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Display information for equation id:math.1351.86 on revision:1351

* Page found: Mechanik des starren Körpers (eq math.1351.86)

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Hash: d6168797f2b41bac490d6102aae96850

TeX (original user input):

\begin{align}
  & \bar{l}={{{\bar{r}}}_{s}}\times M\bar{V}+\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x})\bar{x}}\times \left( \bar{\omega }\times \bar{x} \right) \\
 & \bar{L}=\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x})\bar{x}}\times \left( \bar{\omega }\times \bar{x} \right)=\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x})\left[ {{x}^{2}}\bar{\omega }-\left( \bar{x}\cdot \bar{\omega } \right)\bar{x} \right]} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\bar {l}}={{\bar {r}}_{s}}\times M{\bar {V}}+\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}}){\bar {x}}}\times \left({\bar {\omega }}\times {\bar {x}}\right)\\&{\bar {L}}=\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}}){\bar {x}}}\times \left({\bar {\omega }}\times {\bar {x}}\right)=\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}})\left[{{x}^{2}}{\bar {\omega }}-\left({\bar {x}}\cdot {\bar {\omega }}\right){\bar {x}}\right]}\\\end{aligned}}

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MathML (2.821 KB / 460 B) :

l¯=r¯s×MV¯+d3xρ(x¯)x¯×(ω¯×x¯)L¯=d3xρ(x¯)x¯×(ω¯×x¯)=d3xρ(x¯)[x2ω¯(x¯ω¯)x¯]
<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"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>l</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo stretchy="false">×</mo><mi>M</mi><mover><mi>V</mi><mo>¯</mo></mover><mo stretchy="false">+</mo><msubsup><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>x</mi><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>x</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mover><mi>x</mi><mo>¯</mo></mover></mrow><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>ω</mi><mo>¯</mo></mover><mo stretchy="false">×</mo><mover><mi>x</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>L</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><msubsup><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>x</mi><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>x</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mover><mi>x</mi><mo>¯</mo></mover></mrow><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>ω</mi><mo>¯</mo></mover><mo stretchy="false">×</mo><mover><mi>x</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><msubsup><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>x</mi><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>x</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mover><mi>ω</mi><mo>¯</mo></mover><mo stretchy="false"></mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>x</mi><mo>¯</mo></mover><mo stretchy="false"></mo><mover><mi>ω</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mover><mi>x</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE">]</mo></mrow></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Mechanik des starren Körpers page

Identifiers

  • l¯
  • r¯s
  • M
  • V¯
  • x
  • ρ
  • x¯
  • x¯
  • ω¯
  • x¯
  • L¯
  • x
  • ρ
  • x¯
  • x¯
  • ω¯
  • x¯
  • x
  • ρ
  • x¯
  • x
  • ω¯
  • x¯
  • ω¯
  • x¯

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