Search NASA⌕ Search

SEARCH · Search NASA

Results for “Coordinate Systems”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Boundary-layer equations in generalized curvilinear coordinates

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Panaras, Argyris G.↗

Post-Flight Estimation of Motion of Space Structures: Part 2

A computer program related to the one described in the immediately preceding article estimates the relative position of two space structures that are hinged to each other. The input to the program consists of time-series data on distances, measured by two range finders at different positions on one structure, to a corner-cube retroreflector on the other structure. Given a Cartesian (x,y,z) coordinate system and the known x coordinate of the retroreflector relative to the y,z plane that contains the range finders, the program estimates the y and z coordinates of the retroreflector. The estimation process involves solving for the y,z coordinates of the intersection between (1) the y,z plane that contains the retroreflector and (2) spheres, centered on the range finders, having radii equal to the measured distances. In general, there are two such solutions and the program chooses the one consistent with the design of the structures. The program implements a Kalman filter. The output of the program is a time series of estimates of the relative position of the structures.

Brugarolas, Paul↗

Kamodo’s Model-Agnostic Satellite Flythrough: Lowering the Utilization Barrier for Heliophysics Model Outputs

Heliophysics model outputs are increasingly accessible, but typically are not usable by the majority of the community unless directly collaborating with the relevant model developers. Prohibitive factors include complex file output formats, cryptic metadata, unspecified and often customized coordinate systems, and non-linear coordinate grids. Some pockets of progress exist, giving interfaces to various simulation outputs, but only for a small set of outputs and typically not with open-source, freely available packages. Additionally, the increasing array of tools built upon these sporadic interfaces are typically model-specific. We present Kamodo’s model-agnostic satellite flythrough capabilities as the solution to the utilization barrier for heliophysics model outputs. Developed at the Community Coordinated Modeling Center, these flythrough capabilities are built in Python upon a network of model-agnostic interfaces developed in collaboration with model developers, providing interpolation results the community can trust. Kamodo’s flythrough capabilities present the user with a growing variety of flythrough tools based upon a rapidly expanding library of heliophysics model outputs in several domains, currently including a variety of Ionosphere-Thermosphere-Mesosphere and global magnetosphere model outputs. Each capability is designed to be easily accessible via simplistic model-agnostic syntax, with the entire package freely available in the cloud on Github. Here, we describe the tools developed, include several sample applications for common science questions, demonstrate interoperability with selected packages, and summarize ongoing developments.

Software↗

Two-body linear guidance matrices

Analytical expressions for two-body linear guidance matrices in velocity dependent coordinate system for variant motion equation solutions

COORDINATE SYSTEM↗

Identifiability of linear systems in physical coordinates

Identifiability of linear, time-invariant systems in physical coordinates is discussed. It is shown that identification of the system matrix in physical coordinates can be accomplished by determining a transformation matrix that relates the physical locations of actuators and sensors to the test-data-derived input and output matrices. For systems with symmetric matrices, the solution of a constrained optimization problem is used to characterize all the possible solutions of the transformation matrix. Conditions for the existence of a unique transformation matrix are established easily from the explicit form of the solutions. For systems with limited inputs and outputs, the question about which part of the system can be uniquely identified is also answered. A simple mass-spring system is used to verify the conclusions of this study.

Su, Tzu-Jeng↗

Dynamics Informed Optimization for Resilient Energy Systems

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Programmable remapper with single flow architecture

The invention relates to image processing systems and methods and in particular to a machine which accepts a real time video image in the form of a matrix of picture elements (pixels) and remaps such image according to a selectable one of a plurality of mapping functions to create an output matrix of pixels. Such mapping functions, or transformations, may be any one of a number of different transformations depending on the objective of the user of the system. The system remaps input images from one coordinate system to another using a set of look-up tables for the data necessary for the transform. The transforms, which are operator selectable, are precomputed and loaded into massive look-up tables. Input pixels, via the look-up tables of any particular transform selected, are mapped into output pixels with the radiance information of the input pixels being appropriately weighted. An earlier embodiment of the system included two parallel processors: a collective processor which mapped multiple input pixels into a single output pixel and an interpolative processor. The interpolative processor performed an interpolation among pixels in the input image where a given input pixel may affect the value of many output pixels. Several advantages are provided over previous embodiments in that the two distinct processors are replaced by a single processor capable of performing both types of operations (collective and interpolative) with no more complexity. Previously, there has existed no image processor or 'remapper' that can operate with sufficient speed and flexibility to permit investigating different transformation patterns in real time.

Fisher, Timothy E.↗

Theory of Orbits.

Book on theory of orbits covering restricted problem of three bodies, two bodies in rotating coordinate system and periodic orbits

LIBRATIONAL MOTION↗

How to Enter, Fly In, and Exit the A-Train Constellation

The collaborative science obtained from the satellites in the A-Train is an unparalleled success. The constellation framework that has evolved is well-formulated and documented by its international members. Communication between teams is enhanced by a web-based Constellation Coordination System. Safety and correlated observations are ensured by defining independent control boxes with buffers in between. Each mission stays within its control box by regular drag makeup maneuvers. Annual inclination adjustments are coordinated by all missions to maintain their absolute and relative Mean Local Time of Ascending Node (MLTAN). Since the satellites are in different orbit planes their separation involves a three-dimensional triad made up of the along track separations, reference groundtracks and MLTAN's. For further safety, a Constellation Envelope has been defined to determine safe entry and exit orbits.

MLTAN↗

Smithsonian Astrophysical Observatory Reference System Bulletin, no. 1

The reference system is described which involves timing, scale, coordinate systems and their transformations, and observations of the rotation of the earth. Timing (epochs) and STADAT timing corrections are discussed. The coordinates for locations, and MSL height are listed for each observing station.

Source record↗

Image processing of HCMM-satellite thermal images for superposition with other satellite imagery and topographic and thematic maps

The southwestern part of Central Europe between Basal and Frankfurt was used in a study to determine the accuracy with which a regionally bounded HCMM scene could be rectified with respect to a preassigned coordinate system. The scale to which excerpts from HCMM data can be sensibly enlarged and the question of how large natural structures must be in order to be identified in a satellite thermal image with the given resolution were also examined. Relief and forest and population distribution maps and a land use map derived from LANDSAT data were digitalized and adapted to a common reference system and then combined in a single multichannel data system. The control points for geometrical rectification were determined using the coordinates of the reference system. The multichannel scene was evaluated in several different manners such as the correlation of surface temperature and relief, surface temperature and land use, or surface temperature and built up areas.

Gossmann, H.↗

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from in nity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at in nity with non-zero initial inward velocity; Gautreau-Ho mann (GH) time coordinates are adapted to observers dropped from rest from a nite distance from the black hole horizon. We construct from these an LMP family and a propertime family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lema^tre coordinates as well.

start at infinity with non-zero initial inward vel↗

The Precision Self-Metering Structure (PSMS)

Large, precise space systems such as space lasers, space telescopes, and space power transmitters cannot be realized until certain fundamental meteorological problems are first solved. It must be shown: (1) how a spatially distributed system of elements can be tied together in terms of a master coordinate system, (2) how master coordinates for these distributed elements can be determined with great accuracy, and (3) how mechanical integration of the elements to desired master coordinates of such accuracy can be achieved. Solutions to these problems are discussed.

Yager, W. C.↗

A procedure for calculating laminar, transitional and/or turbulent three-dimensional boundary layers including surface curvature effects about arbitrary blunt-nosed bodies

The governing equations for laminar, transitional and/or turbulent, incompressible, three-dimensional boundary layers are solved numerically. The equations are developed in terms of an orthogonal surface coordinate system and include surface curvature effects. The coordinates are generated numerically, while the inviscid flow is obtained from a general potential flow procedure. The only restrictions on body geometry are that it possess a blunt nose and a plane of symmetry. The boundary-layer equations, after being transformed into similarity type variables, are solved using the implicit finite-difference Krause scheme. Various test cases are presented to establish the accuracy of the resulting computer program.

Dwoyer, D. L.↗