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.

The Multi-Dimensional (MD) Coordinate Systems

Abstract: This paper shows different multi-dimensional coordinate systems that can be applied on science and social sciences This paper offers a serial of multi-dimensional coordinate systems to visualize and analyze from 4-Dimensions until Infinity dimensions into the same graphical space At the inception of multi-dimensional coordinate systems, the following new types of multi-dimensional coordinate systems are presented: Pyramid coordinate system, Diamond coordinate system, 4-Dimensional coordinate system, 5-Dimensional coordinate system, Infinity Dimensional coordinate system and Multi-functional Pictorial coordinate system These six Multi-Dimensional coordinate systems are constructed based on the traditional 3-D space concept, but they represent 4-D, 5-D, 8-D, 9-D and Infinity-Dimension

Calculating method of three-dimensional coordinate value

Abstract: PURPOSE:To reduce the time for calculation of coordinate values with simple constitution by corresponding beforehand rotation numbers and storing the local coordinate system that defines a shape when said system is not inclined with respect to the entire coordinate system. CONSTITUTION:The element of a rotary matrix is any among 0, 1, -1 when a local coordinate axis and the entire coordinate axis coincide. Rotation numbers are provided in correspondence to 24 kinds of the rotary matrix when the local coordinate system is not inclined with respect to the entire coordinate system. Values of x1, y1, z1 are inputted to the register RG-EX of the local coordinate axis and the signals of 1-24 and 25 are generated from a rotation number device RN. A switch SW is changed over so as to pass the output through a code inverter INV when a storage/generation device RVN which emits a control signal in correspondence to the numbers 1-24 outputs -1. Input is made to the register RG-GN of the entire coordinate system through a matrix calculation circuit MTP in the case of the number 25. The coordinate value in the entire coordinate is then calculated by substitution calculations.

Acceleration in general curvilinear coordinate systems

Abstract: Starting from the Lagrange equation, we derive directly the expressions for the physical components of the acceleration of a particle along the coordinate axes of any general curvilinear coordinate system. These expressions are also derived from the Hamilton equation with the help of a lemma. Useful expressions for the physical components of the acceleration in a number of special orthogonal curvilinear coordinate systems are given.

Study on 3-winding system with angular asymmetry part II - eigenvalues of inductance matrix and transformation αβ0

Abstract: One of the most frequently-used coordinate system in theory of electrical circuits is the coordinate system spanned on eigenvectors which leads to diagonal structure of matrix relation between input and output variables. So far, this coordinate system has not been considered in details in relation to a 3-phase system of windings with angular asymmetry. In the paper the characteristic equation is formulated and eigenvalues are determined as function of angles between consecutive windings. The paper is enriched by graphical presentation of equivalent schemes and discussion on possible physical models of 3-winding asymmetrical system in coordinates αβ0 linked with eigenvector coordinate system.