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Display information for equation id:math.2010.8 on revision:2010

* Page found: Kinetische Energie und Trägheitstensor (eq math.2010.8)

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TeX (original user input):

\frac{1}{2}\sum\limits_{i=1}^{n}{{{m}_{i}}{{v}^{(i)}}^{2}}=\frac{1}{2}\sum\limits_{i=1}^{n}{{{m}_{i}}}{{\left( V+\omega \times {{x}^{(i)}} \right)}^{2}}=\frac{1}{2}\sum\limits_{i=1}^{n}{{{m}_{i}}}{{V}^{2}}+V\cdot \sum\limits_{i=1}^{n}{{{m}_{i}}}\left( \omega \times {{x}^{(i)}} \right)+\frac{1}{2}\sum\limits_{i=1}^{n}{{{m}_{i}}}{{\left( \omega \times {{x}^{(i)}} \right)}^{2}}

TeX (checked):

{\frac {1}{2}}\sum \limits _{i=1}^{n}{{{m}_{i}}{{v}^{(i)}}^{2}}={\frac {1}{2}}\sum \limits _{i=1}^{n}{{m}_{i}}{{\left(V+\omega \times {{x}^{(i)}}\right)}^{2}}={\frac {1}{2}}\sum \limits _{i=1}^{n}{{m}_{i}}{{V}^{2}}+V\cdot \sum \limits _{i=1}^{n}{{m}_{i}}\left(\omega \times {{x}^{(i)}}\right)+{\frac {1}{2}}\sum \limits _{i=1}^{n}{{m}_{i}}{{\left(\omega \times {{x}^{(i)}}\right)}^{2}}

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12i=1nmiv(i)2=12i=1nmi(V+ω×x(i))2=12i=1nmiV2+Vi=1nmi(ω×x(i))+12i=1nmi(ω×x(i))2
<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"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munderover><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>V</mi><mo>+</mo><mi>&#x03C9;</mi><mo>&#x00D7;</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munderover><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>V</mi><mo>&#x22C5;</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munderover><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03C9;</mi><mo>&#x00D7;</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munderover><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03C9;</mi><mo>&#x00D7;</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mstyle></mrow></math>

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