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Display information for equation id:math.1255.152 on revision:1255
* Page found: Das d'Alembertsche Prinzip (eq math.1255.152)
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Hash: 9cf083457048b0675a466a6ddd5e3f52
TeX (original user input):
\begin{align}
& {{T}_{11}}=m\left( {{\sin }^{2}}\vartheta {{\cos }^{2}}\phi +{{\sin }^{2}}\vartheta {{\sin }^{2}}\phi +{{\cos }^{2}}\vartheta \right)=m \\
& {{T}_{22}}=m{{r}^{2}}\left( {{\cos }^{2}}\vartheta {{\cos }^{2}}\phi +{{\cos }^{2}}\vartheta {{\sin }^{2}}\phi +{{\sin }^{2}}\vartheta \right)=m{{r}^{2}} \\
& {{T}_{33}}=m{{r}^{2}}({{\sin }^{2}}\vartheta {{\sin }^{2}}\phi +{{\sin }^{2}}\vartheta {{\cos }^{2}}\phi )=m{{r}^{2}}{{\sin }^{2}}\vartheta \\
\end{align}
TeX (checked):
{\begin{aligned}&{{T}_{11}}=m\left({{\sin }^{2}}\vartheta {{\cos }^{2}}\phi +{{\sin }^{2}}\vartheta {{\sin }^{2}}\phi +{{\cos }^{2}}\vartheta \right)=m\\&{{T}_{22}}=m{{r}^{2}}\left({{\cos }^{2}}\vartheta {{\cos }^{2}}\phi +{{\cos }^{2}}\vartheta {{\sin }^{2}}\phi +{{\sin }^{2}}\vartheta \right)=m{{r}^{2}}\\&{{T}_{33}}=m{{r}^{2}}({{\sin }^{2}}\vartheta {{\sin }^{2}}\phi +{{\sin }^{2}}\vartheta {{\cos }^{2}}\phi )=m{{r}^{2}}{{\sin }^{2}}\vartheta \\\end{aligned}}
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MathML (2.864 KB / 424 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msub><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>1</mn></mrow></mrow></msub><mo>=</mo><mi>m</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϕ</mi><mo>+</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϕ</mi><mo>+</mo><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>m</mi></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>2</mn></mrow></mrow></msub><mo>=</mo><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϕ</mi><mo>+</mo><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϕ</mi><mo>+</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mn>3</mn></mrow></mrow></msub><mo>=</mo><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">(</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϕ</mi><mo>+</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>ϑ</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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