Relevant bibliographies by topics / Orthogonal coordinates

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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 'Orthogonal coordinates'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Orthogonal coordinates"

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Chen, Huanyang. "Transformation optics in orthogonal coordinates." Journal of Optics A: Pure and Applied Optics 11, no. 7 (April 20, 2009): 075102. http://dx.doi.org/10.1088/1464-4258/11/7/075102.

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Campos, L. M. B. C., and P. J. S. Gil. "On spiral coordinates with application to wave propagation." Journal of Fluid Mechanics 301 (October 25, 1995): 153–73. http://dx.doi.org/10.1017/s0022112095003843.

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We introduce a possibly new system of orthogonal curvilinear coordinates, whose coordinate curves are logarithmic spirals in the plane, supplemented by a cylindrical coordinate for three dimensions. It is shown that plane spiral coordinates form a oneparameter family, with equal scale factors along the two orthogonal coordinate curves, and constant Christoffel symbols. The equations of magnetohydrodynamics, which include those of fluid mechanics, are written in spiral coordinates and used to find a state of magnetohydrostatic equilibrium under a radial gravity field and spiral magnetic field, and to solve the equation of non-dissipative Alfvén waves in a spiral magnetic field in terms of Bessel functions. This exact solution specifies the evolution of wave perturbations (velocity and magnetic field) and energy variables (kinetic and magnetic energy densities and energy flux) with distance, for waves of arbitrary frequency. Both the frequency and the spiral angle are varied in plots of the waveforms, which show the effect on Alfvén wave propagation of three simultaneous effects: change in the mass density of the medium and in the strength and direction of the external magnetic field.
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Redzic, Dragan V. "The operator ∇ in orthogonal curvilinear coordinates." European Journal of Physics 22, no. 6 (September 21, 2001): 595–99. http://dx.doi.org/10.1088/0143-0807/22/6/304.

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Kane, Thomas R., and David A. Levinson. "Orthogonal Curvilinear Coordinates and Angular Velocity." Journal of Applied Mechanics 57, no. 2 (June 1, 1990): 468–70. http://dx.doi.org/10.1115/1.2892013.

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Zhang, Haitao, Shugui Liu, and Xinghua Li. "A study on the key techniques of application of REVO five-axis system in non-orthogonal coordinate measuring machine." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 231, no. 4 (October 1, 2016): 730–36. http://dx.doi.org/10.1177/0954405416666906.

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REVO five-axis system, designed for the orthogonal coordinate measuring machines, must be reconfigured for the application in the non-orthogonal coordinate measuring machines. First, in this article, error sources of the system and components of measurement data are analyzed; then, scale values of coordinate measuring machine axes, which are essential to derive the coordinates of measured points in non-orthogonal coordinate measuring machine, are separated out. Besides, the mathematical model of REVO is established based on the quasi-rigid body theory, from which the measurement results can be evaluated by data derived instead of that returned by the system. The effectiveness of both separation of scale values and mathematical model of REVO is proved by experiments and practice. The research of this article is of great significance to the application of REVO five-axis system in the non-orthogonal coordinate measuring machine.
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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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Paavola, J., and E. M. Salonen. "Coping with Curvilinear Coordinates." International Journal of Mechanical Engineering Education 26, no. 4 (October 1998): 309–17. http://dx.doi.org/10.1177/030641909802600405.

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A systematic method to generate expressions appearing in physics and engineering and valid in curvilinear orthogonal coordinates is presented. The method, which is called ‘the method of local cartesian coordinates’ achieves the same as ‘the method of moving axes’ presented in Love [1] but with a smaller effort and with more familiar mathematical tools. The main idea is: if we have an expression valid in rectangular cartesian coordinates, a corresponding expression for curvilinear orthogonal coordinates can be formed with simple steps. Some general expressions are generated, but the method can be used equally well to produce the desired formulas directly in specific cases. For this purpose, polar coordinates are employed extensively as a demonstration example.
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DOUZE, E. J. "TUTORIAL LINEAR INVERSE FILTERS IN ORTHOGONAL COORDINATES*." Geophysical Prospecting 33, no. 8 (December 1985): 1093–102. http://dx.doi.org/10.1111/j.1365-2478.1985.tb01354.x.

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Aquilanti, Vincenzo, and Simonetta Cavalli. "Coordinates for molecular dynamics: Orthogonal local systems." Journal of Chemical Physics 85, no. 3 (August 1986): 1355–61. http://dx.doi.org/10.1063/1.451223.

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Williams, R. O. "Orthogonal coordinates for systems of many components." Metallurgical Transactions A 16, no. 5 (May 1985): 929–33. http://dx.doi.org/10.1007/bf02814845.

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Dissertations / Theses on the topic "Orthogonal coordinates"

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PIRES, LUIS FERNANDO GONCALVES. "A NUMERICAL METHOD FOR SOLVING FLOWS USING COVARIANT COMPONENTS IN NON-ORTHOGONAL COORDINATES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1994. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=18621@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O trabalho desenvolveu uma metodologia de solução numérica de escoamentos em geometrias complexas, numa formulação incompressível e bi-dimensional. As equações de conservação são discretizas com o emprego da técnica de volumes finitos em coordenadas não ortogonais. Esta técnica mapeia o espaço real num espaço transformado, no qual as fronteiras do domínio de cálculo coincidem com as fronteiras do domínio físico. Os componentes contravariantes da velocidade foram empregados como variáveis dependentes nas equações de conservação de quantidade de movimento. Estas equações foram obtidas em coordenadas não ortogonais pela manipulação algébrica das equações discretizadas para os componentes cartesianos. Este procedimento, que emprega um sistema de coordenadas auxiliar fixo localmente, evita o surgimento dos diversos termos oriundos da curvutura e da não ortogonalidade da malha, que seriam obtidos caso fosse empregada a análise tensorial para a derivação destas equações. O ocoplamento pressão-velocidade é feito utilizando SIMPLEC. O conjunto de equações algébricas resultante é resolvido por um esquema de solução segregado, no qual é empregado um esquema de solução linha-a-a linha(TDMA), com um processo de correção por blocos para acelerar a convergência. A metodologia desenvolvida foi utilizada para solução de diversos problemas visando analisar o seu desempenho. Foram estudados os seguintes casos-escoamento laminar entre dois cilindros, convecção natural entre dois cilidros excêntricos, escoamento induzido numa cavidade trapezoidal pelo movimento de suas bases, escoamento laminar num canal, escoamento axi-simétrico num duto com estrangulamento.Tendo em vista os bons resultados obtidos para testes, pode-se concluir que as opções realizadas para a confeção do esquema desenvolvido foram corretas, pois geraram um algoritimo efeciente e versátil.
A solution method for bi-dimensional incompressibible fluid flow problems in complex geometrics is developed in this work. The method solves the conservation equations in nonorthogonal coordinate system using the finite volumes technique. The contravariant velocities are kept as dependent variables in the momentum equations. These equations are obtained by an algebric manipulation of the discretization equations written in locally fixed coordinate system. This producedure avoids the treatment of the extra terms if the discretization equations for the curvilinear velocities are obtained in the conventional manner. The coupling of pressure and velocities are performed by the SIMPLEC algorithm. The set of algebric equations are solved using an iterative method in conjunction with coefficient update for linerization. In the computer implementation of the proposed scheme a line-by-line algorithm (TDMA) has been employed with a block corretion procedure to enhance the convergence. The method is tested by solving a variety of problems. The problems include-flow between two concentric rotating cylinders, natural convection in an eccentric annuli, driven flow in a trapezoidal cavity with moving lids, laminar flow in a channel, exismetric flow in duct with reduced cross section and laminar and turbulent flow through a tube with an axisimetric constriction. The objetive of these tests is to establish the validity of the proposed scheme and demonstrate its applicability to a wide variety of problems.
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Turner, David Andrew. "The approximation of Cartesian coordinate data by parametric orthogonal distance regression." Thesis, University of Huddersfield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323778.

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This thesis is concerned with the approximation of Cartesian coordinate data by parametric curves and surfaces, with an emphasis upon a technique known as parametric orthogonal distance regression (parametric ODR). The technique has become increasingly popular in the literature over the past decade and has applications in a wide range of fields, including metrology-the science of measurement, and computer aided design (CAD) modelling. Typically, the data are obtained by recording points measured in the surface of some physical artefact, such as a manufactured part. Parametric ODR involves minimizing the shortest distances from the data to the curve or surface in some norm. Under moderate assumptions, these shortest distances are orthogonal projections from the data onto the approximant, hence the nomenclature ODR. The motivation behind this type of approximation is that, by using a distance-based measure, the resulting best fit curve or surface is independent of the position or orientation of the physical artefact from which the data is obtained. The thesis predominately concerns itself with parametric ODR in a least squares setting, although it is indicated how the techniques described can be extended to other error measures in a fairly straightforward manner. The parametric ODR problem is formulated mathematically, and a detailed survey of the existing algorithms for solving it is given. These algorithms are then used as the basis for developing new techniques, with an emphasis placed upon their efficiency and reliability. The algorithms (old and new) detailed in this thesis are illustrated by problems involving well-known geometric elements such as lines, circles, ellipse and ellipsoids, as well as spline curves and surfaces. Numerical considerations specific to these individual elements, including ones not previously reported in the literature, are addressed. We also consider a sub-problem of parametric ODR known as template matching, which involves mapping in an optimal way a set of data into the same frame of reference as a fixed curve or surface.
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FARIAS, Vera Solange de Oliveira. "Difusão 3d em sólidos com forma arbitrária Usando coordenadas generalizadas." Universidade Federal de Campina Grande, 2011. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/264.

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Submitted by Dilene Paulo (dilene.fatima@ufcg.edu.br) on 2018-02-07T13:41:46Z No. of bitstreams: 1 VERA SOLANGE DE OLIVEIRA FARIAS – TESE PPGEP 2011.pdf: 7179434 bytes, checksum: 4a30c9a95f4a089e00fa550fbf1b42b8 (MD5)
Made available in DSpace on 2018-02-07T13:41:46Z (GMT). No. of bitstreams: 1 VERA SOLANGE DE OLIVEIRA FARIAS – TESE PPGEP 2011.pdf: 7179434 bytes, checksum: 4a30c9a95f4a089e00fa550fbf1b42b8 (MD5) Previous issue date: 2011-04-29
CNPq
Este trabalho apresenta a solução numérica da equação de difusão tridimensional em regime transiente, para um domínio arbitrário. Para atingir os objetivos, a equação de difusão foi discretizada usando coordenadas generalizadas via método dos volumes finitos com uma formulação totalmente implícita, para condições de contorno de equilíbrio e convectiva. Para cada passo no tempo, o sistema de equações obtido para uma dada malha estruturada foi resolvido pelo método de Gauss-Seidel. O código computacional foi desenvolvido em FORTRAN, usando o estúdio CVF 6.6.0, na plataforma Windows Vista. A solução proposta foi validada usando soluções analíticas e numéricas da equação de difusão para várias geometrias, permitindo validar malhas ortogonais e não-ortogonais. A análise e comparação dos resultados mostraram que a solução proposta forneceu resultados coerentes para todos os casos investigados. O código computacional desenvolvido foi aplicado na simulação, a partir de dados experimentais da secagem de telhas cerâmicas para as seguintes condições experimentais: temperaturas de 55,6 °C, 69,7 °C, 82,7 °C e 98,6 °C e teor de umidade inicial variando de 0,2345 até 0,2405 (b.s.). A simulação tornou possível determinar o coeficiente de difusão efetivo em função da razão de umidade e da temperatura do ar de secagem e também o valor do coeficiente de transferência convectivo de massa correspondente para cada temperatura.
This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. The diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium and convective boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. A computational code in FORTRAN, using the CFV 6.6.0 Studio, in a Windows Vista platform was developed. The proposed solution was validated by analytical and numerical solutions of the diffusion equation for several geometries. The geometries tested enabled to validate both orthogonal and non-orthogonal meshes. The analysis and comparison of the results showed that the proposed solution provides correct results for all cases investigated. The developed computational code was applied in the simulation, using experimental data of the drying of ceramic roof tiles, for the following experimental conditions: temperature from 55.6; 69.7; 82.7; 72.8 and 98.7 °C, initial moisture content from 0.2345 up to 0.2405 (d.b.). The simulation makes it possible to determine an expression for the diffusion coefficient as a function of the moisture content and temperature of the drying air, and also the value of the convective mass transfer coefficient corresponding to each temperature.
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Smith, M. A. "Simulating multiplicative neural processes in non-orthogonal coordinate systems, a three-dimensional tensor model of the VOR." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq22877.pdf.

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Pearson, Richard Vincent. "Simulation of shallow water hydrodynamics and species transport using elliptically generated non-orthogonal boundary-fitted coordinate systems." Thesis, University of Salford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308220.

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Elkourdi, Mohamed. "Machine Learning, Game Theory Algorithms, and Medium Access Protocols for 5G and Internet-of-Thing (IoT) Networks." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7782.

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In the first part of this dissertation, a novel medium access protocol for the Internet of Thing (IoT) networks is introduced. The Internet of things (IoT), which is the network of physical devices embedded with sensors, actuators, and connectivity, is being accelerated into the mainstream by the emergence of 5G wireless networking. This work presents an uncoordinated non-orthogonal random-access protocol, which is an enhancement to the recently introduced slotted ALOHA- NOMA (SAN) protocol that provides high throughput, while being matched to the low complexity requirements and the sporadic traffic pattern of IoT devices. Under ideal conditions it has been shown that slotted ALOHA-NOMA (SAN), using power- domain orthogonality, can significantly increase the throughput using SIC (Successive Interference Cancellation) to enable correct reception of multiple simultaneous transmitted signals. For this ideal performance, the enhanced SAN receiver adaptively learns the number of active devices (which is not known a priori) using a form of multi-hypothesis testing. For small numbers of simultaneous transmissions, it is shown that there can be substantial throughput gain of 5.5 dB relative to slotted ALOHA (SA) for 0.07 probability of transmission and up to 3 active transmitters. As a further enhancement to SAN protocol, the SAN with beamforming (BF-SAN) protocol was proposed. The BF-SAN protocol uses beamforming to significantly improve the throughput to 1.31 compared with 0.36 in conventional slotted ALOHA when 6 active IoT devices can be successfully separated using 2×2 MIMO and a SIC (Successive Interference Cancellation) receiver with 3 optimum power levels. The simulation results further show that the proposed protocol achieves higher throughput than SAN with a lower average channel access delay. In the second part of this dissertation a novel Machine Learning (ML) approach was applied for proactive mobility management in 5G Virtual Cell (VC) wireless networks. Providing seamless mobility and a uniform user experience, independent of location, is an important challenge for 5G wireless networks. The combination of Coordinated Multipoint (CoMP) networks and Virtual- Cells (VCs) are expected to play an important role in achieving high throughput independent of the mobile’s location by mitigating inter-cell interference and enhancing the cell-edge user throughput. User- specific VCs will distinguish the physical cell from a broader area where the user can roam without the need for handoff, and may communicate with any Base Station (BS) in the VC area. However, this requires rapid decision making for the formation of VCs. In this work, a novel algorithm based on a form of Recurrent Neural Networks (RNNs) called Gated Recurrent Units (GRUs) is used for predicting the triggering condition for forming VCs via enabling Coordinated Multipoint (CoMP) transmission. Simulation results show that based on the sequences of Received Signal Strength (RSS) values of different mobile nodes used for training the RNN, the future RSS values from the closest three BSs can be accurately predicted using GRU, which is then used for making proactive decisions on enabling CoMP transmission and forming VCs. Finally, the work in the last part of this dissertation was directed towards applying Bayesian games for cell selection / user association in 5G Heterogenous networks to achieve the 5G goal of low latency communication. Expanding the cellular ecosystem to support an immense number of connected devices and creating a platform that accommodates a wide range of emerging services of different traffic types and Quality of Service (QoS) metrics are among the 5G’s headline features. One of the key 5G performance metrics is ultra-low latency to enable new delay-sensitive use cases. Some network architectural amendments are proposed to achieve the 5G ultra-low latency objective. With these paradigm shifts in system architecture, it is of cardinal importance to rethink the cell selection / user association process to achieve substantial improvement in system performance over conventional maximum signal-to- interference plus noise ratio (Max-SINR) and Cell Range Expansion (CRE) algorithms employed in Long Term Evolution- Advanced (LTE- Advanced). In this work, a novel Bayesian cell selection / user association algorithm, incorporating the access nodes capabilities and the user equipment (UE) traffic type, is proposed in order to maximize the probability of proper association and consequently enhance the system performance in terms of achieved latency. Simulation results show that Bayesian game approach attains the 5G low end-to-end latency target with a probability exceeding 80%.
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Brum, Fabiano Becker. "APLICAÇÃO DA TRANSFORMAÇÃO ORTOGONAL NO GEORREFERENCIAMENTO COM DIVISÃO DE ÁREA." Universidade Federal de Santa Maria, 2008. http://repositorio.ufsm.br/handle/1/9525.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The Geodesy methods and equipments progress brings with himself the growing need on geodetic surveys. Thereby, it is possible to make compatible any surveys with no extension boundary like from plane models and with no points overlap. These surveys are usually from geodetic satellites for that specific purpose. However, there are cases under precision restriction by nature of these systems, as well as physical conditions lack and equipments deficiency disables such operations. Thus, it becomes necessary to take place surveys from a topographical origin to a geocentric origin. To other cases, it is not enough just to know the geodetic coordinates but it is necessary to know its equivalent ones in the topographical plan, mostly to section and calculus of areas besides point locations. In these cases a solution of great use is the transformation of the geocentric coordinates to the UTM Projection plane cartographic coordinates, usually being ignored the deformations. Therefore it is a mistaken solution. Among the appropriate solutions to transform coordinates between surfaces from a topographical origin to a geocentric origin it is the Orthogonal Transformation. This method is more concise than the traditional Puissant´s methodology and to make possible the conversion of topographical coordinateds to geocentric coordinates and vice-versa. In this work the precision of Orthogonal Transformation method was compared initially with the Puissant´s method. Also were compared the differences among areas calculated from the UTM cartographic plan coordinates and topographical coordinates, besides having established the position discrepancy among boundary points calculated in a certain plan and implanted in other one without the true conversions. The results shows that the Orthogonal Transformation method precision is equivalent to Puissant´s method for observed ranges. It was possible to note that the values to areas calculated from coordinates related to models or different surfaces presents discrepancy. The areas section and estimation from the UTM cartographic projection plane coordinates, even with scale factor and elevation corrections, has been different to the area from the local topographical plan, although it was similar when under corrections. Points from section of geodetic areas can not to have implant in the topographical plane under use of UTM cartographic projection plane coordinates due to the position difference between it and the topographical coordinates. The more appropriate solution, due to good precision and easiness to section and estimate geodetic areas from geocentric coordinates, is the change to topographical ones using the Orthogonal Transformation. The Orthogonal Transformation of Coordinates is a practice and quick solution to make geodetic points from topographical surveys as well as to plot geodetic points in the topographical plan, and it is possible to implement it in the Electronic Total Stations in a easy way.
O avanço da geodésia, em seus métodos e equipamentos traz consigo a crescente necessidade da realização de levantamentos georreferenciados. Assim é possível compatibilizar vários levantamentos sem limites de extensão impostos pelo modelo plano e sem a sobreposição de pontos. Estes levantamentos geralmente são executados pelo rastreio de satélites que operam para este fim. Contudo, em certos casos as limitações de precisão e acurácia impostos pelos princípios destes sistemas, bem como a falta de condições físicas e deficiência de equipamentos impossibilita tal operação. Torna-se necessário então realizar levantamentos com a origem topocêntrica e transforma-la em geocêntrica. Em outros casos, não basta conhecer somente as coordenadas georreferenciadas, sendo necessário conhecer suas equivalentes no plano topográfico, principalmente para calcular e dividir áreas e implantar pontos no plano local. Nestes casos uma solução de grande utilização é transformação das coordenadas elipsoidicas geocêntricas em coordenadas planas associadas ao plano da Projeção Cartográfica UTM, geralmente ignorando-se as deformações, portanto consistindo em uma solução equivocada. Entre as soluções adequadas para a conversão de coordenadas de uma superfície para outra quando a origem dos sistemas difere entre topocêntrica e geocêntrica é a Transformação Ortogonal. Este método, além de ser mais sucinto que a metodologia de Puissant tradicionalmente utilizada permite a conversão tanto de coordenadas topocêntricas em geocêntricas bem como o inverso. Neste trabalho inicialmente se comparou a precisão do método da Transformação Ortogonal com o método de Puissant. Também foram comparadas as diferenças entre áreas calculadas apartir de coordenadas no plano cartográfico UTM e coordenadas topocêntricas, além de estabelecida a diferença de posição entre pontos de divisa calculados em um plano e implantados em outro sem as devidas conversões. O resultados obtidos demonstraram que a precisão do método de Transformação Ortogonal nas distancias observadas equivale com a metodologia de Puissant. Foi possível observar que os valores referentes a áreas quando calculadas em relação a coordenadas associadas a modelos ou superfícies diferentes apresentam variação. O cálculo e divisão de áreas utilizando coordenadas planas no plano da projeção cartográfica UTM, mesmo com correções de fator de escala e elevação diferiu da área no plano topográfico local, embora tenha se aproximado quando efetuadas correções. Pontos de divisão de áreas georreferenciadas não devem ser implantados no plano topográfico local utilizando-se coordenadas planas no plano da projeção cartográfica UTM, pois existe diferença de posição entre estas e as coordenadas topográficas. A solução mais adequada pela precisão e facilidade para cálculo e divisão de áreas georreferenciadas a partir de coordenadas geocêntricas é a conversão destas para topocêntricas pela transformação ortogonal de coordenadas. A transformação ortogonal de coordenadas constitui-se de uma solução prática e rápida tanto para o georreferenciamento de pontos oriundos de levantamentos topográficos, bem como para implantação de pontos georreferenciados no plano topográfico local, podendo ser inclusive facilmente implementado em estações totais topográficas.
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Chiang, Chen Kun, and 蔣震坤. "Computations of transonic flow with pressure-correction method and collocated non-orthogonal coordinates." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/71908179084123621085.

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Cochran, Caroline. "THE EQUIVALENCE PROBLEM FOR ORTHOGONALLY SEPARABLE WEBS ON SPACES OF CONSTANT CURVATURE." 2011. http://hdl.handle.net/10222/14191.

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This thesis is devoted to creating a systematic way of determining all inequivalent orthogonal coordinate systems which separate the Hamilton-Jacobi equation for a given natural Hamiltonian defined on three-dimensional spaces of constant, non-zero curvature. To achieve this, we represent the problem with Killing tensors and employ the recently developed invariant theory of Killing tensors. Killing tensors on the model spaces of spherical and hyperbolic space enjoy a remarkably simple form; even more striking is the fact that their parameter tensors admit the same symmetries as the Riemann curvature tensor, and thus can be considered algebraic curvature tensors. Using this property to obtain invariants and covariants of Killing tensors, together with the web symmetries of the associated orthogonal coordinate webs, we establish an equivalence criterion for each space. In the case of three-dimensional spherical space, we demonstrate the surprising result that these webs can be distinguished purely by the symmetries of the web. In the case of three-dimensional hyperbolic space, we use a combination of web symmetries, invariants and covariants to achieve an equivalence criterion. To completely solve the equivalence problem in each case, we develop a method for determining the moving frame map for an arbitrary Killing tensor of the space. This is achieved by defining an algebraic Ricci tensor. Solutions to equivalence problems of Killing tensors are particularly useful in the areas of multiseparability and superintegrability. This is evidenced by our analysis of symmetric potentials defined on three-dimensional spherical and hyperbolic space. Using the most general Killing tensor of a symmetry subspace, we derive the most general potential “compatible” with this Killing tensor. As a further example, we introduce the notion of a joint invariant in the vector space of Killing tensors and use them to characterize a well-known superintegrable potential in the plane. xiii
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Chao, Yi-Chuan, and 趙翊荃. "Power Allocation for Non-orthogonal Precoded Coordinated Multi-point Systems." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/e4rtgg.

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碩士
國立交通大學
電控工程研究所
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We propose a mixed precoding strategy for CoMP systems, which allows that the orthogonal Block Diagonalization (BD) and the non-orthogonal Maximum Ratio Transmission (MRT) techniques can be simultaneously used for reducing network backhaul loading. We formulated the issues into two optimization problems. Namely, 1) minimizing the backhaul loading under a minimum target rate constraint and 2) maximizing the sum rate under a minimum target rate constraint. We derive closed-form solutions for these two problems and verify them by the Matlab CVX tool box. The de- rived closed-form solutions can signicantly reduce the computational time compared to the CVX. Simulation results show that the proposed precoding schemes can signicantly reduce the backhaul loading and outperform con- ventional schemes in terms of outage probability in achieving the minimum rate constraint.
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Books on the topic "Orthogonal coordinates"

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Michelassi, V. Solution of the steady state incompressible Navier-Stokes equations in curvilinear non orthogonal coordinates. Rhode Saint Genese, Belgium: von Karman Institute for Fluid Dynamics, 1986.

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Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. 2nd ed. Paris: Gauthier-Villars, 1991.

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Book chapters on the topic "Orthogonal coordinates"

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Aguilera-Navarro, V. C. "Quantum Many-Body Systems: Orthogonal Coordinates." In Condensed Matter Theories, 309–15. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4613-0605-4_32.

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Jog, C. S. "The Equations of Equilibrium in Orthogonal Curvilinear Reference Coordinates." In Methods and Tastes in Modern Continuum Mechanics, 385–95. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-1884-5_25.

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Samarskii, Aleksandr A., and Evgenii S. Nikolaev. "Methods for Solving Elliptic Equations in Curvilinear Orthogonal Coordinates." In Numerical Methods for Grid Equations, 447–87. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-9142-4_11.

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Mitsuishi, Takashi. "Defects in the Defuzzification of Periodic Membership Functions on Orthogonal Coordinates and a Solution." In Fuzzy Logic in Intelligent System Design, 361–70. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67137-6_40.

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Xiaoan, Ren. "Elastic-Plastic Constitutive Equation Using Non-Orthogonal Curvilinear Coordinates and its Application in Numerical Methods." In Computational Mechanics ’86, 711–17. Tokyo: Springer Japan, 1986. http://dx.doi.org/10.1007/978-4-431-68042-0_99.

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Yang, H. Q., K. T. Yang, and J. R. Lloyd. "Finite-Difference Calculations of Three-Dimensional Laminar Buoyant Flows Based on Curvilinear Non-orthogonal Coordinates." In Computational Mechanics ’88, 1605–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61381-4_424.

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Cossali, Gianpietro Elvio, and Simona Tonini. "Orthogonal Curvilinear Coordinate Systems." In Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems, 89–148. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49274-8_4.

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Li, Tian, Xuekun Hao, Guoyan Li, Hui Li, and Xinwei Yue. "Non-orthogonal Multiple Access in Coordinated LEO Satellite Networks." In Communications in Computer and Information Science, 65–78. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1925-3_5.

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Guo, Yecai, and Xueqing Zhao. "Balanced Orthogonal Multi-Wavelet Blind Equalization Algorithm Based on Coordinate Transformation." In Communications in Computer and Information Science, 268–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19853-3_39.

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Schreiber, Tom, and Alain Tissier. "Synthetic Transcription Activator-Like Effector-Activated Promoters for Coordinated Orthogonal Gene Expression in Plants." In Molecular Pharming, 25–42. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2018. http://dx.doi.org/10.1002/9781118801512.ch2.

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Conference papers on the topic "Orthogonal coordinates"

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Zernov, Nikolay N., and Vadim E. Gherm. "Gaussian Beams in Orthogonal Full Ray Trajectory Coordinates." In 2018 2nd URSI Atlantic Radio Science Meeting (AT-RASC). IEEE, 2018. http://dx.doi.org/10.23919/ursi-at-rasc.2018.8471500.

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Lu, Shengnan, Xilun Ding, and Gregory S. Chirikjian. "Rotations in a Non-Orthogonal Frame." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85862.

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This paper is concerned with describing the space of matrices that describe rotations in non-orthogonal coordinates. In scenarios such as in crystallography, conformational analysis of polymers, and in the study of deployable mechanisms and rigid origami, non-orthogonal reference frames are natural. For example, non-orthogonal vectors in the direction of atomic bonds in a molecule, the lattice coordinates of a crystal, or the directions of links in a mechanism are intrinsic. In these cases it is awkward to impose an artificial orthonormal reference frame rather than choosing one that is defined by the geometry of the object being studied. With these applications in mind, we fully characterize the space of all possible non-orthogonal rotations. We find that in the 2D case, this space is a three-dimensional subset of the special linear group, SL(2, R), which is itself a three-dimensional Lie group. In the 3D case we find that the space of nonorthogonal rotations is a seven-dimensional subspace of SL(3, R), which is an eight-dimensional Lie group. In the 2D case we use the Iwasawa decomposition to fully characterize the solution. In the 3D case we parameterize this seven-dimensional space by conjugating elements of the rotation group SO(3) by elements of a discrete family of of four-parameter subgroups of GL(3, R), and using this we derive an inversion formula to extract classical orthogonal rotations from those expressed in non-orthogonal coordinates.
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Tong, Chaofeng, and Yanqiu Meng. "A Numerical Shallow Water Model Based on the Non-Orthogonal Curvilinear Grids." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92424.

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According to the transformation relationships between the Cartesian coordinates and the general curvilinear coordinates, the governing equations of the model are derived as the forms in the general curvilinear coordinates from those in the Cartesian coordinates. In the model, the contravariant velocities are adopted as the independent variables in non-orthogonal grids. The momentum equations keep strongly conservative forms and the boundary conditions can be given easily. The model used a staggered grid arrangement. The discrete equations are solved using the SIMPLIC algorithms. The numerical model has been validated against the bifurcated flow of which the diversion angle is 30 degree. Compared with the measured values, the numerical shallow water model is shown to be capable of simulating the water domains with irregular boundaries.
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Feeny, B. F., P. W. Sternberg, and C. J. Cronin. "Complex Modal Decomposition Applied to Nematode Posturing." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87800.

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The complex orthogonal decomposition (COD), a process of extracting complex modes from complex ensemble data, is summarized, as is the use of complex modal coordinates. A brief assessment is made on how small levels of noise affect the decomposition. The decomposition is applied to the posturing of a wild Caenorhabditis elegans nematode. The decomposition indicates that the worm has a multi-modal posturing behavior, involving at least a dominant locomotion mode and a secondary, steering mode. The locomotion mode is closer to a pure traveling waveform than the steering mode. The characteristic wavelength of the primary mode was estimated in the complex plane. Frequency was obtained from the complex modal coordinate’s complex whirl rate of the complex modal coordinate, and from its fast Fourier transform.
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Gao, Shanguo, Jiyuan Liu, Yaohui Lyu, Jun Song, and Minghua Lu. "A new and fast coupled method in hybric orthogonal curvilinear coordinates." In OCEANS 2017 - Aberdeen. IEEE, 2017. http://dx.doi.org/10.1109/oceanse.2017.8084890.

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Avakov, Vladimir A. "Fatigue Reliability Functions in Semilogarithmic Coordinates." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0009.

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Abstract In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (lnN-lnS). Here, a similar transformation is established using a semi logarithmic (lnN-S) coordinate system. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life distribution.
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Mukira, David. "Finite difference analysis of three dimensional natural convection in non-orthogonal coordinates." In 6th Joint Thermophysics and Heat Transfer Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1994. http://dx.doi.org/10.2514/6.1994-1972.

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Yang, Can, Zheng Chen, Bin Yao, and Bobo Helian. "A Strictly Defined Orthogonal Global Task Coordinate Frame and its Contouring Control Application on Biaxial Systems." In ASME 2019 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/dscc2019-8988.

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Abstract In this paper, a strictly defined new orthogonal global task coordinate frame (NGTCF) based on the false position method is proposed for precision contouring control of biaxial systems. In contrast to the existed global task coordinate frame (GTCF), the value of the normal coordinate in NGTCF directly represents the contour error, rather than the first-order approximation. Moreover, different from the conventional GTCF just suitable for contours with explicit shape functions, the proposed NGTCF can be utilized in various complex contours. The false position method is adopted to calculate the curve coordinates of actual points in NGTCF. Then an adaptive robust controller (ARC) is designed to deal with the effects of strong coupling of the system dynamics in the task space and modeling uncertainties. The proposed NGTCF-based ARC contouring control strategy is tested on a linear motor driven biaxial industrial gantry. Experiments under different contouring tasks with high-speed and large-curvature are conducted to verify the effectiveness of the proposed method, and the experimental results confirm that the excellent contouring performance of the proposed approach can be achieved.
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YANG, H., SAMI HABCHI, and ANDRZEJ PRZEKWAS. "A general strong conservation formulation of Navier-Stokes equationsin non-orthogonal curvilinear coordinates." In 30th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-187.

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Mughal, M. "Stability Analysis of Complex Wing Geometries: Parabolised Stability Equations in Generalised Non-Orthogonal Coordinates." In 36th AIAA Fluid Dynamics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2006. http://dx.doi.org/10.2514/6.2006-3222.

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Reports on the topic "Orthogonal coordinates"

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Rensink, M. E., and T. D. Rognlien. Mapping of orthogonal 2D flux coordinates for two nearby magnetic X-points to logically rectangular domains. Office of Scientific and Technical Information (OSTI), May 2017. http://dx.doi.org/10.2172/1637587.

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Colella, P., D. T. Graves, and J. A. Greenough. A second-order method for interface reconstruction in orthogonal coordinate systems. Office of Scientific and Technical Information (OSTI), January 2002. http://dx.doi.org/10.2172/834475.

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