image of Pluckers conoid

Pluckers conoid

Surfaces

Description

The Plucker's conoid is a ruled surface named after the German mathematician Julius Plucker. It is also called a cylindroid (a cylinder that has an elliptical cross-section) or conical wedge.

Object definitions

Mapping

Mapping of Pluckers conoid
\{x\to v \cos (u),y\to v \sin (u),z\to a \sin (n u)\}
<math> <mrow> <mo>{</mo> <mrow> <mrow> <mi>x</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>v</mi> <mo>&#8290;</mo> <mrow> <mi>cos</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>u</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>v</mi> <mo>&#8290;</mo> <mrow> <mi>sin</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>z</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mrow> <mi>sin</mi> <mo>&#8289;</mo> <mo>(</mo> <mrow> <mi>n</mi> <mo>&#8290;</mo> <mi>u</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </mrow> <mo>}</mo> </mrow> </math>
{x -> v*Cos[u], y -> v*Sin[u], z -> a*Sin[n*u]}
[x = v*cos(u), y = v*sin(u), z = a*sin(n*u)]

Constants

Constants of Pluckers conoid
\{a,n\}
<math> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mo>,</mo> <mi>n</mi> </mrow> <mo>}</mo> </mrow> </math>
{a, n}
[a, n]

Cite this as:

Surfaces: Pluckers conoid from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/Surfaces/Pluckers-Conoid.php

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