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Display information for equation id:math.1285.152 on revision:1285
* Page found: Das d'Alembertsche Prinzip (eq math.1285.152)
(force rerendering)Occurrences on the following pages:
Hash: 4ee8174de78b769609781d9794288bd5
TeX (original user input):
\left( \begin{matrix}
\frac{\partial x}{\partial r} & \frac{\partial x}{\partial \vartheta } & \frac{\partial x}{\partial \phi } \\
\frac{\partial y}{\partial r} & \frac{\partial y}{\partial \vartheta } & \frac{\partial y}{\partial \phi } \\
\frac{\partial z}{\partial r} & \frac{\partial z}{\partial \vartheta } & \frac{\partial z}{\partial \phi } \\
\end{matrix} \right)=\left( \begin{matrix}
\sin \vartheta \cos \phi & r\cos \vartheta \cos \phi & -r\sin \vartheta \sin \phi \\
in\vartheta \sin \phi & r\cos \vartheta \sin \phi & r\sin \vartheta \cos \phi \\
\cos \vartheta & -r\sin \vartheta & 0 \\
\end{matrix} \right)
TeX (checked):
\left({\begin{matrix}{\frac {\partial x}{\partial r}}&{\frac {\partial x}{\partial \vartheta }}&{\frac {\partial x}{\partial \phi }}\\{\frac {\partial y}{\partial r}}&{\frac {\partial y}{\partial \vartheta }}&{\frac {\partial y}{\partial \phi }}\\{\frac {\partial z}{\partial r}}&{\frac {\partial z}{\partial \vartheta }}&{\frac {\partial z}{\partial \phi }}\\\end{matrix}}\right)=\left({\begin{matrix}\sin \vartheta \cos \phi &r\cos \vartheta \cos \phi &-r\sin \vartheta \sin \phi \\in\vartheta \sin \phi &r\cos \vartheta \sin \phi &r\sin \vartheta \cos \phi \\\cos \vartheta &-r\sin \vartheta &0\\\end{matrix}}\right)
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MathML (3.823 KB / 441 B) :
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>r</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϑ</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϕ</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>y</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>r</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>y</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϑ</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>y</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϕ</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>z</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>r</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>z</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϑ</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>z</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϕ</mi></mrow></mrow></mfrac></mrow></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi></mtd><mtd><mi>r</mi><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi></mtd><mtd><mo stretchy="false">−</mo><mi>r</mi><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>ϑ</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi></mtd><mtd><mi>r</mi><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi></mtd><mtd><mi>r</mi><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi></mtd></mtr><mtr><mtd><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi></mtd><mtd><mo stretchy="false">−</mo><mi>r</mi><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi></mtd><mtd><mn>0</mn></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>
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