Showing papers on "Elliptic coordinate system published in 1986"
TL;DR: In this article, an extension of a previous work concerning the calculation of strain histories along streamlines is made to get more complete and useful expressions of Finger's strain tensor in a cylindrical (or Cartesian) coordinate system as well as in an orthogonal streamline coordinate system.
Abstract: An extension of a previous work concerning the calculation of strain histories along streamlines is made to get more complete and useful expressions of Finger's strain tensor in a cylindrical (or Cartesian) coordinate system as well as in an orthogonal streamline coordinate system. One of the results shows that Winter's tracking model is correct. Relations among the recent three results of Winter, Adachi and Crochet et al. are presented clearly. Moreover useful applications of Frenet-Serret's formula to the study of the deformation and flow kinematics along streamlines are shown in comparison with the ordinary tensor approach.
23 citations
TL;DR: In this paper, the authors present a new method for the mobility analysis of planar mechanisms, which utilizes a geometrical representation known as "parallel coordinates", which is a transformation that maps the Euclidean space R N to N parallel coordinates in the projective plane.
17 citations
01 Apr 1986
TL;DR: In this paper, the authors discuss finite difference methods for partial differential equations on polar and spherical coordinate systems and show how to accurately and conveniently determine the solution at the origin for both scalar and vector fields.
Abstract: : This document discusses finite difference methods for partial differential equations on polar and spherical coordinate systems. The distinctive feature of these coordinate systems is the coordinate system singularity at the origin. The authors show how to accurately and conveniently determine the solution at the origin for both scalar and vector fields. They also discuss the Fourier method to approximate derivatives with respect to the angular variable in polar coordinates. Computational examples are presented illustrating the accuracy and efficiency of the method for hyperbolic and elliptic equations, and also for the computation of vector fields at the origin. Keywords: guide(coordinate); quadrative formulas.
6 citations
TL;DR: In this article, the Fourier method is applied to the solution of torsion contact problems for elastic bodies bounded by coordinate surfaces of toroidal and spherical coordinate systems, and the relationship between particular solutions of the Torsion equation in spherical and toroidal coordinates is analyzed.
2 citations
2 citations
01 Jan 1986
1 citations
TL;DR: A vectorial and a tensorial crossing rule are defined in Cartesian coordinate systems and applications are obtained in the simplification of some particular ‘‘3nj’’ coefficients.
Abstract: A vectorial and a tensorial crossing rule are defined in Cartesian coordinate systems. Different applications are given. With a particular choice of the standardization coefficient of vectors the same expression of dot and vector products in the standard and Cartesian coordinate systems results. The crossing rules are thus redefined in a standard coordinate system. Applications are obtained in the simplification of some particular ‘‘3nj’’ coefficients.