The realm of aircraft flight dynamics analysis reaches from local static stability to global dynamic behavior. It includes aircraft performance issues as well as structural concerns. In the particular aspect of dynamic motions of an aircraft and how we understand them, an alternate coordinate system will be introduced that will lend insight and simplification into the understanding of these dynamic motions. The main contribution of this coordinate system is that one can easily visualize how the instantaneous velocity vector relates to the instantaneous rotation vector, the angular rate vector of the aircraft. The out-of-control motion known as the Falling Leaf will be considered under the light of this new coordinate system. This motion is not well understood and can lead to loss of the aircraft and crew. Design guidelines will be presented to predict amplitude and frequency of the Falling Leaf. NOTE: (12/2009) An updated copy of this ETD was added after there were patron reports of problems with the file. / Master of Science

The main objective of this thesis is to take one step forward to practical and realisable devices for antenna and microwave engineering, using the technique of discrete coordinate transformation (DCT), which is a practical implementation of the coordinate transformation method. During this thesis, the DCT technique was demonstrated and analysed from the theory, and was proved to provide an all-dielectric approach to design devices under certain conditions. Two schemes were proposed on how to use this technique in a practical design. The first one is to transform an existing device into a flattened profile, meanwhile maintaining its electromagnetic performance. As examples, a flat reflector and a flat lens were created from a parabolic reflector and a convex lens, respectively. The second scheme is to project the propagating paths of an electromagnetic wave, and then generate a distorted space according to the paths by engineering the electromagnetic properties of the media. In this scheme, two examples of application were presented: an undetectable antenna composed of a carpet cloak and a conducting cavity, and a broadband device which can extraordinarily enhance the transmission through a sub-wavelength aperture. Numerical simulations based on the Finite-Difference Time-Domain (FDTD) method were implemented to verify all the designs. Several specific configurations were employed in the modelling in order to simulate the DCT based devices more efficiently and precisely. Performance of these devices was validated and analysed, and the advantages and disadvantages of this technique were investigated. Realisation and fabrication methods i were also studied, and a prototype was designed, fabricated and measured. At the end, as an extension, a multiple discrete coordinate transformation method was proposed and presented. This multiple transformation was proved to effectively relax the limitation of the one-step transformation, and was used to design an all-dielectric thin absorber from a conventional pyramidal one for demonstration.

Eine in der Geoda¨sie bekannte Regel besagt, dass die Genauigkeit zu transformierender Neupunkte im Schwerpunkt der Anschlusspunkte am höchsten ist. Weniger bekannt ist, unter welchen Voraussetzungen dies generell gilt. Allgemein unbekannt ist bisher, auf welche Koordinatentransformationen man diese Regel ausdehnen kann. Wir zeigen dies auf und untersuchen einen Fall, in dem diese Regel nicht gilt. Es stellt sich heraus, dass der am genauesten transformierbare Neupunkt theoretisch sogar außerhalb der konvexen Hülle der Anschlusspunkte liegen kann. / A rule well-known in Geodesy states that the accuracy of points to be transformed is best in the centre of gravity of the control points. Less well- known is, under which conditions this rule gen- erally applies. The exact set of coordinate transforms, to which we can extend the validity of this rule, is widelyunknown. We demonstrate this and investigate a case, in which this rule does not apply. It turns out that the most accurately transformable point be even be located outside the convex hull of the control points.

No description available.

Para o georreferenciamento das informações extraídas dos mapas digitais são usados modelos matemáticos de transformação geométrica de coordenadas. O desempenho da transformação de coordenadas está diretamente relacionado à exatidão das coordenadas dos pontos de controle identificados no mapa, uma vez que devido ao uso da tecnologia GNSS, não existe mais a dificuldade de se medir com exatidão coordenadas de pontos no terreno. Por esta razão, é possível obter um georreferenciamento admissível se as coordenadas dos pontos de controle forem posicionadas com exatidão sobre o mapa. Entretanto, como na maioria dos municípios do Brasil, os mapas são antigos, ou seja, desatualizados, existe uma dificuldade de se localizar pontos de controle bem determinados dentre os elementos geográficos representados no mapa. Dependendo da qualidade do mapa e pelo modo como foram identificadas no mesmo, estas coordenadas podem apresentar diferentes graus de confiabilidade, em função de suas exatidões. Tal fato, se não for levado em conta, pode prejudicar o desempenho da transformação de coordenadas, e dependendo da escala do mapa, inviabilizar um projeto ou estudo que dependa de uma boa exatidão de coordenadas de pontos oriundas de um produto cartográfico georreferenciado. Para evitar que o desempenho da transformação de coordenadas comprometa a fidelidade do georreferenciamento gerado, é importante que cada coordenada receba um peso apropriado de acordo com a sua exatidão. Neste contexto, o principal objetivo desta pesquisa foi desenvolver um método, validado através de um estudo de caso, que proporcionasse em função da exatidão das coordenadas dos pontos de controle identificadas no mapa digital, um resultado de georreferenciamento admissível a partir do modelo matemático empregado para transformação de coordenadas. Para isso, foi estudado como atribuir o peso ao ponto de controle em função da sua exatidão. A partir disso, o desempenho da transformação de coordenadas usando pesos foi avaliado tanto num mapa de calibração, de boa qualidade, quanto num mapa cuja qualidade posicional era desconhecida. Em ambos os mapas foram realizadas as mais variadas avaliações. Em todas as avaliações efetuadas o desempenho da transformação de coordenadas foi melhor quando foram atribuídos pesos aos pontos de controle em função da sua exatidão. Esta pesquisa levantou uma questão até então desconsiderada, que é a importância de se atribuir pesos às coordenadas dos pontos de controle em função da sua exatidão no mapa digital. O resultado do georreferenciamento se torna admissível quando esta consideração é levada em conta. / The mathematical model for the geometric transformation of coordinates is used to georreference information extrated from digital maps. The performance of coordinate transformation models is directly related to accuracy of control points identified in the map, since by means of the utilization of GNSS technology, it is not difficult to measure the coordinates of a point in the ground with accuracy. For this reason, it is possible to obtain a reliable georreferencing if the coordinates of the control points are accurately positioned on a map. However, as most of brazilian municipal districts maps are old and out-of-date, it is difficult to locate a point accurately out of the geographic elements represented in the map. Depending on both the quality of the digital map and the technique used to locate the points, such coordinates may show distinct levels of reliability as a function of their accuracy. If the different accuracy of the control points is not taking into account, the performance of the coordinate transformation model can be reduced. Depending on map scale, this difference can make impracticable a study that depends on a good accuracy of the coordinates of points obtained from a georreferecend cartographic product. In order to avoid that the performance of the coordinate transformation model reduce the reliability of the georreferencing, it is important that each coordinate receives an appropriate weight according to its accuracy. In this context, the objective of this research was to develop a method, validated through a case study, that could impart reliability to georreferencing, as a function of the accuracy of the coordinates of the control points identified on a map, using a mathematical model to coordinate transformation. The key-point is to attribute a weight to each control point related to its accuracy level. The performance of this procedure was evaluated both for a high quality, standard map, and for a map with unknown quality. Different evaluations were performed and the best results were obtained using the procedure of attributing weights to the control points related its accuracy. As a contribution for the academic and technical areas, this research brought light to a question not considered until now, that is the importance of attributing weights to the coordinates of the control points as a function its accuracy in the digital map. Georreferencing becomes more reliable when this question is taken into account.

This thesis presents a method for simulating fluids on a view dependent grid structure to exploit level-of-detail with distance to the viewer. Current computer graphics techniques, such as the Stable Fluid and Particle Level Set methods, are modified to support a nonuniform simulation grid. In addition, infinite fluid boundary conditions are introduced that allow fluid to flow freely into or out of the simulation domain to achieve the effect of large, boundary free bodies of fluid. Finally, a physically based rendering method known as photon mapping is used in conjunction with ray tracing to generate realistic images of water with caustics. These methods were implemented as a C++ application framework capable of simulating and rendering fluid in a variety of user-defined coordinate systems.

Die Form der Kettenlinie lädt dazu ein, diese als eine Kerbgeometrie zu nutzen. Eine rechtwinklige Aussparung soll im CAD so aufgefüllt werden, dass dies der Kontur der Kettenlinie entspricht. In dem Vortrag wird gezeigt, wie mittels elementarer Elemente der Ingenieurmathematik und der Nutzung von Mathcad die Kettenlinie als eine Kurve mit festem Laufparameter und einem Formparameter dargestellt werden kann. Die Nutzung der Kettenlinie als Kerbgeometrie und die Bestimmung des optimalen Formparameters mittels einer Sensitivitätsanalyse, beschreibt Herr Dr. Jakel im Beitrag "Using a Catenary Equation in Parametric Representation for Minimizing Stress Concentrations at Notches"

In this thesis, three mesh generation software packages have been developed and implemented. The first two were based on structured mesh generation algorithms and used to solve structured surface and volume mesh generation problems of three-dimensional domains. Structured mesh generation algorithms were based on the concept of isoparametric coordinates. In structured surface mesh generation software, quadrilateral mesh elements were generated for complex three-dimensional surfaces and these elements were then triangulated in order to obtain high-quality triangular mesh elements. Structured volume mesh generation software was used to generate hexahedral mesh elements for volumes. Tetrahedral mesh elements were constructed from hexahedral elements using hexahedral node insertion method. The results, which were produced by the mesh generation algorithms, were converted to a required format in order to be saved in output files. The third software package is an unstructured quality tetrahedral mesh generator and was used to generate exact Delaunay tetrahedralizations, constrained (conforming) Delaunay tetrahedralizations and quality conforming Delaunay tetrahedralizations. Apart from the mesh generation algorithms used and implemented in this thesis, unstructured mesh generation techniques that can be used to generate quadrilateral, triangular, hexahedral and tetrahedral mesh elements were also discussed.

Para o georreferenciamento das informações extraídas dos mapas digitais são usados modelos matemáticos de transformação geométrica de coordenadas. O desempenho da transformação de coordenadas está diretamente relacionado à exatidão das coordenadas dos pontos de controle identificados no mapa, uma vez que devido ao uso da tecnologia GNSS, não existe mais a dificuldade de se medir com exatidão coordenadas de pontos no terreno. Por esta razão, é possível obter um georreferenciamento admissível se as coordenadas dos pontos de controle forem posicionadas com exatidão sobre o mapa. Entretanto, como na maioria dos municípios do Brasil, os mapas são antigos, ou seja, desatualizados, existe uma dificuldade de se localizar pontos de controle bem determinados dentre os elementos geográficos representados no mapa. Dependendo da qualidade do mapa e pelo modo como foram identificadas no mesmo, estas coordenadas podem apresentar diferentes graus de confiabilidade, em função de suas exatidões. Tal fato, se não for levado em conta, pode prejudicar o desempenho da transformação de coordenadas, e dependendo da escala do mapa, inviabilizar um projeto ou estudo que dependa de uma boa exatidão de coordenadas de pontos oriundas de um produto cartográfico georreferenciado. Para evitar que o desempenho da transformação de coordenadas comprometa a fidelidade do georreferenciamento gerado, é importante que cada coordenada receba um peso apropriado de acordo com a sua exatidão. Neste contexto, o principal objetivo desta pesquisa foi desenvolver um método, validado através de um estudo de caso, que proporcionasse em função da exatidão das coordenadas dos pontos de controle identificadas no mapa digital, um resultado de georreferenciamento admissível a partir do modelo matemático empregado para transformação de coordenadas. Para isso, foi estudado como atribuir o peso ao ponto de controle em função da sua exatidão. A partir disso, o desempenho da transformação de coordenadas usando pesos foi avaliado tanto num mapa de calibração, de boa qualidade, quanto num mapa cuja qualidade posicional era desconhecida. Em ambos os mapas foram realizadas as mais variadas avaliações. Em todas as avaliações efetuadas o desempenho da transformação de coordenadas foi melhor quando foram atribuídos pesos aos pontos de controle em função da sua exatidão. Esta pesquisa levantou uma questão até então desconsiderada, que é a importância de se atribuir pesos às coordenadas dos pontos de controle em função da sua exatidão no mapa digital. O resultado do georreferenciamento se torna admissível quando esta consideração é levada em conta. / The mathematical model for the geometric transformation of coordinates is used to georreference information extrated from digital maps. The performance of coordinate transformation models is directly related to accuracy of control points identified in the map, since by means of the utilization of GNSS technology, it is not difficult to measure the coordinates of a point in the ground with accuracy. For this reason, it is possible to obtain a reliable georreferencing if the coordinates of the control points are accurately positioned on a map. However, as most of brazilian municipal districts maps are old and out-of-date, it is difficult to locate a point accurately out of the geographic elements represented in the map. Depending on both the quality of the digital map and the technique used to locate the points, such coordinates may show distinct levels of reliability as a function of their accuracy. If the different accuracy of the control points is not taking into account, the performance of the coordinate transformation model can be reduced. Depending on map scale, this difference can make impracticable a study that depends on a good accuracy of the coordinates of points obtained from a georreferecend cartographic product. In order to avoid that the performance of the coordinate transformation model reduce the reliability of the georreferencing, it is important that each coordinate receives an appropriate weight according to its accuracy. In this context, the objective of this research was to develop a method, validated through a case study, that could impart reliability to georreferencing, as a function of the accuracy of the coordinates of the control points identified on a map, using a mathematical model to coordinate transformation. The key-point is to attribute a weight to each control point related to its accuracy level. The performance of this procedure was evaluated both for a high quality, standard map, and for a map with unknown quality. Different evaluations were performed and the best results were obtained using the procedure of attributing weights to the control points related its accuracy. As a contribution for the academic and technical areas, this research brought light to a question not considered until now, that is the importance of attributing weights to the coordinates of the control points as a function its accuracy in the digital map. Georreferencing becomes more reliable when this question is taken into account.

Motorradfahrer gehören zu den am meisten gefährdeten Verkehrsteilnehmern im Straßenverkehr. Häufig ist die Unfallursache ein Kontrollverlust auf Landstraßen, der durch Ausnutzung des physikalischen Potenzials in Form von größeren Schräglagenwinkeln vermieden werden könnte. Gleichzeitig sind in der Realität gefahrene Schräglagen über eine größere Gruppe von Fahrern und eine längere Strecke unbekannt, was vor allem auf die erforderliche spezielle Messtechnik zurückzuführen ist. Der Schwerpunkt liegt daher auf der Entwicklung eines kostengünstigen Messverfahrens zur Messung der Schräglagenwinkel von Motorrädern. Smartphones zeichnen sich in der Regel durch integrierte Inertialsensoren aus, die für die Erfassung der Fahrdynamik von Motorrädern geeignet sind. Mit Hilfe einer auf die Anforderungen zugeschnittenen Smartphone-App zur Erfassung von Messdaten auf dem Motorrad werden die Daten der Sensoren aufgezeichnet. Anschließend werden mittels einer Offline-Auswertung die Drehwinkel zwischen dem Smartphone und dem Motorrad-Koordinatensystem bestimmt, die inertialen Messdaten transformiert und der Schräglagenwinkel berechnet. Ein wesentlicher Bestandteil ist die Validierung der entwickelten Messkette durch einen Vergleich der Ergebnisse mit einem hochpräzisen Messsystem. Dieser wurde auf verschiedenen Strecken zur Bestimmung der Datenqualität durchgeführt. Als Machbarkeitsstudie diente eine Probandenstudie, die die Praxistauglichkeit der Messkette bestätigte. Die Studienergebnisse werden zusätzlich auszugsweise dargestellt und diskutiert. Die erfolgreiche Validierung auf verschiedenen Strecken, die Praxistauglichkeit der Datenerfassung und die Genauigkeit des Messsystems ermutigen dazu, die Smartphone-App auf ein größeres Panel von Testpersonen auszurollen und damit Daten über ein größeres Fahrerkollektiv zu erheben.:Introduction, State of Research, Methods, Measurement Chain Verification, Results and Discussion, Conclusion / Motorcyclists are among the most vulnerable road users in road traffic. Often, the cause of accidents is a loss of control on rural roads which could be averted by making use of the physical potential in terms of larger lean angles. At the same time, in reality driven lean angles over a larger group of riders and a longer route are unknown which is mainly due to the special measuring technology required. The focus is therefore on the development of a low-cost measurement method for measuring the lean angles of motorcycles. Smartphones are usually characterized by integrated inertial sensors, which are suitable for the acquisition of motorcycle driving dynamics. Employing a smartphone app tailored to the requirements for collecting measurement data on the motorcycle, the data of the sensors are recorded. During the offline evaluation, the rotation angles between the smartphone and the motorcycle coordinate system are determined, the inertial measurement data are transformed and the roll angle is calculated. An essential part is the alignment of the developed measurement chain with a high-precision measurement system. This was carried out on different routes and thus the data quality was determined. As a feasibility study, a test person study with several participants was carried out, which confirmed the practical suitability of the measurement chain. Hence, the study outcomes are briefly shown and discussed. The successful validation on different routes, the practical suitability of the data acquisition and the accuracy of the measurement system encourage to roll out the smartphone app to a larger panel of test persons and thus to collect data on a larger driver collective.:Introduction, State of Research, Methods, Measurement Chain Verification, Results and Discussion, Conclusion