Elliptic coordinate system

About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.

Use of boundary-fitted coordinate transformation in neutron diffusion calculations for arbitrary two-dimensional geometries

Abstract: A procedure for numerically solving neutron diffusion equations in two-dimensional multiconnected regions with arbitrarily shaped boundaries is developed by using a boundary-fitted curvilinear coor...

Parametrization of Extremal Trajectories in Sub-Riemannian Problem on Group of Motions of Pseudo Euclidean Plane

Abstract: We consider the sub-Riemannian length minimization problem on the group of motions of hyperbolic plane i.e. the special hyperbolic group SH(2). The system com- prises of left invariant vector fields with 2 dimensional linear control input and energy cost functional. We prove the global controllability of control distribution and use Pon- tryagin Maximum Principle to obtain the extremal control input and sub-Riemannian geodesics. The abnormal and normal extremal trajectories of the system are analyzed qualitatively and investigated for strict abnormality. A change of coordinates trans- forms the vertical subssystem of the normal Hamiltonian system into mathematical pendulum. In suitable elliptic coordinates the vertical and horizontal subsystems are integrated such that the resulting extremal trajectories are parametrized by Jacobi elliptic functions.

Finite Difference Methods for Polar Coordinate Systems.

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.

Analysis of the Out-of-Control Falling Leaf Motion using a Rotational Axis Coordinate System

Abstract: The realm of aircraft flight dynamics analysis reaches from local static stability to global dynamic behavior. It includes aircraft performance issues as well as structural concerns. In the particular aspect of dynamic motions of an aircraft and how we understand them, an alternate coordinate system will be introduced that will lend insight and simplification into the understanding of these dynamic motions. The main contribution of this coordinate system is that one can easily visualize how the instantaneous velocity vector relates to the instantaneous rotation vector, the angular rate vector of the aircraft. The out-of-control motion known as the Falling Leaf will be considered under the light of this new coordinate system. This motion is not well understood and can lead to loss of the aircraft and crew. Design guidelines will be presented to predict amplitude and frequency of the Falling Leaf. Acknowledgments I would like to thank all those who have helped me through the years in reference to this work as well as throughout my life. First and foremost, I'd like to thank my parents for absolutely always being there and caring as to what was happening in my life. I thank my sisters for feeding me good meals and giving me a place to go during my undergraduate days in Blacksburg. Thanks to all my friends, who have been a huge cornerstone in my life, especially friend and roommate Jin Wook Lim. I owe where I am today in my academic career to my advisor, Dr Fred Lutze. He gave me an opportunity to prove myself many years ago when he had no obligation too, and I thank him. The remaining members of my committee, Dr Anderson and Dr Durham have made the academic environment extremely pleasant. I could not have asked for a better committee or mentors in this endeavor. Mr John Foster allowed this project to come my way. He made my short stay at NASA a wonderful learning experience. Although not technically my 'boss', I truly hope all my bosses will be like him. Last but certainly not least, thanks to the SimLab crew (including Josh) for always being there and putting up with the guitar playing.