Search results for "polar coordinate"
showing 10 items of 22 documents
Differences in Technical Development and Playing Space in Three UEFA Champions Leagues
2021
[Abstract] The analysis of football grows exponentially, with many researchers adopting it as an object of study. The thematic range that addresses it, as well as the different methodologies used, are of a very different nature—physical, psychological, technical, tactical—enriching every day the knowledge, and understanding of the game itself. The objective of this study has been to identify the differences between the different styles of play that lead to becoming the champion of the UEFA Champions League in the last 3 years of the pre-COVID stage, by analyzing the spatial performance developed, the association between the players that make up the different lines of the game system and the…
Stiffness design of laminates using the polar method
2001
This paper is devoted to the analysis of elastic properties of anisotropic laminas using the so-called polar representation method: this is an effective mathematical tool to analyse two-dimensional elastic problems. By this method, the authors have been able to find a particular class of solutions to some special inverse problems concerning laminates made by anisotropic layers. The properties of these solutions are described and discussed, along with some general results.
A new method for generating fully isotropic laminates
2002
In this paper the authors propose some new kinds of isotropic laminates, made with identical anisotropic layers. In particular, these laminates satisfy some conditions which generalise the well-known Werren and Norris rules, in order to obtain fully isotropy, that is, isotropy of the three tensors A, B and D. To this purpose, the authors utilise some results found in a preceding research, namely the so-called quasi-trivial solutions. The way to form particular isotropic laminates that do not follow the Werren and Norris rule is also indicated. The paper ends with some numerical examples which illustrate the theoretical results found.
Influence of orientation errors on quasi-homogeneity of composite laminates
2003
This paper presents a study on the effects of layer orientation defects on the property of quasi-homogeneity for composite laminates: a measure of the deviation from quasi-homogeneity, introducing the concept of degree of quasi-homogeneity, is proposed. Complete theoretical developments which lead to exact formulae in the case of a single orientation error on a layer of the laminate are showed and the results of a wide numerical analysis in the case of orientation errors randomly distributed on the stacking sequence are also presented. All the theoretical and numerical calculations are developed thanks to the polar method of representation of fourth order tensors introduced by Verchery.
Physics Contributions Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy b…
2010
Purpose: The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spa- tial locations not included in the radial dose function gL(r) and 2D anisotropy function F(r,θ) table entries for radial dis- tance r and polar angle θ. The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive gL(r) and F(r,θ) from the reported data; 2) to determine the minimum number of entries in gL(r) and F(r,θ) that allow reproduction of dose distributions with sufficient accuracy. Material and methods: Four high-energy photon-emitting brachytherapy sources were studied: 60Co model Co0.A86, 137Cs model CSM-3, 192Ir model I…
Anisotropy and symmetry for elastic properties of laminates reinforced by balanced fabrics
2001
In this article, we present a theoretical study on elastic properties of laminates composed by balanced fabric layers. Using the polar representation method for plane elastic tensors, we first describe some properties of symmetry of a general laminate composed by balanced fabrics and we write the formulas expressing positions of its axes of symmetry. Then, limiting our study to laminates composed of identical plies, we solve two problems of symmetry of the laminate elastic tensors: uncoupling and quasi-homogeneity. We found all the solutions of the uncoupling problem for the case of 3-, 4- and 5-ply laminate and all those of the quasi-homogeneity problem for the case of 4-, 5- and 6-ply lam…
Technical-Tactical Actions Used to Score in Taekwondo: An Analysis of Two Medalists in Two Olympic Championships
2019
Research in taekwondo has traditionally focused on specific aspects athletes' overall technical and tactical skills, while ignoring other important issues such as identifying how successful athletes score points. The aim of the current study was to follow two medalists through two Olympic Championships (2012 and 2016) to discover the effective patterns associated with scoring in taekwondo using an observational methodology. An ad-hoc taekwondo observational tool was used to codify the actions performed by the athletes. An observational descriptive and multivariate analysis of 1,688 actions performed by the athletes was conducted. A lag sequential and polar coordinate analysis was performed …
Emission and null coordinates: geometrical properties and physical construction
2011
A Relativistic Positioning System is defined by four clocks (emitters) broadcasting their proper time. Then, every event reached by the signals is naturally labeled by these four times which are the emission coordinates of this event. The coordinate hypersurfaces of the emission coordinates are the future light cones based on the emitter trajectories. For this reason the emission coordinates have been also named null coordinates or light coordinates. Nevertheless, other coordinate systems used in different relativistic contexts have the own right to be named null or light coordinates. Here we analyze when one can say that a coordinate is a null coordinate and when one can say that a coordin…
Comparison between the fCCZ4 and BSSN formulations of Einstein equations in spherical polar coordinates
2015
Recently, we generalized a covariant and conformal version of the Z4 system of the Einstein equations using a reference metric approach, that we denote as fCCZ4. We successfully implemented and tested this approach in a 1D code that uses spherical coordinates and assumes spherical symmetry, obtaining from one to three orders of magnitude reduction of the Hamiltonian constraint violations with respect to the BSSN formulation in tests involving neutron star spacetimes. In this work, we show preliminary results obtained with the 3D implementation of the fCCZ4 formulation in a fully 3D code using spherical polar coordinates.
Positioning systems in Minkowski space-time: Bifurcation problem and observational data
2012
In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus…