Transformation of the wave equation solution between parallel displaced cylindrical coordinate systems

1984 ◽  
Vol 67 (6) ◽  
pp. 391-394 ◽  
Author(s):  
R. Gesche
Keyword(s):  
Wave Equation ◽  
Coordinate Systems ◽  
Equation Solution ◽  
Cylindrical Coordinate

Analysis of the validity of the asymptotic techniques in the lower hybrid wave equation solution for reactor applications

2007 ◽  
Vol 14 (11) ◽  
pp. 112506 ◽  
Author(s):  
A. Cardinali ◽  
L. Morini ◽  
C. Castaldo ◽  
R. Cesario ◽  
F. Zonca
Keyword(s):  
Wave Equation ◽  
Lower Hybrid ◽  
Hybrid Wave ◽  
Lower Hybrid Wave ◽  
Equation Solution

Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component

2007 ◽  
Vol 364-366 ◽  
pp. 499-503 ◽  
Author(s):  
Guo Jun Dong ◽  
Cheng Shun Han ◽  
Shen Dong
Keyword(s):  
Coordinate System ◽  
Axial Symmetry ◽  
Curvature Radius ◽  
Aspheric Surface ◽  
Coordinate Systems ◽  
Rectangular Coordinate System ◽  
Cylindrical Coordinate ◽  
Complex Models ◽  
Best Fitting ◽  
Spherical Curvature

This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.

scholarly journals Linear Force-free Magnetic Fields and Coronal Models

1989 ◽  
Vol 42 (3) ◽  
pp. 317 ◽  
Author(s):  
CJ Durrant
Keyword(s):  
Boundary Condition ◽  
Magnetic Fields ◽  
Helmholtz Equation ◽  
Normal Component ◽  
Coordinate Systems ◽  
Mathematical Properties ◽  
Cylindrical Coordinate ◽  
Linear Force ◽  
Free Fields

The mathematical properties of linear force-free fields generated by the Helmholtz equation are reviewed, and the solutions in terms of spherical, cartesian and cylindrical coordinate systems are discussed. When only the normal component of the field on a single (photospheric) surface is available as a boundary condition, the solutions are not niquely determined. If further conditions are imposed, solutions may be unique or multiple or may not exist. The

scholarly journals About one method of calculation in the arbitrary curvilinear basis of the Laplace operator and curl from the vector function

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
S. O. Gladkov
Keyword(s):  
Simple Algorithm ◽  
Coordinate Systems ◽  
Method Of Calculation ◽  
Orthonormal Bases ◽  
Christoffel Symbols ◽  
Arbitrary Base ◽  
Cylindrical Coordinate ◽  
The Common ◽  
The Laplace Operator ◽  
Made In

Abstract A simple algorithm for calculating Christoffel symbols, a covariant projection of the result of the Laplace operator's action on the vector, vector curl and other similar operations in an arbitrary oblique base are proposed. For an arbitrary base with ortho ei is found the expressions of vector projections (ΔA) i and (rot A) i , where A is a counter variant vector. Examples of orthonormal bases are considered and general expressions for (ΔA) i and (rot A) i for the bases are also given. As a demonstration of the working capacity of the common formulas obtained, detailed calculations of (ΔA) i and (rot A) i as an example are made in cases of spherical and cylindrical coordinate systems.

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