image of Sphere sine wave

Sphere sine wave

Space Curves

Description

The Sphere sine wave is a curve in three-dimensional space.

Object definitions

Mapping

Mapping of Sphere sine wave
\left\{x\to \cos (t) \sqrt{b^2-c^2 \cos ^2(a t)},y\to \sin (t) \sqrt{b^2-c^2 \cos ^2(a t)},z\to c \cos (a t)\right\}
<math> <mrow> <mo>{</mo> <mrow> <mrow> <mi>x</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mrow> <mi>cos</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&#8290;</mo> <msqrt> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>-</mo> <mrow> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo>&#8290;</mo> <mrow> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mo>(</mo> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </msqrt> </mrow> </mrow> <mo>,</mo> <mrow> <mi>y</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mrow> <mi>sin</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&#8290;</mo> <msqrt> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>-</mo> <mrow> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo>&#8290;</mo> <mrow> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mo>(</mo> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </msqrt> </mrow> </mrow> <mo>,</mo> <mrow> <mi>z</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>c</mi> <mo>&#8290;</mo> <mrow> <mi>cos</mi> <mo>&#8289;</mo> <mo>(</mo> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </mrow> <mo>}</mo> </mrow> </math>
{x -> Cos[t]*Sqrt[b^2 - c^2*Cos[a*t]^2], y -> Sqrt[b^2 - c^2*Cos[a*t]^2]*Sin[t], z -> c*Cos[a*t]}
[x = cos(t)*(b^2-c^2*cos(a*t)^2)^(1/2), y = (b^2-c^2*cos(a*t)^2)^(1/2)*sin(t), z = c*cos(a*t)]

Constants

Constants of Sphere sine wave
\{a,b,c\}
<math> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> </mrow> <mo>}</mo> </mrow> </math>
{a, b, c}
[a, b, c]

Cite this as:

Space Curves: Sphere sine wave from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/SpaceCurves/Sphere-Sine-Wave.php

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