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1
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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Mellace, C., A. P. Lai, A. Gugliotta, N. Bosso, T. Sinokrot, and A. A. Shabana. "Experimental and numerical investigation of railroad vehicle braking dynamics." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 223, no. 3 (June 2, 2009): 255–67. http://dx.doi.org/10.1243/14644193jmbd129.
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One of the important issues associated with the use of trajectory coordinates in railroad vehicle dynamic algorithms is the ability of such coordinates to deal with braking and traction scenarios. In these algorithms, track coordinate systems that travel with constant speeds are introduced. As a result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinates to be effectively used in modelling braking and traction dynamics. One of the objectives of this investigation is 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 modelling braking and traction conditions. 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 an arc length that represents the distance travelled by the body, and five relative coordinates that define the configuration of the body with respect to its track coordinate system. The independent non-linear 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 coordinate 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 results obtained using the trajectory coordinates are compared with the results obtained using the absolute Cartesian-coordinate-based formulations, which allow modelling braking and traction dynamics. In addition to this numerical validation of the trajectory coordinate formulation in braking scenarios, an experimental validation is also conducted using a roller test rig. The comparison presented in this study shows a good agreement between the obtained experimental and numerical results.
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Zängl, Günther. "An Adaptive Vertical Coordinate Formulation for a Nonhydrostatic Model with Flux-Form Equations." Monthly Weather Review 135, no. 1 (January 1, 2007): 228–39. http://dx.doi.org/10.1175/mwr3298.1.
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Abstract The concept of adaptive vertical coordinates is used to upgrade conventional terrain-following σ coordinates to arbitrary hybrid coordinates. Compared with previous approaches for implementing adaptive coordinates, the method presented here combines unrestricted applicability to nonhydrostatic models with the capability to integrate the atmospheric equations in flux form. The coordinate is based on a three-dimensional field carrying the vertical position of the coordinate surfaces, which is made time dependent by introducing a prognostic equation. As a specific example, the adaptive coordinate is used to emulate a hybrid isentropic system. Idealized tests in which the coordinate surfaces are artificially moved reveal that the ensuing spurious motions are small enough to be negligible in realistic applications. Mountain wave tests demonstrate that the hybrid coordinate remains numerically stable under strong forcing. However, the model layer distribution established with the hybrid isentropic coordinate is not optimal for representing the dynamics of breaking gravity waves because the vertical distance between the model levels tends to be too large in the wave breaking region. On the other hand, real case studies demonstrate that the hybrid coordinate significantly improves the representation of the tropopause because of enhanced vertical resolution in the tropopause region.
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Rader, C. M. "Generating rectangular coordinates in polar coordinate order." IEEE Signal Processing Magazine 22, no. 6 (November 2005): 178–80. http://dx.doi.org/10.1109/msp.2005.1550199.
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Bobkov, Valery, Alexey Kudryashov, and Alexander Inzartsev. "Method for the Coordination of Referencing of Autonomous Underwater Vehicles to Man-Made Objects Using Stereo Images." Journal of Marine Science and Engineering 9, no. 9 (September 21, 2021): 1038. http://dx.doi.org/10.3390/jmse9091038.
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The use of an autonomous underwater vehicle (AUV) to inspect underwater industrial infrastructure requires the precise, coordinated movement of the AUV relative to subsea objects. One significant underwater infrastructure system is the subsea production system (SPS), which includes wells for oil and gas production, located on the seabed. The present paper suggests a method for the accurate navigation of AUVs in a distributed SPS to coordinate space using video information. This method is based on the object recognition and computation of the AUV coordinate references to SPS objects. Stable high accuracy during the continuous movement of the AUV in SPS space is realized through the regular updating of the coordinate references to SPS objects. Stereo images, a predefined geometric SPS model, and measurements of the absolute coordinates of a limited number of feature points of objects are used as initial data. The matrix of AUV coordinate references to the SPS object coordinate system is computed using 3D object points matched with the model. The effectiveness of the proposed method is estimated based on the results of computational experiments with virtual scenes generated in the simulator for AUV, and with real data obtained by the Karmin2 stereo camera (Nerian Vision, Stuttgart, Germany) in laboratory conditions.
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Halimy, N. A. A., and N. J. Trilaksono. "Analysis of the influence hybrid mass coordinate on WRF-ARW models to the turbulence simulation of Batik airlines aviation (case study October 24, 2017)." IOP Conference Series: Earth and Environmental Science 893, no. 1 (November 1, 2021): 012032. http://dx.doi.org/10.1088/1755-1315/893/1/012032.
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Abstract The influence of hybrid sigma coordinate is better to represent turbulence in America than basic sigma coordinate. Therefore, it is necessary to search the effect of these coordinates on turbulence simulations in Indonesia due to the analysis of different atmospheric conditions from America. In this research, two experiments are performed using two different vertical coordinates with a case study flight turbulence from Batik Airlines on October 24, 2017. The two different vertical coordinates are the hybrid sigma coordinate and basic sigma coordinate. The data used are NCEP-FNL, Himawari-8 satellite image data, and sounding data. Based on the result of this research, simulation using hybrid sigma coordinate shows isentropic lines that have the potential turbulence during and after turbulence event. Richardson number value about 0.1 – 0.2 and intensity of the energy dissipation rate is 0.06 m 2/3s-1. According to the Richardson number value and intensity of the energy dissipation rate, the hybrid sigma coordinate simulation shows turbulence potential more significant than the basic sigma coordinate.
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Vinogradov, A. V. "Establishment of local coordinate systems in the transition to the geodetic system of coordinates of GSK-2011." Geodesy and Cartography 929, no. 11 (December 20, 2017): 2–10. http://dx.doi.org/10.22389/0016-7126-2017-929-11-2-10.
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Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.
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Foote, Robert L., Bruce E. Pollock, Michael J. Link, Yolanda I. Garces, and Robert W. Kline. "Leksell Gamma Knife coordinate setting slippage: how often, how much?" Journal of Neurosurgery 101, no. 4 (October 2004): 590–93. http://dx.doi.org/10.3171/jns.2004.101.4.0590.
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Object. The aim of this study was to determine the incidence and magnitude of coordinate setting slippage during gamma knife surgery (GKS). Methods. Thirty-six consecutive patients undergoing GKS with a Leksell unit between June and December 2000 had their coordinates (right and left x-, y-, and z-coordinates; 1548 coordinates; 258 isocenters) and gamma angles checked after the delivery of treatment to each isocenter to determine whether the coordinate settings had slipped and, if so, which settings and the magnitude of the slippage. Conclusions. Coordinate setting slippage during GKS with a Leksell unit does occur but is rare. The magnitude of such slippage is typically within the error of the stereotactic system and coordinate reading. The authors noted that coordinate setting slippage is significantly correlated with patient weight.
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Tian, Haoxin, Xipeng Fang, Yubin Lan, Chenyang Ma, Huasheng Huang, Xiaoyang Lu, Dehua Zhao, Hanchao Liu, and Yali Zhang. "Extraction of Citrus Trees from UAV Remote Sensing Imagery Using YOLOv5s and Coordinate Transformation." Remote Sensing 14, no. 17 (August 26, 2022): 4208. http://dx.doi.org/10.3390/rs14174208.
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Obtaining the geographic coordinates of single fruit trees enables the variable rate application of agricultural production materials according to the growth differences of trees, which is of great significance to the precision management of citrus orchards. The traditional method of detecting and positioning fruit trees manually is time-consuming, labor-intensive, and inefficient. In order to obtain high-precision geographic coordinates of trees in a citrus orchard, this study proposes a method for citrus tree identification and coordinate extraction based on UAV remote sensing imagery and coordinate transformation. A high-precision orthophoto map of a citrus orchard was drawn from UAV remote sensing images. The YOLOv5 model was subsequently used to train the remote sensing dataset to efficiently identify the fruit trees and extract tree pixel coordinates from the orchard orthophoto map. According to the geographic information contained in the orthophoto map, the pixel coordinates were converted to UTM coordinates and the WGS84 coordinates of citrus trees were obtained using Gauss–Krüger inverse calculation. To simplify the coordinate conversion process and to improve the coordinate conversion efficiency, a coordinate conversion app was also developed to automatically implement the batch conversion of pixel coordinates to UTM coordinates and WGS84 coordinates. Results show that the Precision, Recall, and F1 Score for Scene 1 (after weeding) reach 0.89, 0.97, and 0.92, respectively; the Precision, Recall, and F1 Score for Scene 2 (before weeding) reach 0.91, 0.90 and 0.91, respectively. The accuracy of the orthophoto map generated using UAV remote sensing images is 0.15 m. The accuracy of converting pixel coordinates to UTM coordinates by the coordinate conversion app is reliable, and the accuracy of converting UTM coordinates to WGS84 coordinates is 0.01 m. The proposed method is capable of automatically obtaining the WGS84 coordinates of citrus trees with high precision.
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NAKAMURA, AKIRA. "SOME NOTES ON PARALLEL COORDINATE GRAMMARS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 05 (October 1995): 753–61. http://dx.doi.org/10.1142/s0218001495000304.
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In a coordinate grammar, the rewriting rules replace sets of symbols having given coordinates by sets of symbols whose coordinates are given functions of the coordinates of the original symbols. Usually, at each step of a derivation, only one rule is applied and only one instance of its left hand side is rewritten. This type is referred to sequential grammars. As a counterpart of this grammar, parallel coordinate grammars are defined as generalized parallel isometric grammars. In the parallel grammars, the rewriting rule are used in parallel in a derivation application. The paper discusses some properties of parallel coordinate grammars and examines a relationship between the sequential coordinate grammars and parallel ones.
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Song, Sha Jia, and Neng He. "Digital Image Processing and Coordinate Transformation for Vic-3D System." Applied Mechanics and Materials 333-335 (July 2013): 1002–6. http://dx.doi.org/10.4028/www.scientific.net/amm.333-335.1002.
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This paper discusses the problem about the processing of the images collected by Vic-3D measurement system and the coordinate transformation between the pixel coordinate and plane coordinate. Correlation analysis on image information is carried out by using Matlab. Template matching method is used to get the pixel coordinates of the marked part on the images. Based on affine transformation and least square method, I transform the pixel coordinates of the marked part on the images into the plane coordinates.
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Toy, Michael D. "A Supercell Storm Simulation Using a Nonhydrostatic Cloud-Resolving Model Based on a Hybrid Isentropic-Sigma Vertical Coordinate." Monthly Weather Review 141, no. 4 (April 1, 2013): 1204–15. http://dx.doi.org/10.1175/mwr-d-12-00215.1.
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Abstract A three-dimensional simulation of a supercell storm is performed with a nonhydrostatic model based on a hybrid isentropic-sigma vertical coordinate. The coordinate is a terrain-following, height-based coordinate near the surface that smoothly transitions to potential temperature with height. Using isentropic coordinates provides the advantage of having zero cross-coordinate vertical mass flux for adiabatic flow, which virtually eliminates the numerical error in the vertical transport. The model uses an adaptive grid algorithm by which the coordinate surfaces may deviate from their target isentropes to maintain a sufficiently smooth mesh, while allowing the turbulence and vertical motion associated with convection to develop. The storm simulated by the hybrid-coordinate model compares well with simulations by Eulerian-coordinate models, but with the key difference being that the cross-coordinate mass flux is significantly smaller in much of the domain with the hybrid-coordinate model. A semi-implicit time-differencing scheme for numerically stabilizing vertically propagating acoustic modes in isentropic coordinates is also presented in the paper.
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Li, Suhua, Jiacheng Xie, Xuewen Wang, Fang Ren, Xin Zhang, and Qingbao Bao. "Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning." Symmetry 13, no. 1 (January 8, 2021): 97. http://dx.doi.org/10.3390/sym13010097.
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As a floating system connecting hydraulic support and scraper conveyor, the path planning of pushing mechanism is of great significance for their coordinated movement. In this paper, a method for path planning of hydraulic support pushing mechanism based on extreme learning machine (ELM) and Descartes path planning is proposed. According to the motion characteristics of moving mechanism, it is transformed into industrial robot model, based on the characteristics of the coordinates of the key points on the ear seat of the scraper conveyor when advancing, a prediction method of the key points coordinates based on ELM is proposed, so the target location of the end-effector is obtained. The path of the joint is determined by polynomial path partition and Descartes path planning method. The path is modified by Gaussian filtering method, and the peak value of path obtained by planning is filtered out, and the path correction is realized. Finally, the virtual simulation test is carried out in Unity3D. The planned coordinate curve has Poisson-like distribution and approximately around the target coordinate curve, and local error and correction error are within 2 cm and 0.1 cm, respectively. The coordinate curve obtained by combining planning and correction has a better effect.
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Li, Suhua, Jiacheng Xie, Xuewen Wang, Fang Ren, Xin Zhang, and Qingbao Bao. "Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning." Symmetry 13, no. 1 (January 8, 2021): 97. http://dx.doi.org/10.3390/sym13010097.
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As a floating system connecting hydraulic support and scraper conveyor, the path planning of pushing mechanism is of great significance for their coordinated movement. In this paper, a method for path planning of hydraulic support pushing mechanism based on extreme learning machine (ELM) and Descartes path planning is proposed. According to the motion characteristics of moving mechanism, it is transformed into industrial robot model, based on the characteristics of the coordinates of the key points on the ear seat of the scraper conveyor when advancing, a prediction method of the key points coordinates based on ELM is proposed, so the target location of the end-effector is obtained. The path of the joint is determined by polynomial path partition and Descartes path planning method. The path is modified by Gaussian filtering method, and the peak value of path obtained by planning is filtered out, and the path correction is realized. Finally, the virtual simulation test is carried out in Unity3D. The planned coordinate curve has Poisson-like distribution and approximately around the target coordinate curve, and local error and correction error are within 2 cm and 0.1 cm, respectively. The coordinate curve obtained by combining planning and correction has a better effect.
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Iofa, Mikhail Z. "Kodama-Schwarzschild versus Gaussian Normal Coordinates Picture of Thin Shells." Advances in High Energy Physics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/5632734.
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Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems: Kodama-Schwarzschild coordinates and Gaussian normal coordinates. We find explicit coordinate transformation between the Kodama-Schwarzschild and Gaussian normal coordinate systems. We show that projections of the metrics on the surface swept by the shell in the 4D spacetime in both cases are identical. In the general case of time-dependent metrics we calculate extrinsic curvatures of the shell in both coordinate systems and show that the results are identical. Applications to the Israel junction conditions are discussed.
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Jin, Li Xin, Lian Jun Wang, and Song Lin Yang. "Movement and Deformation Rules of Gauss Coordinates Based on Ellipsoid Expanded Modal." Advanced Materials Research 368-373 (October 2011): 2211–15. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.2211.
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This paper studies on deducing the analytic formulae on Gauss coordinates displacement before or after the increase of major radius of ellipsoid expanded modals, which is based on the partial derivatives of geodetic coordinates in Gauss coordinates deducing from direct solution formulae of the Gauss projection coordinates in conjunction with differential coefficient formulae and variable of geodetic coordinates. On this theoretical foundation, analyzing the relationships between Gauss coordinates displacement and other mathematical parameter . The relationship of graphics between point displacement components of latitudinal coordinate dy and longitudes is similar to the straight lines. The relationship of graphics between point displacement components of longitudinal coordinate dx and latitudinal coordinate dy, and the geodetic height is similar to the straight lines.
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Jin, Li Xin, Lian Jun Wang, and Song Lin Yang. "Displace Regulation of Gauss Coordinates Based on Ellipsoid Expanded Modal." Applied Mechanics and Materials 105-107 (September 2011): 1333–37. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.1333.
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This paper studies on deducing the analytic formulae on Gauss coordinates displacement before or after the increase of major radius of ellipsoid expanded modals, which is based on the partial derivatives of geodetic coordinates in Gauss coordinates deducing from direct solution formulae of the Gauss projection coordinates in conjunction with differential coefficient formulae and variable of geodetic coordinates. On this theoretical foundation, analyzing the relationships between Gauss coordinates displacement and other mathematical parameter . The relationship of graphics between point displacement components of latitudinal coordinate dy and longitudes is similar to the straight lines. The relationship of graphics between point displacement components of longitudinal coordinate dx and latitudinal coordinate dy, and the geodetic height is similar to the straight lines.
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Kuzikov, Sergey, D. V. Kenigsberg, Yuliya Salamatina, and O. A. Prokhorov. "Comparison of Methods for Computing Highly Accurate Daily GNSS Positions." Civil Engineering Journal 9, no. 2 (February 1, 2023): 305–18. http://dx.doi.org/10.28991/cej-2023-09-02-04.
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In Central Asia, the level of geodynamic displacements of the Earth's crust does not significantly exceed the accuracy of their measurement methods. Therefore, we need to choose the most accurate methods of calculating coordinates for cosmogeodetic stations. In this work, based on the data of 8 days of GPS measurements at 10 stations, 7 sets of average daily geocentric XYZ coordinates were calculated using different methods. To determine the positions, we used 3 calculation methods in the GAMIT/GLOBK program, 2 methods in the Bernese GNSS software, and 2 web services. To estimate the differences between 7 coordinate sets, we used parameters based on the Euclidean distance between these coordinate samples. The difference analysis of all pair combinations for 7 coordinate sets was carried out by 3D radius vectors, individual coordinate axes, and individual observation stations. The calculations showed that the positioning accuracy and precision depended not only on the coordinate calculation method but also on the selected reference frame. Methods using the international terrestrial reference frame (ITRF) provide station positions with regular deviations of <2 mm and individual deviations up to 5 cm. Methods using the regional and "point" reference frames have regular discrepancies for individual coordinates up to 2 cm and maximum deviations up to 1 m. Converting XYZ coordinates to UVW with the local reference frame reduces the difference between UVW sets by at least 25%. Due to the spatial orientation relative to the studied stations, the X (U) coordinate is reproduced 2-3 times with smaller deviations than other coordinates. The average deviation level of coordinate sets can be an indicator of the quality of conditions for receiving a GNSS signal at one station. We have identified the station group that has a coordinate deviation level several times lower than other stations. Doi: 10.28991/CEJ-2023-09-02-04 Full Text: PDF
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Konakoglu, B., L. Cakır, and E. Gökalp. "2D COORDINATE TRANSFORMATION USING ARTIFICIAL NEURAL NETWORKS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W1 (October 26, 2016): 183–86. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w1-183-2016.
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Two coordinate systems used in Turkey, namely the ED50 (European Datum 1950) and ITRF96 (International Terrestrial Reference Frame 1996) coordinate systems. In most cases, it is necessary to conduct transformation from one coordinate system to another. The artificial neural network (ANN) is a new method for coordinate transformation. One of the biggest advantages of the ANN is that it can determine the relationship between two coordinate systems without a mathematical model. The aim of this study was to investigate the performances of three different ANN models (Feed Forward Back Propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Radial Basis Function Neural Network (RBFNN)) with regard to 2D coordinate transformation. To do this, three data sets were used for the same study area, the city of Trabzon. The coordinates of data sets were measured in the ED50 and ITRF96 coordinate systems by using RTK-GPS technique. Performance of each transformation method was investigated by using the coordinate differences between the known and estimated coordinates. The results showed that the ANN algorithms can be used for 2D coordinate transformation in cases where optimum model parameters are selected.
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Idrizi, Bashkim. "Harmonization of different type of coordinate systems used for North Macedonian official spatial data." Proceedings of the ICA 2 (July 10, 2019): 1–6. http://dx.doi.org/10.5194/ica-proc-2-46-2019.
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<p><strong>Abstract.</strong> From the beginning of developing vector data sets in Macedonia, till now, three type of coordinate values for North Macedonian spatial data have been used.</p><p>Law for real estate cadaster and Regulation for basic geodetic works are the official legal bases for definition of official state coordinate system. In both legal documents, state coordinate system is defined by Ellipsoid of Bessel 1841, Datum of Hermannskogel, and Gauss-Kruger projection with central meridian 21&deg;&thinsp;E, scale factor 0.9999, false easting 500000&thinsp;m, false northing 0&thinsp;m and 7th projecting zone per 3&deg;. Based on mentioned parameters, the coordinate systems EPSG 6204 and EPSG 6316 are defined and internationally recognized. The core deferens between them is false easting value. As a result of both coordinate systems parameters, the values of easting coordinates are far from each other for 7000&thinsp;km!</p><p>Beside EPSG 6204 and 6316, official spatial data sets defined in CAD software were digitized by excluding first digits of easting and northing coordinates, by excluding digits 7 for easting and 4 for northing coordinates of spatial data.</p><p>Using three types of coordinate values, requires process of data harmonization before their usage in same project, in order to reach the spatial data overlapping. Third type of coordinate system, due to the lack of coordinate system parameters, can not be automatically overlapped with data defined in EPSG6204 and EPSG6316, which requires defining of intermediate coordinate system for third type of data in order to establish the mathematical base for data harmonization/overlapping by transformation of coordinates between three systems.</p>
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Obidenko, V. I. "The methodology of geodetic supporting Russian Federation digital economy." Geodesy and Cartography 954, no. 12 (January 20, 2020): 42–55. http://dx.doi.org/10.22389/0016-7126-2019-954-12-42-55.
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In the article the researches on developing modern methodology of supporting the national program “Digital economy of the Russian Federation” with geospatial data and, first of all, its base component, the systems of coordinate support are presented. As the main sentences of upgrading coordinate support it is offered to pass to kinematic model of evolution of coordinates in the state coordinate system GSK-2011 completely. The coordinates in this model are to be given to the consumer not on some separate instants (an initial epoch of installation of a coordinate system, an epoch of the last adjustment etc.), but for the current date, using a federal network of differential geodetic stations as the main tool for implementing this methodology. In order to avoid inconveniences of application the reference system for practical operations (as the coordinates are time-dependent), it is offered to use the additional coordinate system, “fixed” to an appropriate tectonic plate, spun round Euler’s pole within the state reference system GSK-2011.
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Lee, Wooyoung, Minchul Lee, Myoungho Sunwoo, and Kichun Jo. "Fast Online Coordinate Correction of a Multi-Sensor for Object Identification in Autonomous Vehicles." Sensors 19, no. 9 (April 29, 2019): 2006. http://dx.doi.org/10.3390/s19092006.
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Multi-sensor perception systems may have mismatched coordinates between each sensor even if the sensor coordinates are converted to a common coordinate. This discrepancy can be due to the sensor noise, deformation of the sensor mount, and other factors. These mismatched coordinates can seriously affect the estimation of a distant object’s position and this error can result in problems with object identification. To overcome these problems, numerous coordinate correction methods have been studied to minimize coordinate mismatching, such as off-line sensor error modeling and real-time error estimation methods. The first approach, off-line sensor error modeling, cannot cope with the occurrence of a mismatched coordinate in real-time. The second approach, using real-time error estimation methods, has high computational complexity due to the singular value decomposition. Therefore, we present a fast online coordinate correction method based on a reduced sensor position error model with dominant parameters and estimate the parameters by using rapid math operations. By applying the fast coordinate correction method, we can reduce the computational effort within the necessary tolerance of the estimation error. By experiments, the computational effort was improved by up to 99.7% compared to the previous study, and regarding the object’s radar the identification problems were improved by 94.8%. We conclude that the proposed method provides sufficient correcting performance for autonomous driving applications when the multi-sensor coordinates are mismatched.
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Luo, Huadong, Jun Yan, Haifeng Ling, Guangna Zhang, Qing Wang, Hongchuan Luo, and Tao Zhu. "Research on target location of unmanned aerial vehicles in parallel path." MATEC Web of Conferences 309 (2020): 04002. http://dx.doi.org/10.1051/matecconf/202030904002.
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This paper mainly studies how to use the stereo vision system that combines the monocular vision with parallel path search to locate the target. When the unmanned aerial vehicle (UAV) searches in the mission area according to the parallel path, the SSD image detection algorithm based on deep learning is adopted to detect and identify the target in the area. The image coordinate information is inversely calculated by using the pixel coordinate information fed back by machine vision. The auxiliary coordinate system is established according to the relationship of angle position between the track line and the basic coordinate system in the parallel path. Combining the position relation and the attitude direction information of UAV, the target position conversion relation between the imaging coordinate system and the auxiliary coordinate system is solved by using the direction cosine matrix. Combined with the coordinate information of UAV, the coordinate position of the target point in the basic coordinate system is finally solved through three coordinate conversion operations. In order to avoid the single calculating error of the target coordinates, the weighted average operation is carried out. On the basis of not changing the search trip of the parallel path, the target location function is preliminarily realized through the reverse solution and the weighted average operation of the target coordinates.
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Meng, Qing Wu, and Lu Meng. "Research of Transformation Models between Urban Independent Coordinates and CGCS2000 Coordinates." Applied Mechanics and Materials 522-524 (February 2014): 1202–6. http://dx.doi.org/10.4028/www.scientific.net/amm.522-524.1202.
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In case of no errors of known coincidence points coordinates the plane coordinate transformation model equation with four parameters and the plane coordinate transformation model equation with six parameters are derived, this algorithm needs not composed normal equation from error equation, which is verified by examples about transformation between the urban plane coordinate and CGCS2000 plane coordinate. Finally the some beneficial conclusions have been got.
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IUKHNO, Alona, Dmytro SOPOV, and Dmytro HOPTSII. "PERFORMANCE OF ENGINEERING SURVEYS AS AN INTEGRAL PART OF LAND AND CADASTRE WORKS IN PREPARATION OF LAND PLOTS FOR REGISTRATION IN THE BASE OF THE STATE LAND CADASTER." Ukrainian Journal of Applied Economics 6, no. 3 (September 2, 2021): 273–80. http://dx.doi.org/10.36887/2415-8453-2021-3-37.
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Performing engineering surveys is a mandatory part of the development of technical documentation on land management. Surveys allow to confirm the accuracy of the performed geodetic or topographic survey. In particular, the accuracy of determining the geodetic coordinates of the turning points of the boundaries of the land, to link the turning points of the boundaries of the land to the geodetic points of the State Geodetic Network of Ukraine. The main purpose of the article is to reflect the main components of engineering surveys as part of land cadastral works in preparation of land for registration in the database of the State Land Cadastre. The coordinate basis for land management is the State Geodetic Reference Coordinate System USK-2000, the geodetic basis for land management – points of the State Geodetic Network 1-3 classes, points of geodetic networks of compaction 4 class, 1 and 2 categories, points of the surveying network. The coordinates of the points of the State Geodetic Network of Ukraine, geodetic networks of condensing and turning points of the boundaries of geospatial objects are determined by rectangular coordinates (x, y) in the Gauss-Krueger projection in the USC-2000 coordinate system or local coordinate systems. related to the USC-2000 coordinate system. The control of the differential field of coordinate corrections when working with the use of RTK technologies is carried out at least at the two nearest points of DGM and GMZ, the coordinates of which are obtained from the administrator of the geodetic data bank. The difference in the values of the coordinates of control points should not exceed 0.1 m in cities of regional importance, 0.2 m - in other cities and towns, 0.3 m - in rural areas and 0.5 m - outside the settlements. Keywords: engineering surveys, State Geodetic Network of Ukraine, land cadastral works, coordinate system, State Land Cadastre.
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Dil, Emre, and Talha Zafer. "Transformation Groups for a Schwarzschild-Type Geometry in f(R) Gravity." Journal of Gravity 2016 (November 2, 2016): 1–8. http://dx.doi.org/10.1155/2016/7636493.
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We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of f(R) gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates.
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Lei, Kin, Dongxu Qi, and Xiaolin Tian. "A New Coordinate System for Constructing Spherical Grid Systems." Applied Sciences 10, no. 2 (January 16, 2020): 655. http://dx.doi.org/10.3390/app10020655.
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In astronomy, physics, climate modeling, geoscience, planetary science, and many other disciplines, the mass of data often comes from spherical sampling. Therefore, establishing an efficient and distortion-free representation of spherical data is essential. This paper introduces a novel spherical (global) coordinate system that is free of singularity. Contrary to classical coordinates, such as Cartesian or spherical polar systems, the proposed coordinate system is naturally defined on the spherical surface. The basic idea of this coordinate system originated from the classical planar barycentric coordinates that describe the positions of points on a plane concerning the vertices of a given planar triangle; analogously, spherical area coordinates (SACs) describe the positions of points on a sphere concerning the vertices of a given spherical triangle. In particular, the global coordinate system is obtained by decomposing the globe into several identical triangular regions, constructing local coordinates for each region, and then combining them. Once the SACs have been established, the coordinate isolines form a new class of global grid systems. This kind of grid system has some useful properties: the grid cells exhaustively cover the globe without overlapping and have the same shape, and the grid system has a congruent hierarchical structure and simple relationship with traditional coordinates. These beneficial characteristics are suitable for organizing, representing, and analyzing spatial data.
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MA, ZHENGMING, and JING CHEN. "THE HUFFMAN-LIKE ALIGNMENT IN MANIFOLD LEARNING." International Journal of Pattern Recognition and Artificial Intelligence 28, no. 04 (June 2014): 1451005. http://dx.doi.org/10.1142/s0218001414510057.
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In manifold learning, the neighborhood is often called a patch of the manifold, and the corresponding open set is called the local coordinate of the patch. The so-called alignment is to align the local coordinates in the d-dimensional Euclidean space to get the global coordinate of the manifold. There are two kinds of alignment methods: global and progressive alignment methods. The global alignment methods align the local coordinates of the manifold all at one time by solving an eigenvalue problem. The progressive alignment methods often take the local coordinate of a patch as the basic local coordinate and then attach other local ordinates to the basic local coordinate patch-by-patch until the basic local coordinate evolves into the global coordinate of the manifold. In this paper, a new progressive alignment method is proposed, where only the local coordinates of the two patches with the largest intersection at the current stage of progressive alignment will be aligned into a larger local coordinate. It is inspired by the famous Huffman coding, where two random events with the smallest probabilities at the current phase will be merged into a random event with a larger probability. Therefore, the proposed method is a Huffman-like alignment method. The experiments on benchmark data show that the proposed method outperforms both the global alignment methods and the other progressive alignment methods and is more robust to the changes of data size. The experiments on real-world data show the feasibility of the proposed method.
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Feng, Rongquan, and Hongfeng Wu. "A Mean Value Formula for Elliptic Curves." Journal of Numbers 2014 (August 25, 2014): 1–5. http://dx.doi.org/10.1155/2014/298632.
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It is proved in this paper that, for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its n-division points is n times that of its y-coordinate.
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Toy, Michael D. "Incorporating Condensational Heating into a Nonhydrostatic Atmospheric Model Based on a Hybrid Isentropic–Sigma Vertical Coordinate." Monthly Weather Review 139, no. 9 (September 2011): 2940–54. http://dx.doi.org/10.1175/mwr-d-10-05015.1.
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Using isentropic coordinates in atmospheric models has the advantage of eliminating the cross-coordinate vertical mass flux for adiabatic flow, and virtually eliminating the associated numerical error in the vertical transport. This is a significant benefit since much of the flow in the atmosphere is approximately adiabatic. Nonadiabatic processes, such as condensational heating, result in a nonzero vertical velocity [Formula: see text] in isentropic coordinates. A method for incorporating condensational heating into a nonhydrostatic atmospheric model based on a hybrid isentropic–sigma vertical coordinate is presented. The model is tested with various 2D moist simulations and the results are compared with those using a traditional terrain-following, height-based sigma coordinate. With the hybrid coordinate, there are improvements in the representation of the developing cloud field in a mountain wave experiment. In a simulation of deep convection, the adaptive hybrid coordinate successfully simulates the turbulent nature of the convection, while maintaining the quasi-Lagrangian nature of the isentropic coordinate in the surrounding dry air. The vertical cross-coordinate mass flux is almost zero in the environmental air, as well as in the stratosphere above the convective tower.
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Gustafsson, Björn, and Jaak Peetre. "Notes on projective structures on complex manifolds." Nagoya Mathematical Journal 116 (December 1989): 63–88. http://dx.doi.org/10.1017/s0027763000001690.
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Consider a Riemann surface X equipped with a projective structure, that is, a covering of X with coordinate neighborhoods U and corresponding (holomorphic) local coordinates {t} such that in the intersection U ∩ U′ of any two such coordinate neighborhoods U and U′ change of local coordinates is mediated by a fractional linear transformation
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Платонова, Marina Platonova, Драпалюк, Mikhail Drapalyuk, Платонов, and Aleksey Platonov. "Justification of kinematic scheme small of the manipulator forestry machines." Forestry Engineering Journal 5, no. 3 (November 15, 2015): 234–39. http://dx.doi.org/10.12737/14652.
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This article discusses the the selection and justification of the reference system and of the generalized coordinates for the kinematic scheme developed by of the manipulator taking into account these factors. The absolute (inertial) coordinate system associated with the center of the support member (eg turntable), joins the arm to the base machine and the subsequent coordinate system formed in accordance with the rules. On the whole, to describe the position of the investigated little detail of the manipulator in the space of generalized coordinates must be four and five right-hand orthogonal coordinate systems.
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Brumberg, V. A. "Relativistic Aspects of Reference Systems and Time Scales." Highlights of Astronomy 9 (1992): 133–39. http://dx.doi.org/10.1017/s1539299600008856.
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Mindful of the fact that any time and space coordinates of General Relativity Theory (GRT) are not, in general, physically meaningful and measurable quantities, one may choose between three possibilities in applying GRT to ephemeris astronomy: 1)avoid coordinates completely, i.e., construct coordinate-independent theories of light propagation and solar system body motion involving the removal of all coordinate-dependent quantities from the present system of astronomical constants;2)use any coordinate system to describe observational procedures and to solve dynamics problems, provided that one and the same coordinates be used for both the kinematics and dynamics of a specific problem;3)adopt IAU recommendations specifying reference systems and time scales to be used in ephemeris astronomy.
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Dong, Guo Jun, Cheng Shun Han, and Shen Dong. "Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component." Key Engineering Materials 364-366 (December 2007): 499–503. http://dx.doi.org/10.4028/www.scientific.net/kem.364-366.499.
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This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.
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Nagy, Benedek, and Khaled Abuhmaidan. "A Continuous Coordinate System for the Plane by Triangular Symmetry." Symmetry 11, no. 2 (February 9, 2019): 191. http://dx.doi.org/10.3390/sym11020191.
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The concept of the grid is broadly used in digital geometry and other fields of computer science. It consists of discrete points with integer coordinates. Coordinate systems are essential for making grids easy to use. Up to now, for the triangular grid, only discrete coordinate systems have been investigated. These have limited capabilities for some image-processing applications, including transformations like rotations or interpolation. In this paper, we introduce the continuous triangular coordinate system as an extension of the discrete triangular and hexagonal coordinate systems. The new system addresses each point of the plane with a coordinate triplet. Conversion between the Cartesian coordinate system and the new system is described. The sum of three coordinate values lies in the closed interval [−1, 1], which gives many other vital properties of this coordinate system.
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Leuenberger, Daniel, Marcel Koller, Oliver Fuhrer, and Christoph Schär. "A Generalization of the SLEVE Vertical Coordinate." Monthly Weather Review 138, no. 9 (September 1, 2010): 3683–89. http://dx.doi.org/10.1175/2010mwr3307.1.
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Abstract Most atmospheric models use terrain-following coordinates, and it is well known that the associated deformation of the computational mesh leads to numerical inaccuracies. In a previous study, the authors proposed a new terrain-following coordinate formulation [the smooth level vertical (SLEVE) coordinate], which yields smooth vertical coordinate levels at mid and upper levels and thereby considerably reduces numerical errors in the simulation of flow past complex topography. In the current paper, a generalization of the SLEVE coordinate is presented by using a modified vertical decay of the topographic signature with height. The new formulation enables an almost uniform thickness of the lowermost computational layers, while preserving the fast transition to smooth levels in the mid and upper atmosphere. This allows for a more consistent and more stable coupling with planetary boundary layer schemes, while retaining the advantages over classic sigma coordinates at upper levels. The generalized SLEVE coordinate is implemented and successfully tested in real-case simulations using an operational nonhydrostatic atmospheric model.
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PILOT, CHRISTOPHER, and SUBHASH RAJPOOT. "A SUPERSPACE OF (1, 1/2)+(1/2, 1) FERMIONIC COORDINATES." International Journal of Modern Physics A 05, no. 19 (October 10, 1990): 3801–9. http://dx.doi.org/10.1142/s0217751x90001628.
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A superspace is constructed in which the elements of the superspace consist of the four Minkowski space-time coordinates and a set of vector-spinor coordinates that belong to the irreducible (1, 1/2)+(1/2, 1) representation of the Lorentz group. It is shown that a translation in the vector-spinor coordinates leads to a vector-spinor coordinate dependent translation in the space-time coordinate xμ. The super covariant derivatives are also constructed.
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Halynskyi, V. P. "Marching algorithm to calculate supersonic flow past a tilting-nose rocket." Technical mechanics 2022, no. 1 (April 26, 2022): 16–25. http://dx.doi.org/10.15407/itm2022.01.016.
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This paper presents a marching algorithm for the calculation of supersonic flow past a tilting-nose rocket. A feature of the algorithm is that the marching direction of supersonic flow calculation for the nose does not coincide with that for the main part of the rocket surface. Because of this, at first flow past the nose is calculated in a cylindrical coordinate system, the flow field parameters being stored at marching cross-sections. The start and the end of the parameter storage interval in the flow field are determined from the condition of the intersection of the bow shock wave with a plane in which an initial flow field is to be specified for the calculation of flow past the main part of the rocket surface. The flow field is interpolated in two stages, First, in the cylindrical coordinate system bound to the main part of the rocket surface in the initial data plane, the radial coordinates of the bow shock wave are determined at meridional sections. From the radial coordinates of points on the rocket surface and the bow shock wave, new computational grid node coordinates are determined at meridional sections in the cylindrical coordinate system of the main part. Using the new computational grid coordinates specified in the cylindrical coordinate system of the main part, old coordinates specified in the cylindrical coordinate system of the nose are determined with the use of expressions that relate the two coordinate systems to each other. The flow parameters at a point with the calculated coordinates are calculated using linear interpolation of the stored flow field parameters in the cylindrical coordinate system bound to the nose. The calculated flow field is used as initial data for the marching calculation of the main part of the rocket, The paper presents the results of calculation of the aerodynamic characteristics of a tilting-nose rocket in a supersonic flow at different values of the nose angle. The proposed algorithm may be used in a prompt calculation of the aerodynamic characteristics of rockets with tilting elements. In doing so, use may be made of a standard program of rocket flow calculation with an added block for the storage and interpolation of the flow field in a tilted cylindrical coordinate system with a shifted origin, which allows the marching direction to be changed.
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Christensen, A. P., and A. A. Shabana. "Exact Modeling of the Spatial Rigid Body Inertia Using the Finite Element Method." Journal of Vibration and Acoustics 120, no. 3 (July 1, 1998): 650–57. http://dx.doi.org/10.1115/1.2893879.
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In the classical finite element literature beams and plates are not considered as isoparametric elements since infinitesimal rotations are used as nodal coordinates. As a consequence, exact modeling of an arbitrary rigid body displacement cannot be obtained, and rigid body motion does not lead to zero strain. In order to circumvent this problem in flexible multibody simulations, an intermediate element coordinate system, which has an origin rigidly attached to the origin of the deformable body coordinate system and has axes which are parallel to the axes of the element coordinate system in the undeformed configuration was introduced. Using this intermediate element coordinate system and the fact that conventional beam and plate shape functions can describe an arbitrary rigid body translation, an exact modeling of the rigid body inertia can be obtained. The large rigid body translation and rotational displacements can be described using a set of reference coordinates that define the location of the origin and the orientation of the deformable body coordinate system. On the other hand, as demonstrated in this investigation, the incremental finite element formulations do not lead to exact modeling of the spatial rigid body mass moments and products of inertia when the structures move as rigid bodies, and such formulations do not lead to the correct rigid body equations of motion. The correct equations of motion, however, can be obtained if the coordinates are defined in terms of global slopes. Using this new definition of the element coordinates, an absolute nodal coordinate formulation that leads to a constant mass matrix for the element can be developed. Using this formulation, in which no infinitesimal or finite rotations are used as nodal coordinates, beam and plate elements can be treated as isoparametric elements.
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Alexandrov, Sergei, Elena Lyamina, and Prashant Date. "A Method of Calculating Principal Stress Trajectories in Powder and Porous Materials Obeying a Piece-wise Linear Yield Criterion." MATEC Web of Conferences 220 (2018): 01002. http://dx.doi.org/10.1051/matecconf/201822001002.
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The present paper deals with the system of equations comprising the pyramid yield criterion together with the stress equilibrium equations under plane strain conditions. The stress equilibrium equations are written relative to a coordinate system in which the coordinate curves coincide with the trajectories of the principal stress directions. The general solution of the system is found giving a relation connecting the two scale factors for the coordinate curves. This relation is used for developing a method for finding the mapping between the principal lines and Cartesian coordinates with the use of a solution of a hyperbolic system of equations. In particular, the mapping between the principal lines and Cartesian coordinates is given in parametric form with the characteristic coordinates as parameters.
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Byeon, Gongkyu, and Sunjin Yu. "Mobile AR Contents Production Technique for Long Distance Collaboration." Webology 19, no. 1 (January 20, 2022): 4491. http://dx.doi.org/10.14704/web/v19i1/web19296.
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This study proposes that mobile AR users with different physical spaces can use one collaboration coordinate by synchronizing each other's coordinates. When each user uses mobile AR remote contents from a distance, it is difficult to maintain the same working environment depending on their physical environment. In order for physical spaces to maintain the same working environment in different situations, the coordinates of the virtual object must be matched to the direction of each client. To solve this problem, this paper proposes a coordinate synchronization technology using a shared coordinate flag. Through this technique, the interaction of all subsequent objects can be performed based on the shared coordinate system of the local client. The user installs a coordinate synchronization flag on a map formed based on each physical space. Through this flag, the location of the virtual object may be synchronized based on each client to perform collaboration. To verify the proposed technology, the mobile AR remote technology was implemented as a painting contents application. Three users synchronized the coordinate system together on three Android mobile devices to verify the feasibility of the technology proposed in this paper.