Oblate spheroidal
3D Coordinate Systems
Description
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci.
References
Object definitions
Mapping
- TeX
- MathML
- Mathematica input
- Maple input
\{x\to a \cosh (u) \cos (v) \cos (w),y\to a \cosh (u) \cos (v) \sin (w),z\to a \sinh (u) \sin (v)\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mrow>
<mi>x</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mrow>
<mi>cosh</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<mi>cos</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<mi>cos</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>w</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>y</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mrow>
<mi>cosh</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<mi>cos</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>w</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>z</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mrow>
<mi>sinh</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
</math>
{x -> a*Cos[v]*Cos[w]*Cosh[u], y -> a*Cos[v]*Cosh[u]*Sin[w], z -> a*Sin[v]*Sinh[u]}
[x = a*cos(v)*cos(w)*cosh(u), y = a*cos(v)*cosh(u)*sin(w), z = a*sin(v)*sinh(u)]
Constants
- TeX
- MathML
- Mathematica input
- Maple input
\{a\}
<math>
<mrow>
<mo>{</mo>
<mi>a</mi>
<mo>}</mo>
</mrow>
</math>
{a}
[a]
Cite this as:
3D Coordinate Systems: Oblate spheroidal from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/3DCoordinateSystems/Oblate-Spheroidal.php
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