Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Coordinate transformations”

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 505 records · Page 28

Reference coordinate systems: An update. Supplement 11

A common requirement for all geodetic investigations is a well-defined coordinate system attached to the earth in some prescribed way, as well as a well-defined inertial coordinate system in which the motions of the terrestrial frame can be monitored. The paper deals with the problems encountered when establishing such coordinate systems and the transformations between them. In addition, problems related to the modeling of the deformable earth are discussed. This paper is an updated version of the earlier work, Reference Coordinate Systems for Earth Dynamics: A Preview, by the author.

Mueller, Ivan I.↗

Möbius mirrors

An accelerating boundary (mirror) acts as a horizon and black hole analog, radiating energy with some particle spectrum. In this work, we demonstrate that a Möbius transformation on the null coordinate advanced time mirror trajectory uniquely keeps invariant not only the energy flux but the particle spectrum. We clarify how the geometric entanglement entropy is also invariant. The transform allows generation of families of dynamically distinct trajectories, including $\mathcal{PT}$ -symmetric ones, mapping from the eternally thermal mirror to the de Sitter horizon, and different boundary motions corresponding to Kerr or Schwarzschild black holes

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lunar targeting study: Lunar and planetary Ephemeris tapes

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.

Green, W. G.↗

Progress in development of a Navier-Stokes solver for evaluation of iced airfoil performance

A method is being developed for evaluation of the flow field behavior about an airfoil with significant ice accretion on the leading edge. The computer code, being evaluated for this purpose, solves the Navier-Stokes equations in a body-fitted curvilinear coordinate system. This requires the use of a grid generation code to transform the x-y coordinates of the physical space into xi-eta coordinates of the computational space. Evaluation of the suitability of these two codes for predicting iced airfoil performance is presently being carried out in anticipation of use in an overall icing analysis effort. Results of this evaluation to date indicate good correlation with known information on clean airfoils. Preliminary results for rime and glaze, iced airfoil shapes are also presented.

Potapczuk, M. G.↗

Canonical transformations for space trajectory optimization

Canonical transformations are developed between the Cartesian coordinates, equinoctial elements, trajectory variables, and orbital elements for coplanar space trajectory optimization problems. The canonical transformations permit the state and adjoint or their solution, transversality conditions, the optimal control, and integrals of the motion, to be transformed between any of the common sets of coordinates for planar space trajectory optimization problems. Variations on the canonical transformations shown are straightforward to develop given the group properties of the canonical transformations.

Haissig, Christine M.↗

Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by 'shock capturing'. Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10,000, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.

Warsi, Z. U. A.↗

Finite element appendage equations for hybrid coordinate dynamic analysis.

The increasingly common practice of idealizing a spacecraft as a collection of interconnected rigid bodies to some of which are attached linearly elastic flexible appendages leads to equations of motion expressed in terms of a combination of discrete coordinates describing the arbitrary rotational motions of the rigid bodies and distributed or modal coordinates describing the small, time-varying deformations of the appendages: such a formulation is said to employ a hybrid system of coordinates. In the present paper the existing literature is extended to provide hybrid coordinate equations of motion for a finite element model of a flexible appendage attached to a rigid base undergoing unrestricted motions and some of the advantages of the finite element approach are noted. Transformations to the modal coordinates appropriate for the general case are provided.

Likins, P. W.↗

Coordinate perturbation and multiple scale in gasdynamics.

A simple way of applying the coordinate perturbation technique is developed which bypasses the usual transformations of the equations to perturbed coordinates, and which provides the appropriate coordinate stretching by simple algebraic manipulations on the nonuniformly valid expansion obtained by a straightforward expansion from the original equations. Interesting results are obtained by applying the procedure to two gasdynamical problems. In the first, the flowfield around a supersonic two-dimensional wing is determined up to third order, including a uniformly valid representation of the front shock shape. The second concerns the oscillations in a closed tube following an arbitrary initial disturbance, both when the two ends are closed, and when one of the two ends contains an oscillating piston.

Crocco, L.↗

A dynamic transformation method for modal synthesis.

This paper presents a condensation method for large discrete parameter vibration analysis of complex structures that greatly reduces truncation errors and provides accurate definition of modes in a selected frequency range. A dynamic transformation is obtained from the partitioned equations of motion that relates modes not explicity in the condensed solution to the retained modes at a selected system frequency. The generalized mass and stiffness matrices, obtained with existing modal synthesis methods, are reduced using this transformation and solved. Revised solutions are then obtained using new transformations at the calculated eigenvalues and are also used to assess the accuracy of the results. If all the modes of interest have not been obtained, the results are used to select a new set of retained coordinates and a new transformation frequency, and the procedure is repeated for another group of modes.

Kuhar, E. J.↗

Minimization of deviations of gear real tooth surfaces determined by coordinate measurements

The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

Litvin, F. L.↗

Effects of joint rate and displacement constraints on stability regions

A block diagram showing plant dynamics in normal mode coordinates, a linear feedback controller with command limits, and actuator dynamics with rate and displacement limits is given. The objective is to examine the effects of joint rate and displacement saturation limits on the stability regions. An unstable short period dynamic model is transformed into normal mode coordinates and is augmented with actuator dynamics. A linear feedback controller is used to provide closed-loop stability. The stability with constrained actuator rate limits under varying bandwidth, displacement and command limits is examined.

Shrivastava, P. C.↗

Influence of Aqueous Phase Acidity on Ln(III) Coordination by N , N , N ', N '-Tetraoctyldiglycolamide

Here, this study highlights the importance of combining distribution ratio measurements with multiple spectroscopic techniques to provide a more comprehensive understanding of organic phase Ln coordination chemistry. Solvent extraction investigations with N,N,N',N'-tetraoctyldiglycolamide (TODGA) in n-heptane reveal the sensitivity of Ln complexation to the HNO 3 concentration. Distribution ratio measurements in tandem with UV–Vis demonstrated that increasing the concentration of HNO3 above 0.5 M with a constant NO 3 – of 1 M increases the number of coordinating TODGA molecules, from a 1:2 to a 1:3 Ln:TODGA complex. At each concentration of HNO 3 considered herein (from 0.01 to 1 M), Eu lifetime analysis demonstrated no evidence of H 2 O coordination. Results from Fourier transform infrared investigations suggest the presence of inner-sphere NO 3 – under low concentrations of HNO 3 when the 1:2 Ln:TODGA complex is present. Increasing the HNO 3 concentration above 0.5 M increases the propensity for outer-sphere interactions by removing the coordinated NO 3 – and saturating the Ln coordination sphere with three TODGA molecules, resulting in the well-established cationic, trischelate homoleptic [Ln(TODGA) 3 ] 3+ complex. This work demonstrates the importance in considering the NO 3 – source for solvent extraction systems. In particular, for systems with an affinity for outer-sphere interactions with molar concentrations of HNO 3 , changing the NO 3 – source can change the inner-sphere coordination of the Ln complex, which, in turn, affects the separation efficacy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Getting a Cohesive Answer from a Common Start: Scalable Multidisciplinary Analysis through Transformation of a System Model

One of the challenges of systems engineering is in working multidisciplinary problems in a cohesive manner. When planning analysis of these problems, system engineers must tradeoff time and cost for analysis quality and quantity. The quality is associated with the fidelity of the multidisciplinary models and the quantity is associated with the design space that can be analyzed. The tradeoff is due to the resource intensive process of creating a cohesive multidisciplinary system model and analysis. Furthermore, reuse or extension of the models used in one stage of a product life cycle for another is a major challenge. Recent developments have enabled a much less resource-intensive and more rigorous approach than handwritten translation scripts or codes of multidisciplinary models and their analyses. The key is to work from a core system model defined in a MOF-based language such as SysML and in leveraging the emerging tool ecosystem, such as Query-View- Transform (QVT), from the OMG community. SysML was designed to model multidisciplinary systems and analyses. The QVT standard was designed to transform SysML models. The Europa Hability Mission (EHM) team has begun to exploit these capabilities. In one case, a Matlab/Simulink model is generated on the fly from a system description for power analysis written in SysML. In a more general case, a symbolic mathematical framework (supported by Wolfram Mathematica) is coordinated by data objects transformed from the system model, enabling extremely flexible and powerful tradespace exploration and analytical investigations of expected system performance.

Cole, Bjorn↗

Image Segmentation, Registration, Compression, and Matching

A novel computational framework was developed of a 2D affine invariant matching exploiting a parameter space. Named as affine invariant parameter space (AIPS), the technique can be applied to many image-processing and computer-vision problems, including image registration, template matching, and object tracking from image sequence. The AIPS is formed by the parameters in an affine combination of a set of feature points in the image plane. In cases where the entire image can be assumed to have undergone a single affine transformation, the new AIPS match metric and matching framework becomes very effective (compared with the state-of-the-art methods at the time of this reporting). No knowledge about scaling or any other transformation parameters need to be known a priori to apply the AIPS framework. An automated suite of software tools has been created to provide accurate image segmentation (for data cleaning) and high-quality 2D image and 3D surface registration (for fusing multi-resolution terrain, image, and map data). These tools are capable of supporting existing GIS toolkits already in the marketplace, and will also be usable in a stand-alone fashion. The toolkit applies novel algorithmic approaches for image segmentation, feature extraction, and registration of 2D imagery and 3D surface data, which supports first-pass, batched, fully automatic feature extraction (for segmentation), and registration. A hierarchical and adaptive approach is taken for achieving automatic feature extraction, segmentation, and registration. Surface registration is the process of aligning two (or more) data sets to a common coordinate system, during which the transformation between their different coordinate systems is determined. Also developed here are a novel, volumetric surface modeling and compression technique that provide both quality-guaranteed mesh surface approximations and compaction of the model sizes by efficiently coding the geometry and connectivity/topology components of the generated models. The highly efficient triangular mesh compression compacts the connectivity information at the rate of 1.5-4 bits per vertex (on average for triangle meshes), while reducing the 3D geometry by 40-50 percent. Finally, taking into consideration the characteristics of 3D terrain data, and using the innovative, regularized binary decomposition mesh modeling, a multistage, pattern-drive modeling, and compression technique has been developed to provide an effective framework for compressing digital elevation model (DEM) surfaces, high-resolution aerial imagery, and other types of NASA data.

Yadegar, Jacob↗

Reversible transformations between the non-porous phases of a flexible coordination network enabled by transient porosity

Abstract Flexible metal–organic materials that exhibit stimulus-responsive switching between closed (non-porous) and open (porous) structures induced by gas molecules are of potential utility in gas storage and separation. Such behaviour is currently limited to a few dozen physisorbents that typically switch through a breathing mechanism requiring structural contortions. Here we show a clathrate (non-porous) coordination network that undergoes gas-induced switching between multiple non-porous phases through transient porosity, which involves the diffusion of guests between discrete voids through intra-network distortions. This material is synthesized as a clathrate phase with solvent-filled cavities; evacuation affords a single-crystal to single-crystal transformation to a phase with smaller cavities. At 298 K, carbon dioxide, acetylene, ethylene and ethane induce reversible switching between guest-free and gas-loaded clathrate phases. For carbon dioxide and acetylene at cryogenic temperatures, phases showing progressively higher loadings were observed and characterized using in situ X-ray diffraction, and the mechanism of diffusion was computationally elucidated.

Chemistry↗

An analytical transformation technique for generating uniformly spaced computational mesh

An analytical transformation method which can map arbitrary physical coordinate grid distribution into desired computational coordinate with uniform grid distribution is derived. The transformation function and its higher derivatives are differentiable. Salient features include; (1) precise control of grid sizes; (2) more than one location of clustered grids; (3) exact positioning of particular computational nodes in the physical plane; and (4) ensuring several patches of uniformly spaced grids in the physical plane for the higher accuracies (such as at the boundaries), etc., while keeping the variation of grid spacing continuous to avoid numerical instability.

Oh, Y. H.↗

Getting a Cohesive Answer from a Common Start: Scalable Multidisciplinary Analysis through Transformation of a Systems Model

One of the challenges of systems engineering is in working multidisciplinary problems in a cohesive manner. When planning analysis of these problems, system engineers must trade between time and cost for analysis quality and quantity. The quality often correlates with greater run time in multidisciplinary models and the quantity is associated with the number of alternatives that can be analyzed. The trade-off is due to the resource intensive process of creating a cohesive multidisciplinary systems model and analysis. Furthermore, reuse or extension of the models used in one stage of a product life cycle for another is a major challenge. Recent developments have enabled a much less resource-intensive and more rigorous approach than hand-written translation scripts between multi-disciplinary models and their analyses. The key is to work from a core systems model defined in a MOF-based language such as SysML and in leveraging the emerging tool ecosystem, such as Query/View/Transformation (QVT), from the OMG community. SysML was designed to model multidisciplinary systems. The QVT standard was designed to transform SysML models into other models, including those leveraged by engineering analyses. The Europa Habitability Mission (EHM) team has begun to exploit these capabilities. In one case, a Matlab/Simulink model is generated on the fly from a system description for power analysis written in SysML. In a more general case, symbolic analysis (supported by Wolfram Mathematica) is coordinated by data objects transformed from the systems model, enabling extremely flexible and powerful design exploration and analytical investigations of expected system performance.

Operational QVT↗

Zn speciation and fate in soils and sediments along the ground transportation route of Zn ore to a smelter

We discuss assessment of Zn toxicity/mobility based on its speciation and transformations in soils as critical for maintaining human and ecosystem health. Zn-concentrate (56% Zn as ZnS, sphalerite) has been imported through a seaport and transported to a Zn-smelter for several decades, and smelting processes resulted in aerial deposition of Zn and sulfuric acids in two geochemically distinct territories around the smelter (mountain-slope and riverside). XAFS analysis showed that the mountain-slope soils contained franklinite (ZnFe 2 O 4 ) and amorphous (e.g., sorbed) species of Zn(II), whereas the riverside sediments contained predominantly hydrozincite [Zn 5 (OH) 6 (CO 3 ) 2 ], sphalerite, and franklinite. The mountain-slope soils had low pH and moderate levels of total Zn (~1,514 ppm), whereas the riverside sediments had neutral pH and higher total Zn (12,363 ppm). The absence of sphalerite and the predominance of franklinite in the mountain-slope soils are attributed to the susceptibility of sphalerite and the resistance of franklinite to dissolution at acidic pH. These results are compared to previous Zn analyses along the transportation routes, which showed that Zn-concentrate spilled along the roadside in dust and soils underwent transformation to various O-coordinated Zn species. Overall, Zn-concentrate dispersed in soils and sediments during transportation and smelting transforms into Zn phases of diverse stability and bioavailability during long-term weathering.

36 MATERIALS SCIENCE↗