisting of surface and rover subtrees. Actual frame transforms are updated by their owner. FM updates site and saved frames for the surface tree. As the rover drives to a new area, a new site frame with an incremented site index can be created. Several clients including ARM and RSM (Remote Sensing Mast) update their related rover frames that they own. Through the onboard centralized FM frame tree database, client modules can query transforms between any two frames. Important applications include target image pointing for RSM-mounted cameras and frame-referenced arm moves. The use of frame tree eliminates cumbersome, error-prone calculations of coordinate entries for commands and thus simplifies flight operations significantly.
quaternion↗
On the uniqueness of space-time spectra and synoptic maps derived from polar-orbiting satellite data
The frequency transform method of Hayashi (1983a) and the asynoptic space-time transform method of Salby (1982b) for deriving space-time spectra are compared. The comparison reveals that the Galilean transformation used by Hayashi and the asynoptic coordinate transformation used by Salby produce identical spectra. The mapping between asynoptic data and the space-time Fourier spectrum is examined. The operation which maps a series of asynoptic measurements into the correct sequence of synoptic maps is described. It is observed that this linear transformation is unique and recovers the correct spectrum over wavenumber and frequency for a satellite observed field.
Salby, M. L.↗
A combined Eulerian-Lagrangian analysis for computation of two-phase flows
A combined Eulerian-Lagrangian analysis, which combines a linearized block implicit Navier-Stokes analysis for the continuous phase with a Lagrangian analysis for the motion of the droplet phase to simulate evaporating two-phase flows, has been developed. A unique aspect of this analysis is that the Lagrangian equations for the droplet motion have been transformed into the Eulerian computational space using coordinate transformation resulting in better computational efficiency. Use of the present implicit procedure for the continuous phase makes it possible to efficiently use a locally highly refined mesh. The coupling of the continuous phase and the droplet phase analyses is such that it allows the use of convergence acceleration techniques for steady-state problems, as well as making it possible to simulate transient flows. A rapidly evaporating two-phase flow caused by spray of liquid nitrogen in gaseous nitrogen has been used as a test problem to demonstrate the computer code using this analysis.
Sabnis, J. S.↗
Viscous/inviscid interaction procedure for high-amplitude oscillating airfoils
A coupling procedure between an inviscid potential theoretical panel method and an unsteady interactive boundary layer calculation procedure has been developed for calculating unsteady airloads on oscillating airfoils in the high-incidence regime. A coordinate transformation into a time-dependent surface coordinate has been incorporated into the boundary layer code to avoid a quasi-steady treatment of the viscous flow equations in the leading edge region. The upper and lower sides of the airfoil are calculated with the complete set of unsteady equations. The interactive region of the boundary layer calculation can be straightforwardly extended over the complete upper surface of the airfoil while accounting for interaction areas in the region of strong adverse pressure gradients with incipient separation. Comparisons of sample calculations with experimental data show reasonably good agreement even for unsteady drag coefficients.
Geissler, W.↗
Application of a patched-grid algorithm to the F/A-18 forebody-leading-edge extension configuration
A patched-grid algorithm for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver is presented. Results from both a spatial-flux and a time-flux conservation approach to patching across zonal boundaries are presented. A generalized coordinate transformation with a biquadratic geometric element is used at the zonal interface in order to treat highly stretched viscous grids and arbitrarily shaped zonal boundaries. Applications are made to the F/A-18 forebody-Ieading-edge extension configuration at subsonic, high-alpha conditions. Computed surface flow patterns compare well with ground-based and flight-test results; the large effect of Reynolds number on the forebody flowfield is shown.
Leading edge extension↗
A Patched-Grid Algorithm for Complex Configurations Directed Towards the F/A-18 Aircraft
A patched-grid algorithm for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver is presented. Results from both a spatial-flux and a time-flux conservation approach to patching across zonal boundaries are presented. A generalized coordinate transformation with a biquadratic geometric element is used at the zonal interface in order to treat highly stretched viscous grids and arbitrarily-shaped zonal boundaries. Applications are made to the F-18 forebody-strake configuration at subsonic, high-alpha conditions. Computed surface flow patterns compare well with ground-based and flight-test results; the large effect of Reynolds number on the forebody flow-field is shown.
High alpha research vehicle↗
Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight
Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.
Roberts, G. O.↗
An adaptive pseudospectral method for discontinuous problems
The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.
Augenbaum, Jeffrey M.↗
An adaptive pseudospectral method for discontinuous problems
The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.
Augenbaum, J. M.↗
Synthesis and Control of Flexible Systems with Component-Level Uncertainties
An efficient and computationally robust method for synthesis of component dynamics is developed. The method defines the interface forces/moments as feasible vectors in transformed coordinates to ensure that connectivity requirements of the combined structure are met. The synthesized system is then defined in a transformed set of feasible coordinates. The simplicity of form is exploited to effectively deal with modeling parametric and non-parametric uncertainties at the substructure level. Uncertainty models of reasonable size and complexity are synthesized for the combined structure from those in the substructure models. In particular, we address frequency and damping uncertainties at the component level. The approach first considers the robustness of synthesized flexible systems. It is then extended to deal with non-synthesized dynamic models with component-level uncertainties by projecting uncertainties to the system level. A numerical example is given to demonstrate the feasibility of the proposed approach.
Maghami, Peiman G.↗
An implicit finite-difference code for inviscid and viscous cascade flow
An implicit finite-difference code is developed to solve either inviscid or viscous flow about two-dimensional cascade blade elements. General coordinate transformations are used so that boundaries can coincide with coordinate lines, and an automatic grid generation routine based on elliptic partial differential equations is employed to mesh arbitrary cascade elements. Characteristic combinations of the differential equations are used at inflow and outflow boundaries. Computed results for both inviscid and viscous flow are compared with other existing cascade solutions and experimental data.
Steger, J. L.↗
Numerical analysis of the scramjet inlet flow field using two-dimensional Navier-Stokes equations
A computer code has been developed to solve the full two-dimensional Navier-Stokes equations in a scramjet inlet. The analysis uses a numerical coordinate transformation which generates a set of boundary fitted curvilinear coordinates. The explicit finite-difference algorithm of MacCormack is used to solve the governing equations. A two-layer eddy viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with multiple struts in the flow field. Detailed results are presented for two model problems and two scramjet inlets with one and two struts. The application of the two-dimensional analysis in the preliminary design of the actual scramjet inlet is briefly discussed.
Kumar, A.↗