Relevant bibliographies by topics / Coordinate

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Coordinate'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 March 2023

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Journal articles on the topic "Coordinate"

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Shrestha, Kalyan Gopal. "An Approach to Determine Coordinate Transformation Parameter for Nepal GPS Network." Journal on Geoinformatics, Nepal 10 (June 30, 2011): 9–13. http://dx.doi.org/10.3126/njg.v10i0.23187.

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The Surveying and Mapping community now has the benefit of 3-dimensional coordinates at the centimeter level, through the Global Positioning System (GPS). The reference frame for GPS, World Geodetic System of 1984 (WGS84), within which a user ascertains these coordinates is essentially geocentric. All coordinated data and mapping in Nepal are based on a non-geocentric coordinate system known as the Everest Datum of 1830. This paper tries to present a practical approach to define transformation parameters between the two coordinate systems for Nepal.
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Zhang, Xian Min, Ya Liu, Gang Li, and Fei Xia. "Study and Application on Airport Clearance Based on Secant Method in Gauss Projection Algorithm for Inverse Solution." Advanced Materials Research 790 (September 2013): 669–72. http://dx.doi.org/10.4028/www.scientific.net/amr.790.669.

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This article adopts WGS-84 Coordinate, applying the Secant Method successive approximation to solve geographic coordinates according to the Gauss-Krueger formula, realizing the transformation from plane rectangular coordinates to geographic coordinates, using the coordinate translation and rotation formula to achieve the transformation between the airport coordinate and Gauss plane rectangular coordinates, thus geographic coordinate, gauss plane rectangular coordinates and the airport coordinate can change into each other.
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Shanurov, G. A., and A. D. Manilova. "Mobile scanning complex positioning accuracy depending on the coordinate systems used." Geodesy and Cartography 919, no. 1 (February 20, 2017): 13–17. http://dx.doi.org/10.22389/0016-7126-2017-919-1-13-17.

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Inertial coordinate system and geodetic (terrestrial) coordinate system are used in processing of results of topographic survey, carried out with a mobile scanning complex. Mobile scanning complex geodetic coordinates, in turn, are presented in geodetic three-dimensional rectangular coordinate system form, in geodetic ellipsoidal coordinate system form and in the form of coordinates on a geodetic projection plane. The results of research, carried out earlier [4–7], suggest that the coordinate transformation on large areas distorts geodetic points coordinates. The article presents the results of similar investigations, but applied to a local area, limited by a mobile scanning complex surveying area. The accuracy of the mobile scanning complex coordinates is characterized by the mobile scanning complex coordinates errors cofactor matrix. It turned out that the local site sequential coordinate transformation procedure from one coordinate system to another coordinate system does not introduce any distortion into the mobile scanning complex coordinates.
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Eckermann, Stephen. "Hybrid σ–p Coordinate Choices for a Global Model." Monthly Weather Review 137, no. 1 (January 1, 2009): 224–45. http://dx.doi.org/10.1175/2008mwr2537.1.

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Abstract A methodology for choosing a hybrid σ–p (sigma–pressure) vertical coordinate of the Simmons–Strüfing form for a global model is presented. The method focuses on properties of the vertical derivative of the terrain-following coefficient, which affect the smoothness and shape of layer thickness profiles and determines the coordinate’s monotonicity over variable terrain. The method is applied to characterize and interrelate existing hybrid coordinate choices in NWP and climate models, then to design new coordinates with specific properties. Offline tests indicate that the new coordinates reduce stratospheric errors in models due to vertical truncation effects in the computation of the pressure gradient force over steep terrain. When implemented in a global model, the new coordinates significantly reduce vorticity and divergence errors at all altitudes in idealized simulations. In forecasting experiments with a global model, the new coordinates slightly reduce the stability of the semi-implicit time scheme. Resetting the reference pressure in the scheme to ∼800 hPa solves the problem for every coordinate except the Sangster–Arakawa–Lamb hybrid, which remains intrinsically less stable than the others. Impacts of different coordinates on forecast skill are neutral or weakly positive, with the new hybrid coordinates yielding slight improvements relative to earlier hybrid choices. This essentially neutral impact indirectly endorses the wide variety of hybrid coordinate choices currently used in NWP and climate models, with the proviso that these tests do not address the impact over longer time scales or on data assimilation.
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Funahashi, Shintaro. "Coordinate Transformation from Retinotopic Coordinates to Craniotopic Coordinates." Equilibrium Research 57, no. 4 (1998): 353–68. http://dx.doi.org/10.3757/jser.57.353.

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Zhang, X., J. Zhang, L. Zhang, and J. Liu. "ANALYSIS OF COMMON QUALITY PROBLEMS IN COORDINATE TRANSFORMATION BETWEEN REFERENCE COORDINATE SYSTEM AND GEOCENTRIC COORDINATE SYSTEM." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W13 (June 5, 2019): 1281–86. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w13-1281-2019.

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<p><strong>Abstract.</strong> In the working of the existing reference coordinate system transformed into the coordinate system of the geocentric coordinate system, many experts and scholars have in-depth research on the transformation methods such as geodetic control point results (including GNSS base station coordinates, GNSS control point coordinates, triangle point coordinates), basic geographic information data results (including DLG, DOM, DEM, DRG, DSM, etc.) and other spatial information data. On the basis of these studies, many provinces and cities have completed the coordinate system transformation of surveying and mapping results in China. This paper expounds the method of transforming the existing reference coordinate system into the geocentric coordinate system, summarizes and sorts out the common quality problems in the process of different data and different methods, and analyses the causes of the problems and the impact on the transforming results. Based on the above work, The paper provides reference and suggestions for the transforming work, which is aimed to improve the transformation quality in the future.</p>
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Meng, Qing Wu, and Lu Meng. "Influencing of Coordinate Transformation on Based CGCS2000 on Topographic Map with Large Scales." Applied Mechanics and Materials 522-524 (February 2014): 1207–10. http://dx.doi.org/10.4028/www.scientific.net/amm.522-524.1207.

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Using three dimensional coordinate transformation model with 7 parameters the coordinate transformation parameters are solved. Comparing the coordinates of the kilometer grid point on topographic maps in Beijing54, Xian80 and Urban Independent Coordinate System with the observation coordinates of same point inCGCS2000, Through watching their coordinate changes the moving changes regularity on topographic maps are discovered between Beijing54 and CGCS2000, between Xian 80 and CGCS2000, Urban Independent Coordinate System and CGCS2000
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Nepoklonov, Vicktor, Mayya Maximova, and Ivan Sukharev-Krylov. "Monitoring of spatial data coordinate basis integrity using coordinate transformations." E3S Web of Conferences 310 (2021): 03009. http://dx.doi.org/10.1051/e3sconf/202131003009.

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The modern spatial data coordinate basis (SDCB) is built taking into account the variety of existing and used today geodetic networks, models of physical fields of the Earth, cartographic models, as well as coordinate systems (СS). One of the requirements for SDCB from the standpoint of system analysis is the requirement of integrity, which presupposes the unity of the determination of coordinates, that is, the consistency of the results of determining the coordinates of the same points in different CSs. The article is devoted to the monitoring of the accuracy characteristics of the available software for coordinate transformations in terms of single-stage and multi-stage transitions between ellipsoidal coordinates of different systems.
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Zhao, Yun Peng, and Nan Li. "Research on Coordinate System Transformation in Flexible Rope FEA." Advanced Materials Research 753-755 (August 2013): 1785–89. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1785.

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This paper focuses on the transform relationships between each element and between elements with inertial system under different attitude coordinate system in the finite element multi-body system mechanical analysis of the flexible rope process. It mainly research the attitude coordinate transformation matrix between the of flexible rope Micro-element and inertial system under the four coordinate system which are the direction cosine coordinates, finite rotation four element coordinates, Euler angle coordinate and Cardan angle coordinates, and the relationship between the connecting base on the element type and inertial reference based.
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Lu, Xiaohong, Yongquan Wang, Jie Li, Yang Zhou, Zongjin Ren, and Steven Y. Liang. "Three-dimensional coordinate measurement algorithm by optimizing BP neural network based on GA." Engineering Computations 36, no. 6 (July 8, 2019): 2066–83. http://dx.doi.org/10.1108/ec-09-2018-0410.

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Purpose The purpose of this paper is to solve the problem that the analytic solution model of spatial three-dimensional coordinate measuring system based on dual-position sensitive detector (PSD) is complex and its precision is not high. Design/methodology/approach A new three-dimensional coordinate measurement algorithm by optimizing back propagation (BP) neural network based on genetic algorithm (GA) is proposed. The mapping relation between three-dimensional coordinates of space points in the world coordinate system and light spot coordinates formed on dual-PSD has been built and applied to the prediction of three-dimensional coordinates of space points. Findings The average measurement error of three-dimensional coordinates of space points at three-dimensional coordinate measuring system based on dual-PSD based on GA-BP neural network is relatively small. This method does not require considering the lens distortion and the non-linearity of PSD. It has simple structure and high precision and is suitable for three-dimensional coordinate measurement of space points. Originality/value A new three-dimensional coordinate measurement algorithm by optimizing BP neural network based on GA is proposed to predict three-dimensional coordinates of space points formed on three-dimensional coordinate measuring system based on dual-PSD.
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Dissertations / Theses on the topic "Coordinate"

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Carbonari, Giulia. "Coordinate isoterme." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10116/.

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Questa tesi si propone di verificare l'esistenza di coordinate isoterme su una superficie. Le coordinate isoterme danno localmente una mappa conforme da una varietà riemanniana bidimensionale al piano Euclideo. Se la superficie è orientabile, allora si può dare un atlante di carte isoterme, cioè le cui coordinate associate siano isoterme. Queste coordinate esistono a patto che vengano soddisfatte certe condizioni. Il risultato nelle classi di Holder è dovuto a Korn e Lichtensten. Chern ha notevolmente semplificato la loro dimostrazione.
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Andrei, Octavian. "3D affine coordinate transformations." Thesis, KTH, Geodesi och satellitpositionering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-199846.

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This thesis investigates the three-dimensional (3D) coordinate transformation from a globalgeocentric coordinate system to a national terrestrial coordinate system. Numerical studies arecarried out using the Swedish geodetic data SWEREF 93 and RT90/RH70. Based on theHelmert transformation model with 7-parameters, two new models have been studied: firstly ageneral 3D affine transformation model has been developed using 9-parameters (threetranslations, three rotations and three scale factors) and secondly the model with 8-parameters(three translations, three rotations and two scale factors) has been derived. To estimate the 3Dtransformation parameters from given coordinates in the two systems, the linearizedobservation equations were derived. Numerical tests were carried out using a local (North,East, Up) topocentric coordinate system derived from the given global geocentric system. Thetransformation parameters and the residuals of the coordinates of the common points werecomputed. The investigation shows the horizontal scale factor is significantly different by thevertical scale factor. The residuals of the control points were expressed in a separate (North,East, Up) coordinate system for each control point. Some investigations on the weightingprocess between horizontal and vertical components were also carried out, and an optimalweighting model was derived in order to reduce the residuals in horizontal componentswithout changing the coordinates.
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Hodgson, Timothy Lewis. "Coordinate systems in visual orienting." Thesis, Birkbeck (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338843.

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De, Brito e. Cunha Goncalo. "Incremental parsing of coordinate constructions." Thesis, University of Sussex, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283149.

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Fidalgo-Marijuan, Arkaitz. "Normal-Coordinate Structural Decomposition Engine." Revista de Química, 2017. http://repositorio.pucp.edu.pe/index/handle/123456789/123959.

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Muadz, Husni. "Coordinate structures: A planar representation." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185527.

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In this dissertation, I pursue the idea suggested in Chomsky (1982) that coordination should be treated as an object with three dimensions. I propose a planar model to account for the longstanding problems of coordination. The types of phenomena studied here are related to Phrasal Coordinations, Gapping, Verb Phrase Deletion, and Right-Node Raising. I claim that a coordinate sentence, unlike a simple one, is too expansive a domain for the Principles of Universal Grammar (UG) to hold. The relevant domain for the application of UG principles is each separate "component part" of the coordinate sentence. The "component parts", referred to here as planes, are elements of the coordinate sentence which have the same formal properties as simple sentences. Thus, under the planar model, a coordinate sentence has a number of "simple sentences" or planes. Intuitively, a plane, like a simple sentence, can be thought of as a complete functional complex in which all grammatical functions compatible with its head are realized. Given this, I argue that the well-formedness of a coordinate structure depends on whether or not each of its planes obeys the principles of UG. The planar model adopts the idea that conjuncts or disjuncts in coordination are based generated at D-Structure. It is claimed that no deletions or empty nodes exists in any type of coordinate structures. I show that the absence of some elements in coordination, e.g. a verb in Gapping, is a phonetic phenomenon, which occurs only as a result of the linearization process. At the other levels of representation, such as D-Structure, S-Structure, and Logical Form, all materials are present in each plane; thus, under the planar model, we do not need to invoke a deletion rule or the existence of some empty node in those levels of representation. Given this model, I show that the principles and parameters approach of GB can in fact give a unified treatment of coordination. I demonstrate that this can be done without recourse to construction-specific stipulation.
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Iannuzzi, Alessandra. "Introduzione di coordinate nei piani affini." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15835/.

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Si considera il classico problema della coordinatizzazione, nell'ambito dei piani affini: dato un piano affine sintetico sotto quali ipotesi sintetiche possiamo costruire un piano affine su un corpo, ad esso isomorfo? Abbiamo presentato un'esposizione di tale problema ed una sua soluzione, seguendo l'impostazione data da R. Lingenberg e A. Bauer. Abbiamo esposto le ipotesi sotto forma di validità di teoremi di chiusura, sotto forma di esistenza di particolari collineazioni o di alcune loro specifiche proprietà ed abbiamo esplicitato l'equivalenza tra queste ipotesi.
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Bronder, Axel Viking. "Visualization of a SWEPOS Coordinate Analysis." Thesis, KTH, Geoinformatik och Geodesi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-45986.

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Lantmäteriet, The Swedish Mapping, Cadastral and Land Registration Authority, is responsible for the operation and maintenance of SWEPOS and SWEREF99 (the Swedish official reference frame) and there-fore also responsible for control and verification of the data provided by the reference stations.Clas-Göran Persson at Lantmäteriet has created a new controlling procedure, including software, to analyze the position uncertainties of the SWEPOS stations using various statistical methods. The soft-ware evaluates the daily calculated coordinate data of the stations subsequently; it will not be installed directly on the actual stations. The primary goal is to study the stability of SWEPOS from a SWEREF 99 point of view, not to analyze SWEPOS real-time service. The controlling procedure is referred to as “the CGP Program”.The CGP Program is a toolbox of statistical methods created in MATLAB, determining standard devia-tion, correlation, distribution (outliers) and more. Its main purpose is to determine if the SWEPOS data consists of uniform uncorrelated normal distributed deviations, known as white noise, or not.The purpose of my Thesis is to; based on this new controlling procedure, create a graphical overview of the current status of the SWEPOS network for Lantmäteriet. Instead of making a thorough analysis of each station the maps created in this Thesis will visualize the outcome on an overall basis and identify the stations and areas of interest for further analysis.Together with representatives from Lantmäteriet we decided that three different map types where of interest. All the maps were to be based on SWEPOS data from 2010, analyzed by the CGP program, and visualized on a nationwide basis. They differ in their cartographic appearance and they all describe dif-ferent characteristics of the SWEPOS stations.Conclusions from the maps and the numerical analyzes: * There is a clear "winter effect", most obvious in the height coordinate. Removal of the snow-period results in lower standard deviations and fewer unwanted systematic effects. * The Northing coordinate has a slightly higher standard deviation than the Easting coordinate. The standard deviation in Height is around 50% larger than the horizontal standard deviation. * There is no evidence for physical movements, when comparing the official SWEREF 99 coordinates with the 2010 positions.
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Zuzan, Harry. "Coordinate-free self-organizing feature maps." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ31913.pdf.

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Ragan, Jennifer D. "A study of particular coordinate systems." Thesis, Wichita State University, 2011. http://hdl.handle.net/10057/3968.

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This thesis is a study of the properties and relationships between isothermal, harmonic and characteristic coordinate systems. The proof of the existence of isothermal and characteristic coordinates on a manifold which is a graph is given using the Uniformization theorem. Equations of prescribed mean curvature are discussed and the relationship between equations of minimal surface type and mean curvature type are shown. It is also proven that the map from a domain parameterized by characteristic coordinates to the domain parameterized by isothermal coordinates is quasiconformal.
Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.
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Books on the topic "Coordinate"

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Sładek, Jerzy A. Coordinate Metrology. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-48465-4.

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Coordinate d'Oriente. Milano: Piemme, 2014.

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Coordinate geometry. Mineola, N.Y: Dover Publications, 2005.

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Morris, A. S. Coordinate transformations and programming for small resolute coordinate robots. Sheffield: University, Dept. ofControl Engineering, 1985.

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Jessie, Daniel T., and Donald G. Saari. Coordinate Systems for Games. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-35847-1.

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M, Pang K., ed. Calculus and coordinate geometry. Hong Kong: Vision, 1992.

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United States. Dept. of the Interior, ed. The Geographic Coordinate Data Base. [Washington, D.C.?: U.S. Dept. of the Interior, 1989.

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Mueller, Ivan Istvan. Reference coordinate systems: An update. Columbus, Ohio: Ohio State University Research Foundation, 1988.

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Neumann, Hans-Joachim. Coordinate metrology: Technology and application. Landsberg: Verlag Moderne Industrie, 1990.

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Mueller, Ivan I. Reference coordinate systems: An update. Columbus, Ohio: Dept. of Geodetic Science and Surveying, Ohio State University, 1988.

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Book chapters on the topic "Coordinate"

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Shapiro, Ilya L. "Curvilinear Coordinates, Local Coordinate Transformations." In Undergraduate Lecture Notes in Physics, 45–54. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26895-4_4.

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Sładek, Jerzy A. "Introduction." In Coordinate Metrology, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_1.

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Sładek, Jerzy A. "Measurement Uncertainty and Requirements of Production System. Selected Issues of Measurement Uncertainty Theory." In Coordinate Metrology, 15–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_2.

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Sładek, Jerzy A. "Classic (Nonsimulative) Methods of Measurement Accuracy Assessment." In Coordinate Metrology, 55–129. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_3.

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Sładek, Jerzy A. "Analysis of the Accuracy of Coordinate Measuring Systems." In Coordinate Metrology, 131–225. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_4.

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Sładek, Jerzy A. "Simulation Methods for Assessing Accuracy of Measurements." In Coordinate Metrology, 227–335. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_5.

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Sładek, Jerzy A. "Accuracy of Modern Coordinate Measuring Systems." In Coordinate Metrology, 337–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_6.

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Sładek, Jerzy A. "Summary and Directions for Future Works on Coordinate Measurements Accuracy." In Coordinate Metrology, 383–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48465-4_7.

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Maliska, Clovis R. "Coordinate Transformation—General Curvilinear Coordinate Systems." In Fundamentals of Computational Fluid Dynamics, 263–331. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-18235-8_12.

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Weiland, Claus. "Coordinate Systems." In Aerodynamic Data of Space Vehicles, 333–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54168-1_8.

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Conference papers on the topic "Coordinate"

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Gao, Zehua, Mingjing Zhu, and Yuxi Tan. "Zone coordinates: A new coordinate system." In 2017 IEEE 17th International Conference on Communication Technology (ICCT). IEEE, 2017. http://dx.doi.org/10.1109/icct.2017.8359934.

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Mellace, Claudio, Antonio Gugliotta, Tariq Sinokrot, and Ahmed A. Shabana. "Simulations of Dynamic Braking of Railroad Vehicles Using Trajectory Coordinates." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34016.

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One of the important issues associated with the use of the trajectory coordinates in railroad vehicle simulations is the ability of such coordinates in dealing with braking and traction scenarios. In existing specialized railroad computer algorithms, the trajectory coordinates instead of the absolute Cartesian coordinates are often used. In these algorithms, track coordinate systems that travel with constant speeds are employed to define the configuration of the components in railroad vehicle systems. As the result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible, as reported in recent investigations [2]. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinate systems to be effectively used in modeling braking and traction scenarios. It is the objective of this investigation to demonstrate that by using track coordinate systems that can have an arbitrary motion, the trajectory coordinates can be used as the basis for developing computer algorithms for modeling braking and traction scenarios. To this end, a set of six generalized trajectory coordinates is used to define the configuration of each rigid body in the railroad vehicle system. This set of coordinates consists of one absolute coordinate, which is an arc length that represents the distance traveled by the body, and five relative coordinates. The arc length parameter defines the location of the origin and the orientation of a track coordinate system that follows the motion of the body. The other five relative coordinates are two translations that define the position of the origin of body coordinate system with respect to the track coordinate system in directions lateral and normal to the track, and three Euler angles that define the orientation of the body coordinate system with respect to its track coordinate system. The independent state equations of motion associated with the trajectory coordinates are identified and integrated forward in time in order to determine the trajectory coordinates and velocities. The results obtained in this study show that when the track coordinates systems are allowed to have an arbitrary motion, the resulting set of trajectory coordinates can be used effectively in the study of braking and traction conditions. The numerical examples presented in this paper include two different vehicle models subjected to several braking conditions. The results obtained are compared with the results obtained using the absolute Cartesian coordinate based formulations which allow modeling braking and traction scenarios.
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Hirokawa, Keishun, Kosuke Hayashi, Akira Sou, Akio Tomiyama, and Naoki Takada. "Numerical Simulation of Single Drops in a Vertical Pipe Using Various Coordinate Systems." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37491.

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The effects of the diameter ratio λ (= d/D, where d and D are the diameters of a drop and a pipe, respectively), the Morton number M and the viscosity ratio κ (= μd/μc, where μ is the viscosity and the subscripts d and c are the dispersed fluid particle and the continuous phase, respectively) on terminal velocities and shapes of single drops rising through stagnant liquids in a vertical pipe are investigated experimentally. Then, the drops in the pipe are simulated using a volume tracking method with various coordinate systems, i.e., three-dimensional (3D) cylindrical coordinates, 3D general curvilinear coordinates and 3D Cartesian coordinates. Predicted velocities and shapes of the drops using three coordinate systems are compared with the measured data to examine the effects of coordinate systems on the accuracy of prediction. As a result, (1) The velocity ratio VT/VT0 (VT and VT0 are the terminal velocity in a pipe and infinite liquid, respectively) decreases as λ increases, and it depends not only on λ but also on M and κ, (2) Good predictions for the terminal velocities and shapes of drops are obtained not only with cylindrical coordinates and curvilinear coordinates but also with Cartesian coordinates, provided that the spatial resolution is high, (3) When the spatial resolution is low, effects of coordinate systems on a drop shape are larger for Cartesian coordinate systems than for cylindrical coordinate and general curvilinear coordinate systems, and (4) Errors in predicted drop velocities are not so large even with very low spatial resolution.
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Batson, B. W. "Invariant Coordinate Systems for Compressor Control." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-240.

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To protect a compressor from surge, it is necessary to accurately calculate the location of the interface between stable operation and surge. Describing the Surge Limit Interface in certain coordinate systems results in a surface which is invariant to compressor suction conditions such as temperature and molecular weight. We refer to these coordinates as invariant coordinates. We explore these invariant coordinate systems and some nearly invariant systems useful for antisurge control. Some of them are commonly used in the industry, others are quite novel. This work serves to point out the unifying basis of them all. The applications for these methods are mainly industrial compressors. Varying molecular weight represents the main challenge since a real-time measurement for this parameter is unavailable. We present compressor maps constructed from test data in these coordinates. The validity of this approach is well supported by these data.
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5

Wang, J. Y., H. J. Yeh, T. C. Lin, and J. K. Wu. "Mathematical Model for Kinematic Analysis of Working Coordinates of General Mechanisms." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0094.

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Abstract Mathematical models have been derived for the kinematic analysis of working coordinates, which contain the formulation of the working coordinates constraint equations in terms of the relative joint coordinates, the transformation of the Jacobian matrix of the associated constraint equations from the Cartesian coordinate space to the relative joint coordinate space, and formulation for velocity and acceleration calculation. Such models lay out a solid foundation for the computational inverse kinematic analysis. In addition, moveable working coordinates are derived for both local and global coordinate systems. Application of this can be the working path design of general manipulators.
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6

Fogle, Martin A., and J. Kirk Wu. "A Relative Coordinate Formulation for Variational Solid Modeling." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0102.

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Abstract A minimal formulation using relative coordinates is presented for variational solid modeling. Computational methods developed for the kinematic modeling of mechanical systems are used to derive a minimal problem formulation. First, the concept of arbitrary coordinates is introduced to reduce the dimension of the constraint vector. Next, the variational problem is divided into two sub-problems. This is done by modeling the problem as a graph, which is then analyzed to identify open loops and decoupled loops. The third method used to reduce the size of the variational problem is to transform the sub-problems from a Cartesian coordinate formulation to a relative coordinate formulation. Once identified, the open loop sub-problem is solved trivially. Finally, the decoupled loop sub-problem is solved by optimization techniques which minimize the total constraint violation. Compared to the traditional approach, the relative coordinate method has a much smaller formulation, is highly convergent, and is able to evaluate under constrained geometry.
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7

Yakoub, R. Y., and A. A. Shabana. "A Numerical Approach to Solving Flexible Multibody Systems Using the Absolute Nodal Coordinate Formulation." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8204.

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Abstract By utilizing the fact that the absolute nodal coordinate formulation leads to a constant mass matrix, a Cholesky decomposition of the mass matrix can be used to obtain a constant velocity transformation matrix. This velocity transformation can be used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. In this case, the inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motions. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this paper. A flexible four-bar linkage is presented in this paper in order to demonstrate the use of Cholesky coordinates in the simulation of the small and large deformations in flexible multibody applications. The results obtained from the absolute nodal coordinate formulation are compared to those obtained from the floating frame of reference formulation.
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8

Garci´a-Vallejo, D., J. L. Escalona, J. Mayo, J. Domi´nguez, and A. A´lvarez. "Describing Rigid-Flexible Multibody Systems Using Natural and Absolute Nodal Coordinates." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48328.

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This paper deals with the dynamic description of interconnected rigid and flexible bodies. The absolute nodal coordinate formulation is used to describe the motion of flexible bodies and natural coordinates are used to describe the motion of the rigid bodies. The absolute nodal coordinate formulation is a non-incremental finite element procedure specially suitable for the dynamic analysis of flexible bodies exhibiting rigid body motion and large deformations. Nodal coordinates, that include global position vectors and global slopes, are all defined in a global inertial coordinate system. The advantages of using the absolute nodal coordinate formulation include constancy in the mass matrix, and the need for only a minimal set of non-linear constraint equations when connecting different flexible bodies with kinematic joints. When bodies within the system can be considered rigid, the above-mentioned advantages of the equations of motion can be preserved provided natural coordinates are used. In the natural coordinates method, the coordinates used to describe rigid bodies include global position vectors of basic points and global unit vectors. As in the absolute nodal coordinate formulation, rotational coordinates are avoided and the mass matrix is also constant. This paper provides computer implementation of this formulation that only uses absolute coordinates for general two-dimensional multibody systems. The constraint equations needed to define kinematic joints between different bodies can be linear or non-linear. The linear constraint equations, that include those needed to define rigid connections and revolute joints, are used to define constant connectivity matrices that reduce the size of the system coordinates. These constant connectivity matrices are also used to obtain the system mass matrix and the system generalized forces. However, the non-linear constraint equations that account for sliding joints, require the use of the Lagrange multipliers technique. Numerical examples are provided and compared to the results of other existing formulations.
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9

McPhee, John J. "A Unified Formulation of Multibody Kinematic Equations in Terms of Absolute, Joint, and Indirect Coordinates." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21333.

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Abstract This paper reviews some of the coordinate sets employed in multibody dynamic formulations, including absolute, joint, absolute angular, and indirect coordinates. Linear graph theory is then combined with the concept of a “virtual joint” to develop a unified modelling methodology that is capable of representing any of these coordinate sets. An algorithm is proposed and demonstrated for generating the kinematic constraint equations for dependent coordinates, plus kinematic transformations between coordinates (e.g. velocity transformations). The effects of different coordinates on the dynamic equations for a simple manipulator are shown.
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10

Anderson, Kurt S., and James H. Critchley. "Methods of Recursive Coordinate Reduction." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48316.

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The method of Recursive Coordinate Reduction (RCR) offers solutions to the forward problem of multibody dynamics in a number of operations linear in both the number of generalized coordinates, n, and the number of independent algebraic constraints, m (e.g. O(n + m)). However, the RCR is presently restricted in applicability (although broad) and susceptible to formulation singularities. This paper develops two methods for avoiding formulation singularities as well as a recursive general coupled loop solution which extends the RCR to the complete set of multibody systems. The existing RCR coupled with these developments constitute a Generalized Recursive Coordinate Reduction method which should be used in place of the traditional “O(n)” constraint technique (truly O(n + nm2 + m3)) for superior O(n + m) computational performance.
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Reports on the topic "Coordinate"

1

Adams, Terry. Coordinate Transformations. Office of Scientific and Technical Information (OSTI), September 2022. http://dx.doi.org/10.2172/1888203.

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2

Beckett, William. Coordinate Free LAP. Fort Belvoir, VA: Defense Technical Information Center, July 1986. http://dx.doi.org/10.21236/ada169982.

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3

MacKay, W., and S. Peggs. Accelerator Physics Coordinate Conventions. Office of Scientific and Technical Information (OSTI), November 1993. http://dx.doi.org/10.2172/1119408.

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4

Bong, E. LCLS Undulator Coordinate System. Office of Scientific and Technical Information (OSTI), January 2005. http://dx.doi.org/10.2172/839681.

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5

Hanshaw, R. A. Coordinate Standard Measurement Development. Office of Scientific and Technical Information (OSTI), February 2000. http://dx.doi.org/10.2172/751342.

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MacKay, W. Local Beam Line Coordinate System. Office of Scientific and Technical Information (OSTI), October 1995. http://dx.doi.org/10.2172/1119464.

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7

Harary, Howard, and Shaw Feng. U.S. Navy coordinate measuring machines:. Gaithersburg, MD: National Institute of Standards and Technology, 1993. http://dx.doi.org/10.6028/nist.ir.5379.

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Yamin, S. P. The internal bunch coordinate monitor (IBCM). Office of Scientific and Technical Information (OSTI), November 1988. http://dx.doi.org/10.2172/6615011.

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9

Zund, J. D. Hotine's (Omega, Phi, Nu) Coordinate System. Fort Belvoir, VA: Defense Technical Information Center, August 1993. http://dx.doi.org/10.21236/ada270108.

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10

Rothacker, F. Using Rexx to coordinate relational commands. Office of Scientific and Technical Information (OSTI), February 1990. http://dx.doi.org/10.2172/7015315.

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