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↗
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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↗
Geodetic interpretation of the results.
Standard earth geodetic coordinate system and Baker-Nunn camera station positions
TRACKING STATION↗
Orientation of a rigid torque-free body by use of star transits.
Time dependent orientation of body fixed coordinate system relative to stars for spinning rigid torque-free body
PRECESSION↗
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↗
Time variations of geomagnetic H and D at disturbed stations.
Cylindrical coordinate system describing geomagnetic field analyzed, noting consequences in magnetic cartography when going from field to time gradients
TIME FACTOR↗
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.↗
Comparison of relativistic effects in barycentric and Earth-centered coordinates and implications for determination of GM for Earth
The results of an investigation of relativistic effects which have an influence on the determination of GM sub E (M sub E is the mass of the Earth, G is the Newtonian gravitaional constant) are summarized. The detailed arguments and derivations are discussed. The Parametrized Post-Newtonian (PPN) coordinates; Eddington-Clark (EC) coordinates; a coordinate system based on barycentric dynamical time (TBC coordinates); and Local Inertial coordinates are discussed.
Ashby, Neil↗
Application of a monotonic upstream-biased transport scheme to three-dimensional constituent transport calculations
The application of van Leer's scheme, a monotonic, upstream-biased differencing scheme, to three-dimensional constituent transport calculations is shown. The major disadvantage of the scheme is shown to be a self-limiting diffusion. A major advantage of the scheme is shown to be its ability to maintain constituent correlations. The scheme is adapted for a spherical coordinate system with a hybrid sigma-pressure coordinate in the vertical. Special consideration is given to cross-polar flow. The vertical wind calculation is shown to be extremely sensitive to the method of calculating the divergence. This sensitivity implies that a vertical wind formulation consistent with the transport scheme is essential for accurate transport calculations. The computational savings of the time-splitting method used to solve this equation are shown. Finally, the capabilities of this scheme are illustrated by an ozone transport and chemistry model simulation.
Allen, Dale J.↗
Application of the generalized vertical coordinate ocean model for better representing satellite data
It is found that two adaptive parametric functions can be introduced into the basic ocean equations for utilizing the optimal or hybrid features of commonly used z-level, terrain- following, isopycnal, and pressure coordinates in numerical ocean models. The two parametric functions are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara (1 974), the Jacobian pressure gradient formulation of Song (1 998), and a newly developed metric factor that permits both compressible (non-Boussinesq) and incompressible (Boussinesq) approximations. Based on the new formulation, an adaptive modeling strategy is proposed and a staggered finite volume method is designed to ensure conservation of important physical properties and numerical accuracy. Implementation of the combined techniques to SCRUM (Song and Haidvogel1994) shows that the adaptive modeling strategy can be applied to any existing ocean model without incurring computational expense or altering the original numerical schemes. Such a generalized coordinate model is expected to benefit diverse ocean modelers for easily choosing optimal vertical structures and sharing modeling resources based on a common model platform. Several representing oceanographic problems with different scales and characteristics, such as coastal canyons, basin-scale circulation, and global ocean circulation, are used to demonstrate the model's capability for multiple applications. New results show that the model is capable of simultaneously resolving both Boussinesq and non-Boussinesq, and both small- and large-scale processes well. This talk will focus on its applications of multiple satellite sensing data in eddy-resolving simulations of Asian Marginal Sea and Kurosio. Attention will be given to how Topex/Poseidon SSH, TRMM SST; and GRACE ocean bottom pressure can be correctly represented in a non- Boussinesq model.
numerical ocean model generalized coordinate syste↗
Magnetic flux ropes in the Venus ionosphere - Observations and models
Pioneer Venus Orbiter data are used as evidence of naturally occurring magnetic field filamentary structures which can be described by a flux rope model. The solar wind is interpreted as piling up a magnetic field on the Venus ionosphere, with the incident ram pressure being expressed as magnetic field pressure. Currents flowing at the ionopause shield out the field, allowing magnetic excursions to be observed with magnitudes of tens of nT over an interval of a few seconds. A quantitative assessment is made of the signature expected from a flux rope. It is noted that each excursion of the magnetic field detected by the Orbiter magnetometer was correlated with variations in the three components of the field. A coordinate system is devised which shows that the Venus data is indicative of the presence of flux ropes whose parameters are the coordinates of the system and would yield the excursions observed in the spacecraft crossings of the fields.
Elphic, R. C.↗