O sistema de referência da rede de satélites GPS (Global Positioning System) é o sistema geocêntrico World Geodetic System 1984 (WGS-84). As coordenadas de pontos obtidos usando o GPS são definidas para este sistema de referência. Entretanto, o engenheiro ao utilizar as coordenadas destes pontos geodésicos, requer que estejam referenciados no sistema local. O sistema local está associado a um elipsóide que melhor se adapta à área de trabalho. No Brasil, é adotado o sistema não geocêntrico South American Datum SAD-69. Uma vez que o WGS-84 é um sistema geocêntrico e o local não é, algumas transformações de coordenadas são necessárias. Os parâmetros de transformação das coordenadas entre os dois sistemas, publicados pelo IBGE para todo o Brasil, apresentam divergências se comparados a parâmetros obtidos para uma determinada região. Assim este trabalho tem por finalidade discutir alguns métodos possíveis de serem empregados para determinar os parâmetros de transformação entre os sistemas WGS-84 e o SAD-69, para a região de São Carlos-SP. / The reference system of the satellites network GPS (Global Positioning System) is the geocentric system WGS-84. When the coordinates of a point in the Earth’s surface are computed by using a GPS receiver, they are computed for this reference system. However, for practical purposes is desirable that the computed point be in the local coordinate system of the user, which is associated to an ellipsoid that best fits the region of work. In the Brazil, is accepted the system geocentric not South American Datum 1969 (SAD-69). Considering that the WGS-84 system is a geocentric system and that the local system is not, it is necessary to perform some transformation of coordinates. The transformation parameters of the coordinates between two system, published by IBGE all over Brazil, present regional divergency. From this point of view, this paper discus some methods that can be applied to determine the transformation parameters between WGS-84 and SAD-69 systems, for the region of São Carlos-SP.

O sistema de referência da rede de satélites GPS (Global Positioning System) é o sistema geocêntrico World Geodetic System 1984 (WGS-84). As coordenadas de pontos obtidos usando o GPS são definidas para este sistema de referência. Entretanto, o engenheiro ao utilizar as coordenadas destes pontos geodésicos, requer que estejam referenciados no sistema local. O sistema local está associado a um elipsóide que melhor se adapta à área de trabalho. No Brasil, é adotado o sistema não geocêntrico South American Datum SAD-69. Uma vez que o WGS-84 é um sistema geocêntrico e o local não é, algumas transformações de coordenadas são necessárias. Os parâmetros de transformação das coordenadas entre os dois sistemas, publicados pelo IBGE para todo o Brasil, apresentam divergências se comparados a parâmetros obtidos para uma determinada região. Assim este trabalho tem por finalidade discutir alguns métodos possíveis de serem empregados para determinar os parâmetros de transformação entre os sistemas WGS-84 e o SAD-69, para a região de São Carlos-SP. / The reference system of the satellites network GPS (Global Positioning System) is the geocentric system WGS-84. When the coordinates of a point in the Earth’s surface are computed by using a GPS receiver, they are computed for this reference system. However, for practical purposes is desirable that the computed point be in the local coordinate system of the user, which is associated to an ellipsoid that best fits the region of work. In the Brazil, is accepted the system geocentric not South American Datum 1969 (SAD-69). Considering that the WGS-84 system is a geocentric system and that the local system is not, it is necessary to perform some transformation of coordinates. The transformation parameters of the coordinates between two system, published by IBGE all over Brazil, present regional divergency. From this point of view, this paper discus some methods that can be applied to determine the transformation parameters between WGS-84 and SAD-69 systems, for the region of São Carlos-SP.

Este trabalho tem o objetivo de apresentar a revisão do clássico procedimento geodésico, adotado pela DSG - Diretoria do Serviço Geográfico do Exército, para o cálculo do transporte de coordenadas geográficas-geodésicas dos vértices da rede fundamental implantados no Brasil entre 1940 e 1970, antes do surgimento das técnicas de posicionamento. Neste trabalho, uma aplicação prática do método foi desenvolvida, empregando-o na solução de um problema específico da projeção cartográfica UTM, que é o transporte de coordenadas na passagem do limite entre fusos. Para isto foi escolhida uma área localizada na divisa entre os municípios de São Carlos e Ibaté no Estado de São Paulo, atravessada pelo meridiano de 48º, limite entre os fusos 22 e 23 desta projeção. Na área implantou-se duas bases geodésicas determinadas através de técnicas de observação do Sistema de Posicionamento Global, sendo uma base posicionada no fuso 22 e outra no fuso 23. Inicialmente, entre estas bases, desenvolveu-se uma poligonal de adensamento constituída de 7 vértices, que teve seus lados e ângulos observados com estação total, possibilitando o cálculo de suas coordenadas geográficas-geodésicas pelo método clássico em pauta. Numa segunda etapa do trabalho, foram observados com receptores GPS de uma freqüência, os 8 vetores relativos aos lados da poligonal de adensamento, empregando o método diferencial estático. Cada um dos 7 vértices da poligonal teve suas coordenadas geográficas-geodésicas determinadas por pós-processamento, permitindo a comparação entre os resultados obtidos nos dois procedimentos utilizados. Na etapa final, comparando-se os resultados obtidos pelos dois diferentes métodos, pode-se verificar que apesar da técnica em desuso empregada pelo método clássico, ela conduziu os cálculos com o rigor e aproximação adequados, produzindo coordenadas de valores significativamente próximos aos valores determinados pela mais avançada tecnologia empregada nos dias atuais que é a tecnologia GPS. / The main objective of this job, is a review about the classic mathematical proceedings applied to the polygonals which cross the fuses limits of the Universal Traverse of Mercator projection. In this cases, the poligonal begin to be measured in a baseline located in a private fuse and finishs in a different baseline located in the next fuse, where the coordinates are refered to a different origin. In this conditions, the rules of UTM projection defines a range of 30 minutes over the fuse limit, where the coordinates can be calculated either in the first or int the second fuse. However, there are specials situations where the polygonals has a baseline for ending so far over this 30 minutes range. In this cases, the mathematical proceeding is to calculate the transportation of geodetic-coordinates in the ellipsoid obtaining the latitude \'fi\' and the longitude \'lâmbda\' for all points in the polygonal and after, making the transformation, observing in which fuse each point is positioned, to get the UTM planned coordinates. The Global Positioning System will be used in this job to do the control over the classic measurements and over the classic calculated coordinates, offering conditions to the comparison between them.

Esta dissertação tem por objetivo testar procedimentos para analise da geometria dos aeródromos do estudo através de levantamento topográfico com o uso do nível e GPS (Global Positioning System). Os testes foram conduzidos em quatro aeródromos do Estado de São Paulo, administrados pelo DAESP (Departamento Aeroviário do Estado de São Paulo), a saber: Araraquara, Bauru, Marília e São José do Rio Preto. Foram analisados as declividades longitudinais, transversais, comprimento e largura da pista e a altitude do ponto de referência. O documento normativo usado como referência foi o \"Anexo XIV\" (Aerodromes) da ICAO (International Civil Aviation Organization). Foram feitos levantamentos cadastrais dos projetos originais dos aeródromos e levantamentos de campo. Em cada aeródromo o receptor GPS foi instalado em ponto de coordenadas e altitude conhecidas. Na etapa final foram comparados os dados de projeto com os valores encontrados no campo. Os valores encontrados mostraram algumas variações com os de projeto, principalmente quanto à declividade transversal onde a norma recomenda que seja de 1,5%. Foram encontrados valores com declividades menores que esse e até valores negativos. O sistema GPS mostrou-se, eficiente e preciso para esse tipo de levantamento. / The objective of this work is to test procedures for analysis of the geometry of aerodromes, through topographical survey with level and GPS (Global Positioning System) instrument. The tests were led in four aerodromes of the São Paulo State, administered by DAESP (Departamento Aeroviário do Estado de São Paulo), namely: Araraquara, Bauru, Marília and São José do Rio Preto. The longitudinal slopes, transverse slopes, length of runway, width of runway, the elevation of reference point were analyzed. The normative document used as reference was the Annex XIV (Aerodromes) of ICAO (International Civil Aviation Organization). For each aerodrome it was made a cadastral research of the original project and field survey. For each aerodrome the GPS receiver was located in a point of known coordinates and altitude. In the final stage the original project data were compared with the ones found in the field survey. The values from field have some variations in relation to those found in the project mainly with in the case of transverse slope where the norm recommends that it must be 1,5%. The survey had shown values less than 1,5% and also negative slopes. The GPS system has shown to be efficient and enough accurate for this kind of survey.

This thesis presents the first-known exact solutions for vibration of stepped circular Mindlin plates. The considered circular plate is of several step-wise variation in thickness in the radial direction. The Mindlin first order shear deformable plate theory is employed to derive the governing differential equations for the annular and circular segments. The exact solutions to these differential equations may be expressed in terms of the Bessel functions of the first and second kinds and the modified Bessel functions of the first and second kinds. The governing homogenous system of equations is assembled by implementing the essential and natural boundary conditions and the segment interface conditions. Vibration solutions are presented for circular Mindlin plates of different edge support conditions and various combinations of step-wise thickness variations. These exact vibration results may serve as important benchmark values for researchers to validate their numerical methods for such circular plate problems / Master of Engineering (Civil)

In General Relativity, the Einstein field equations allow us to study the evolution of a spacelike 3-manifold, provided that its metric and extrinsic curvature satisfy a system of geometric constraint equations. The so-called Einstein constraint equations, arise as a consequence of the fact that the 3-manifold in question is necessarily a submanifold of the spacetime its evolution defines. This thesis is devoted to a study of the structure of the Einstein constraint system in the special case when the spacelike 3-manifold also satisfies the quasispherical ansatz of Bartnik [B93]. We make no mention of the generality of this gauge; the extent to which the quasispherical ansatz applies remains an open problem. After imposing the quasispherical gauge, we give an argument to show that the resulting Einstein constraint system may be viewed as a coupled system of partial differential equations for the parameters describing the metric and second fundamental form. The hencenamed quasisperical Einstein constraint system, consists of a parabolic equation, a first order elliptic system and (essentially) a system of ordinary differential equations. The question of existence of solutions to this system naturally arises and we provide a partial answer to this question. We give conditions on the initial data and prescribable fields under which we may conclude that the quasispherical Einstein constraint system is uniquley solvable, at least in a region surrounding the unit sphere. The proof of this fact is centred on a linear iterative system of partial differential equations, which also consist of a parabolic equation, a first order elliptic system and a system of ordinary differential equations. We prove that this linear system consistently defines a sequence, and show via a contraction mapping argument, that this sequence must converge to a fixed point of the iteration. The iteration, however, has been specifically designed so that any fixed point of the iteration coincides with a solution of the quasispherical Einstein constraints. The contraction mapping argument mentioned above, relies heavily on a priori estimates for the solutions of linear parabolic equations. We generalise and extend known results 111 concerning parabolic equations to establish special a priori estimates which relate a useful property: the L2-Sobolev regularity of the solution of a parabolic equation is greater than that of the coefficients of the elliptic operator, provided that the initial data is sufficiently regular. This 'smoothing' property of linear parabolic equations along with several estimates from elliptic and ordinary differential equation theory form the crucial ingredients needed in the proof of the existence of a fixed point of the iteration. We begin in chapter one by giving a brief review of the extensive literature concerning the initial value problem in General Relativity. We go on, after mentioning two of the traditional methods for constructing spacetime initial data, to introduce the notion of a quasispherical foliation of a 3-manifold and present the Einstein constraint system written in terms of this gauge. In chapter two we introduce the various inequalities and tracts of analysis we will make use of in subsequent chapters. In particular we define the, perhaps not so familiar, complex differential operator 9 (edth) of Newman and Penrose. In chapter three we develop the appropriate Sobolev-regularity theory for linear parabolic equations required to deal with the quasispherical initial data constraint equations. We include a result due to Polden [P] here, with a corrected proof. This result was essential for deriving the results contained in the later chapters of [P], and it is for this reason we include the result. We don't make use of it explicitly when considering the quasispherical Einstein constraints, but the ideas employed are similar to those we use to tackle the problem of existence for the quasispherical constraints. Chapter four is concerned with the local existence of quasispherical initial data. We firstly consider the question of existence and uniqueness when the mean curvature of the 3-manifold is prescribed, then after introducing the notion of polar curvature, we also present another quasispherical constraint system in which we consider the polar curvature as prescribed. We prove local existence and uniqueness results for both of these alternate formulations of the quasispherical constraints. This thesis was typeset using LATEXwith the package amssymb.

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.

A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.