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Display information for equation id:math.1142.5 on revision:1142
* Page found: Trägheitstensor (eq math.1142.5)
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Hash: beeb9893c455bf46d3e24ab4aa4d963c
TeX (original user input):
T=\frac{1}{2}\sum\limits_{i=1}^{N}{{{m}_{i}}{{\left( {{{\dot{r}}}_{0}}+\left( \omega \times {{r}_{i}} \right) \right)}^{2}}}=\frac{1}{2}M{{\dot{r}}_{0}}^{2}+\sum\limits_{i=1}^{N}{{{m}_{i}}{{{\dot{r}}}_{0}}\centerdot \left( \omega \times {{r}_{i}} \right)}+\frac{1}{2}\sum\limits_{i=1}^{N}{{{m}_{i}}{{\left( \omega \times {{r}_{i}} \right)}^{2}}}
TeX (checked):
T={\frac {1}{2}}\sum \limits _{i=1}^{N}{{{m}_{i}}{{\left({{\dot {r}}_{0}}+\left(\omega \times {{r}_{i}}\right)\right)}^{2}}}={\frac {1}{2}}M{{\dot {r}}_{0}}^{2}+\sum \limits _{i=1}^{N}{{{m}_{i}}{{\dot {r}}_{0}}\centerdot \left(\omega \times {{r}_{i}}\right)}+{\frac {1}{2}}\sum \limits _{i=1}^{N}{{{m}_{i}}{{\left(\omega \times {{r}_{i}}\right)}^{2}}}
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MathML (3.067 KB / 436 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>T</mi><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">∑</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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo>×</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><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><mi>M</mi><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><munderover><mo form="prefix" texclass="OP">∑</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><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo variantform="True">⋅</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo>×</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></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">∑</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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo>×</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mstyle></mrow></math>
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