Search results for "Jacobian matrix"
showing 10 items of 47 documents
Locating Objects Away from Earth Surface: Positioning Accuracy
2013
The motion of the Galileo and GPS satellite constellations is simulated in Schwarzschild space-time, whereas photons travel in Minkowski space-time. This is a good enough approach to deal with the main goal of this paper: the study of positioning accuracy in the framework of the so-called relativistic positioning. Our study is based on numerical 4D simulations. In this meeting, the contribution of J.A. Morales-Lladosa contains some basic ideas which have been important to perform our numerical calculations. For four chosen emitters (satellites) of a certain constellation, many receivers located at different distances from Earth surface and in distinct directions are considered. Thus, we ver…
Mappings of exponentially integrable distortion: Decay of the Jacobian
2018
We establish an integrability result on the reciprocal of the Jacobian determinant for a mapping of exponentially integrable distortion and thus answer a question raised by S. Hencl and P. Koskela.
Mappings of Finite Distortion:¶Discreteness and Openness
2001
We establish a sharp integrability condition on the partial derivatives of a mapping with L p -integrable distortion for some p>n− 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.
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…
Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials.
2014
In this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von Mises materials under plane strain conditions is shown. The proposed approach works with the Symmetric Galerkin Boundary Element Method applied to multidomain problems using a mixed variables approach, to obtain a more stringent solution. The elastoplastic analysis is carried out as the response to the loads and the plastic strains, the latter evaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictor phase, for trial stress evaluation and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active…
A new method for creating sparse design velocity fields
2006
We present a novel method for the computation of mesh node sensitivities with respect to the boundary node movement. The sensitivity field is sparse in a sense that movement of each boundary node affects only given amount of inner mesh nodes, which can result in considerable savings in the storage space. The method needs minimal control from the user, and it does not place any restrictions (such as block structure) on the mesh. Use of the method is demonstrated with a shape optimization problem using CAD-free parametrization. A solution to the classical die-swell free boundary problem by coupling the boundary node locations with the state variables is also presented. In that case, sparsity …
Using the witness method to detect rigid subsystems of geometric constraints in CAD
2010
International audience; This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorit…
Mappings of finite distortion: the degree of regularity
2005
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)⩾1 be a measurable function defined on a domain Ω⊂Rn,n⩾2, and such that exp(βK(x))∈Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|n⩽K(x)J(x,f) for a.e. x∈Ω and such that the Jacobian determinant J(x,f) is locally in L1log−c1(n)βL. Then automatically J(x,f) is locally in L1logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite disto…
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
2007
Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique
2003
This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T. The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newton’s method. For polynomial nonlinearities of cubic order, exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation o…