Search results for "Coordinate system"
showing 10 items of 118 documents
$n$-harmonic coordinates and the regularity of conformal mappings
2014
This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with $C^r$ metric tensors ($r > 1$) is a $C^{r+1}$ conformal (local) diffeomorphism. This result was proved in [12, 27, 33], but we give a new proof of this fact. The proof is based on $n$-harmonic coordinates, a generalization of the standard harmonic coordinates that is particularly suited to studying conformal mappings. We establish the existence of a $p$-harmonic coordinate system for $1 < p < \infty$ on any Riemannian manifold.
Full modal analysis of confocal coaxial elliptical waveguides
2000
An efficient method for analysing confocal coaxial elliptical waveguides is presented. Using elliptical coordinates, the differential Helmholtz equation is transformed into a linear matrix eigenvalue problem by means of the method of moments. The expressions of the vector mode functions for the full spectrum of these guides are constructed, including the TEM, TM and TE modes. The convergence of the method is very good, giving an efficient and accurate code. Comparisons with numerical results found in the technical literature validate the presented theory.
Interactive simulation of one-dimensional flexible parts
2006
Computer simulations play an ever growing role for the development of automotive products. Assembly simulation, as well as many other processes, are used systematically even before the first physical prototype of a vehicle is built in order to check whether particular components can be assembled easily or whether another part is in the way. Usually, this kind of simulation is limited to rigid bodies. However, a vehicle contains a multitude of flexible parts of various types: cables, hoses, carpets, seat surfaces, insulations, weatherstrips... Since most of the problems using these simulations concern one-dimensional components and since an intuitive tool for cable routing is still needed, w…
Computational general relativistic force-free electrodynamics
2020
General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole shadows from the galactic center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as black holes an…
RESIDUAL STRESS ANALYSIS OF ORTHOTROPIC MATERIALS BY THE THROUGH-HOLE DRILLING METHOD
2007
The present study deals with the development and the application of the through-hole drilling method for the residual stress analysis in orthotropic materials. Through a systematic theoretical study of the stress field present on orthotropic plates with a circular hole, the relationships between the relaxed strains measured by a rectangular strain gauge rosette and the Cartesian components of the unknown residual stresses are obtained. The theoretical formulas of each influence coefficient allow the user an easy application of the method to the analysis of uniform-residual stresses on a generic homogeneous orthotropic material. Furthermore, to extend the method to the analysis of the residu…
Software for automated application of a reference-based method fora posterioridetermination of the effective radiographic imaging geometry
2005
Objectives: Presentation and validation of software developed for automated and accurate application of a reference-based algorithm (reference sphere method: RSM) inferring the effective imaging geometry from quantitative radiographic image analysis. Methods: The software uses modern pattern recognition and computer vision algorithms adapted for the particular application of automated detection of the reference sphere shadows (ellipses) with subpixel accuracy. It applies the RSM algorithm to the shadows detected, thereby providing threedimensional Cartesian coordinates of the spheres. If the three sphere centres do not lie on one line, they uniquely determine the imaging geometry. Accuracy …
Measurement and storage of a network of jacobians as a method for the visual positioning of a robot arm
1996
The goal of this paper is to describe a method to position a robot arm at any visible point of a given workspace without an explicit on line use of the analytical form of the transformations between real space and camera coordinates (camera calibration) or between cartesian and joint coordinates (direct or inverse kinematics of the robot arm). The formulation uses a discrete network of points distributed all over the workspace in which a procedure is given to measure certain Jacobian matrices which represent a good local linear approximation to the unknown compound transformation between camera and joint coordinates. This approach is inspired by the biological observation of the vestibulo-o…
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.