image of Elliptic cylindrical

Elliptic cylindrical

3D Coordinate Systems

Description

Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in the perpendicular z-direction. Hence, the coordinate surfaces are prisms of confocal ellipses (see Ellipse) and hyperbolae (see Hyperbola).

References

Moon & Spencer
Murray R. Spiegel

Object definitions

Mapping

  • TeX
  • MathML
  • Mathematica input
  • Maple input
Mapping of Elliptic cylindrical
\{x\to a \cosh (u) \cos (v),y\to a \sinh (u) \sin (v),z\to w\}
<math> <mrow> <mo>{</mo> <mrow> <mrow> <mi>x</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mrow> <mi>cosh</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>&#8290;</mo> <mrow> <mi>cos</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>y</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mrow> <mi>sinh</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>&#8290;</mo> <mrow> <mi>sin</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>z</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mi>w</mi> </mrow> </mrow> <mo>}</mo> </mrow> </math>
{x -> a*Cos[v]*Cosh[u], y -> a*Sin[v]*Sinh[u], z -> w}
[x = a*cos(v)*cosh(u), y = a*sin(v)*sinh(u), z = w]

Constants

  • TeX
  • MathML
  • Mathematica input
  • Maple input
Constants of Elliptic cylindrical
\{a\}
<math> <mrow> <mo>{</mo> <mi>a</mi> <mo>}</mo> </mrow> </math>
{a}
[a]

Cite this as:

3D Coordinate Systems: Elliptic cylindrical from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/3DCoordinateSystems/Elliptic-Cylindrical.php

Terms of use:

You can use the contents of DG Library pages for education, research, professional needs and enjoyment.
If you use this library, please, cite DG Library as the source of the data.

Pages of DG Library may not be copied, mirrored, redistributed, printed, or reproduced in bulk without permission. Usage for any commercial purposes without permission is prohibited.
 

DG Library is database of over 580 objects for differential geometry and its applications. Read more...

  • Share via email
  • Share via Twitter
  • Share via Facebook

Related links