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Coordinate Systems and Vector Algebra
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
Geometry is a branch of mathematics that deals with the measurement, property, and relations of lines, angles, surfaces, and volumes. A practical device or part thereof in which the field distribution is to be studied for its behavior requires representation of its shape and size in such a way that all its physical aspects fully conform to the geometry. The system that deals with geometrical aspects of an object is referred to as a coordinate system. The necessity to enhance these limits has led to the development of number of tools. A coordinate system helps us to visualize relative positions of independent points or those belong to a line, a surface or a volume. Thus, while introducing the coordinate systems, it is presumed that a reader fully understands the meanings of point, line, surface, and volume, and also is aware of normal, tangent, and geometrical properties. Furthermore, as and when any point on, or a segment in terms of line, area, or volume of, the system is to be represented (or identified), it should fit in well in the coordinate system selected. The following subsections describe the types of coordinate systems.
Information-Centric Framework for the IoT: Traffic Modeling and Optimization
Published in Fadi Al-Turjman, Multimedia-enabled Sensors in IoT, 2018
The request for information from the Internet has been observed to be cyclic by nature [33,34]. In our proposed method, we first obtain the period of the cycle in which the IoT traffic is supposed to repeat its pattern, and then, from that period, the frequency of the request is mapped to a polar system. A polar system is a two-dimensional coordinate system in which any point is given by the distance from a reference point and the angle from a reference direction. In this system, coordinated data traffic points form an oval shape called an ellipse. Thus, the ellipse in our study represents the data traffic pattern/behavior per cycle. This ellipse has a number of parameters (such as the semimajor and semiminor axis length, the orientation angle, and the eccentricity parameter) that have been used in quantifying/measuring the targeted IoT traffic in this study. In Table 9.2, a brief definition per parameter with an illustrative diagram in Figure 9.3 is presented.
Preliminaries
Published in William J. Bottega, Engineering Vibrations, 2014
The actual coordinate system employed may be any convenient system, such as Cartesian, polar or spherical. Further, since all quantities involved are now continuous functions of the spatial coordinates, summations over discrete masses are replaced by integrals over the entire mass, and hence volume, of the body. Thus, for any quantity λ, () ∑p=1Nmpλ→p(t)→∫mλ→(x,y,z,t)dm
A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates
Published in International Journal of Mathematical Education in Science and Technology, 2020
Vahid Borji, Hedyeh Erfani, Vicenç Font
The polar coordinate system is defined as a two-dimensional coordinate system where each point on the plane has two indicators: a distance from the pole, , as the first coordinate and an angle from a reference direction, , as the second coordinate. In many of undergraduate courses, polar coordinate system is taught with a focus on geometric interpretations, conversions between polar and Cartesian coordinates and sketching polar graphs [1,4].
Physically motivated lumped-parameter model for proportional magnets
Published in International Journal of Fluid Power, 2018
The origin of the coordinate system can be chosen depending on the application and on available measurement data. When modelling pressure valves for example, the origin may be set to the static armature position at zero flow. Thus, the force characteristic in x= 0 can be determined by using the control face areas and measuring the controlled pressure over current. For directional valves, the highest air gap length is most suitable.
Gaussian Process Modeling Using the Principle of Superposition
Published in Technometrics, 2019
This section gives three examples of IBVPs of the form (13) that often need to be solved numerically in engineering applications. Numerical simulation results for all three IBVP examples shall be given in Section 5. In all three examples, a Cartesian coordinate system is employed as the spatial coordinate system. Many other IBVPs with widespread applications can be found in the literature on PDE models (e.g., see Jeffrey 2003).