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Computer program transforming spherical harmonic coefficients into arbitrarily tilted coordinate systems, tabulating coefficients of International Geomagnetic Reference Field 1965 in dipole coordinate system
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.
A computer model is developed in order to calculate fluence for a generalized spacecraft in orbital flight based on mass spectrometer and incoherent scatter (MSIS) measurements of ambient density. The calculations are used to identify criteria for the selection of materials for the construction of an LEO Space Station. The model is generalized such that the surfaces for study can be oriented in any direction with respect to: a body coordinate system fixed to the spacecraft (E surfaces); and a solar inertial coordinate system. A parametric study was performed in order to evaluate the effects of altitude, inclination, and solar activity on atomic oxygen fluence. Values are obtained for samples of Mylar, Kevlar, Kapton, Tedlar, Teflon and sulfone, as well as for some ethylene polymers. The range of values for material reactivities is from 360 microns for ram-facing surfaces to 200 microns for solar power surfaces during each cycle of solar activity. The possibility of improving reactivity by employing certain chemical coatings is also discussed.
A magnetic spring, or a spring and motor combination, providing a linear spring force characteristic in each direction from a neutral position, in which the spring action may occur for any desired coordinate of a typical orthogonal coordinate system. A set of magnets are disposed, preferably symmetrically about a coordinate axis, poled orthogonally to the desired force direction. A second set of magnets, respectively poled opposite the first set, are arranged on the sprung article. The magnets of one of the sets are spaced a greater distance apart than those of the other, such that an end magnet from each set forms a pair having preferably planar faces parallel to the direction of spring force, the faces being offset so that in a neutral position the outer edge of the closer spaced magnet set is aligned with the inner edge of the greater spaced magnet set. For use as a motor, a coil can be arranged with conductors orthogonal to both the magnet pole directions and the direction of desired spring force, located across from the magnets of one set and fixed with respect to the magnets of the other set. In a cylindrical coordinate system having axial spring force, the magnets are radially poled and motor coils are concentric with the cylinder axis.
This report documents the two primary coordinate systems used on the X-57 project and their relationship. The coordinate systems (CS) are the Tecnam OEM CS and the X-57 Project CS. All project measurements, unless noted, are taken from the X-57 Project CS. Also, other important locations on the COTS aircraft and the X-57 composite wing are noted and documented. This report also documents the X-57 wing baseline location and other important geometric aspects of the wing. All dimensions are in inches unless otherwise noted.
A method has been studied for predicting the acoustic field of the SR-3 transonic propfan using flow data generated by two versions of the NASPROP-E computer code. Since the flow fields calculated by the solvers include the shock-wave system of the propeller, the nonlinear quadrupole noise source term is included along with the monopole and dipole noise sources in the calculation of the acoustic near field. Acoustic time histories in the near field are determined by transforming the azimuthal coordinate in the rotating, blade-fixed coordinate system to the time coordinate in a nonrotating coordinate system. Fourier analysis of the pressure time histories is used to obtain the frequency spectra of the near-field noise.
A method for numerical solution of the Navier-Stokes equations for the flow about arbitrary airfoils or other bodies is presented. This method utilizes a numerically generated curvilinear coordinate system having a coordinate line coincident with the body contour. Streamlines, velocity profiles, and pressure and force coefficients for several airfoils and an arbitrary rock are given. Potential flow solutions are also presented. The procedure capable of treating multiple-element airfoils, and potential flow results are presented.
Large convective electric fields of the order of 10 mV/m (sometimes as high as 22 mV/m) are observed at rotational magnetopause discontinuities. These observations were made with the long cylindrical (179-m base line) probes carried on the ISEE 1 satellite. These electric field observations yield convective velocity magnitudes (equal to the cross product of the vector E and the vector B, the latter divided by the square of the magnitude of B) of the order of 150 km/s. In this format for the convective velocity magnitudes, some of these observations are similar to the high speed plasma velocity observations that were made at the magnetopause with the plasma experiment carried on the ISEE 1 satellite. It is shown that, for many of these magnetopause crossings, there exists a special moving coordinate system where the observed electric fields vanish. Such a unique reference system is often used in theoretical studies of magnetic discontinuities. This special coordinate system does not move at the local plasma velocity but moves instead at a velocity intermediate between the convective velocity and the local Alfven velocity. It is used here as a diagnostic tool for the experimental investigation of rotational discontinuities at the magnetopause.
Algebraic grid generation is the direct expression of a physical coordinate system as a function of a uniform grid in a rectangular computational coordinate system. Algebraic grid generation is based on mathematical interpolation and is presented in general terms of multivariate transfinite interpolation. The multisurface method and the two-boundary technique are described as univariate procedures that can be applied within the context of transfinite interpolation. A technique for grid clustering is described. Problems that are commonly encountered in three-dimensional grid generation are discussed and approaches for dealing with complex physical domains using multiple computational grid blocks are presented.
We wanted to make a satellite altitude magnetic anomaly map of the large magnetic anomaly in the Central African Republic, the Bangui magnetic anomaly, with data from the Swarm satellites. In the first part of our study, we summarize the earlier investigations and their interpretation. In the second we discuss our data processing applied to produce a magnetic anomaly map. We used the IGRF 12th to remove the long-wavelength regional anomalies. We will use an inverse procedure, which always requires a solution of the direct problem, and a horizontal polygonal prism given in the Descartes coordinate system. For this, reason the total magnetic anomaly was transformed into the Descartes coordinate system. The magnetization and its direction were used from our previous paper. The inverse problem is solved by the Simplex procedure. Our selected polygon has 14 geometrical parameters however, the inverse problem that is the numerical determination of the minimum problem is solved in the 14 dimensions. The result of our inverse problem was the 12 horizontal coordinates and the two upper and lower data of the polygon. The origin of the Bangui anomaly has been discussed in several scientific reports, either as a deep crustal tectonic feature or the result of a large external impactor. However, according to our inversion computations we cannot make any unambiguous finding for the origin of this feature. The inaccuracy in our total anomaly map is given by the Gaussian error propagation.
The Univac 1108 computer tape data formats are documented for the ephermeris tape generated by the Jet Propulsion Laboratory and the ephemeris tape used by the Quick Response Targeting Program (QRTP). Ephermeris tapes are used as the data source for the position and velocity components of those celestial bodies being considered in an integrated trajectory simulation program. The QRTP ephemeris tape has data only for lunar mission simulations. The JPL ephemeris tape has data for the moon and the nine planets. The ephemeris tapes, the data formats, the coordinate systems, and units are defined. The transformation from the mean-of-1950 coordinate system to the nearest mean Besselian year is given.
A compressible Navier-Stokes solution procedure is applied to the flow about an isolated airfoil. Two major problem areas were investigated. The first area is that of developing a coordinate system and an initial step in this direction has been taken. An airfoil coordinate system obtained from specification of discrete data points developed and the heat conduction equation has been solved in this system. Efforts required to allow the Navier-Stokes equations to be solved in this system are discussed. The second problem area is that of obtaining flow field solutions. Solutions for the flow about a circular cylinder and an isolated airfoil are presented. In the former case, the prediction is shown to be in good agreement with data.
The James Webb Space Telescope (JWST) is a 6.6m diameter, segmented, deployable telescope for cryogenic IR space astronomy (approximately 40K). The JWST Observatory architecture includes the Optical Telescope Element (OTE) and the Integrated Science Instrument Module (ISIM) element that contains four science instruments (SI) including a Guider. The SIs and Guider are mounted to a composite metering structure with outer dimensions of 2.1 x 2.2 x 1.9m. The SI and Guider units are integrated to the ISIM structure and optically tested at NASA/Goddard Space Flight Center as an instrument suite using an OTE SIMulator (OSIM). OSIM is a high-fidelity, cryogenic JWST telescope simulator that features a approximately 1.5m diameter powered mirror. The SIs are aligned to the structure's coordinate system under ambient, clean room conditions using laser tracker and theodolite metrology. Temperature-induced mechanical SI alignment and structural changes are measured using a photogrammetric measurement system at ambient and cryogenic temperatures. OSIM is aligned to the ISIM mechanical coordinate system at the cryogenic operating temperature via internal mechanisms and feedback from alignment sensors in six degrees of freedom. SI performance, including focus, pupil shear and wavefront error, is evaluated at the operating temperature using OSIM. We present an updated plan for the assembly and ambient and cryogenic optical alignment, test and verification of the ISIM element.
This investigation was to determine the transformation parameters (three rotations, three translations and a scale factor) between two Cartesian coordinate systems from sets of coordinates given in both systems. The objective was the determination of well separated transformation parameters with reduced correlations between each other, a problem especially relevant when the sets of coordinates are not well distributed. The above objective is achieved by preliminarily determining the three rotational parameters and the scale factor from the respective direction cosines and chord distances (these being independent of the translation parameters) between the common points, and then computing all the seven parameters from a solution in which the rotations and the scale factor are entered as weighted constraints according to their variances and covariances obtained in the preliminary solutions. Numerical tests involving two geodetic reference systems were performed to evaluate the effectiveness of this approach.
"Montage" is the name of a service of the National Virtual Observatory (NVO), and of software being developed to implement the service via the World Wide Web. Montage generates science-grade custom mosaics of astronomical images on demand from input files that comply with the Flexible Image Transport System (FITS) standard and contain image data registered on projections that comply with the World Coordinate System (WCS) standards. "Science-grade" in this context signifies that terrestrial and instrumental features are removed from images in a way that can be described quantitatively. "Custom" refers to user-specified parameters of projection, coordinates, size, rotation, and spatial sampling. The greatest value of Montage is expected to lie in its ability to analyze images at multiple wavelengths, delivering them on a common projection, coordinate system, and spatial sampling, and thereby enabling further analysis as though they were part of a single, multi-wavelength image. Montage will be deployed as a computation-intensive service through existing astronomy portals and other Web sites. It will be integrated into the emerging NVO architecture and will be executed on the TeraGrid. The Montage software will also be portable and publicly available.
The contravariant Navier-Stokes equations in weak conservation form are well suited to certain fluid flow analysis problems. Three dimensional contravariant momentum equations may be used to obtain Navier-Stokes equations in weak conservation form on a nonplanar two dimensional surface with varying streamsheet thickness. Thus a three dimensional flow can be simulated with two dimensional equations to obtain a quasi-three dimensional solution for viscous flow. When the Navier-Stokes equations on the two dimensional nonplanar surface are transformed to a generalized body fitted mesh coordinate system, the resulting equations are similar to the equations for a body fitted mesh coordinate system on the Euclidean plane. Contravariant momentum components are also useful for analyzing compressible, three dimensional viscous flow through an internal duct by parabolic marching. This type of flow is efficiently analyzed by parabolic marching methods, where the streamwise momentum equation is uncoupled from the two crossflow momentum equations. This can be done, even for ducts with a large amount of turning, if the Navier-Stokes equations are written with contravariant components.
We used surface-based representations to analyze functional specializations in the human cerebral cortex. A computerized reconstruction of the cortical surface of the Visible Man digital atlas was generated and transformed to the Talairach coordinate system. This surface was also flattened and used to establish a surface-based coordinate system that respects the topology of the cortical sheet. The linkage between two-dimensional and three-dimensional representations allows the locations of published neuroimaging activation foci to be stereotaxically projected onto the Visible Man cortical flat map. An analysis of two activation studies related to the hearing and reading of music and of words illustrates how this approach permits the systematic estimation of the degree of functional segregation and of potential functional overlap for different aspects of sensory processing.