Sphere sine wave
Space Curves
Description
The Sphere sine wave is a curve in three-dimensional space.
References
Object definitions
Mapping
- TeX
- MathML
- Mathematica input
- Maple input
\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>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mrow>
<mi>cos</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<msqrt>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
<mo>⁢</mo>
<mrow>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</msqrt>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>y</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<msqrt>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
<mo>⁢</mo>
<mrow>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</msqrt>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>z</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>c</mi>
<mo>⁢</mo>
<mrow>
<mi>cos</mi>
<mo>⁡</mo>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mo>⁢</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
- TeX
- MathML
- Mathematica input
- Maple input
\{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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