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Display information for equation id:math.1255.118 on revision:1255

* Page found: Das d'Alembertsche Prinzip (eq math.1255.118)

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TeX (original user input): 

\begin{align}
  & \frac{d}{dt}\left( \frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{j}}} \right)=\sum\limits_{k=1}^{{}}{\left( \frac{{{\partial }^{2}}{{{\bar{r}}}_{i}}}{\partial {{q}_{k}}\partial {{q}_{j}}} \right)}{{{\dot{q}}}_{k}}+\frac{{{\partial }^{2}}}{\partial {{q}_{j}}\partial t}{{{\bar{r}}}_{i}} \\
 & \frac{\partial }{\partial {{q}_{j}}}{{{\vec{v}}}_{i}}=\frac{\partial }{\partial {{q}_{j}}}\left\{ \sum\limits_{k=1}^{{}}{\left( \frac{\partial {{{\bar{r}}}_{i}}}{\partial {{q}_{k}}} \right)}{{{\dot{q}}}_{k}}+\frac{\partial }{\partial t}{{{\bar{r}}}_{i}} \right\}=\sum\limits_{k=1}^{{}}{\left( \frac{{{\partial }^{2}}{{{\bar{r}}}_{i}}}{\partial {{q}_{k}}\partial {{q}_{j}}} \right)}{{{\dot{q}}}_{k}}+\frac{{{\partial }^{2}}}{\partial {{q}_{j}}\partial t}{{{\bar{r}}}_{i}} \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\frac {d}{dt}}\left({\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{j}}}}\right)=\sum \limits _{k=1}^{}{\left({\frac {{{\partial }^{2}}{{\bar {r}}_{i}}}{\partial {{q}_{k}}\partial {{q}_{j}}}}\right)}{{\dot {q}}_{k}}+{\frac {{\partial }^{2}}{\partial {{q}_{j}}\partial t}}{{\bar {r}}_{i}}\\&{\frac {\partial }{\partial {{q}_{j}}}}{{\vec {v}}_{i}}={\frac {\partial }{\partial {{q}_{j}}}}\left\{\sum \limits _{k=1}^{}{\left({\frac {\partial {{\bar {r}}_{i}}}{\partial {{q}_{k}}}}\right)}{{\dot {q}}_{k}}+{\frac {\partial }{\partial t}}{{\bar {r}}_{i}}\right\}=\sum \limits _{k=1}^{}{\left({\frac {{{\partial }^{2}}{{\bar {r}}_{i}}}{\partial {{q}_{k}}\partial {{q}_{j}}}}\right)}{{\dot {q}}_{k}}+{\frac {{\partial }^{2}}{\partial {{q}_{j}}\partial t}}{{\bar {r}}_{i}}\\\end{aligned}}

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ddt(∂r¯i∂qj)=∑k=1(∂2r¯i∂qk∂qj)q˙k+∂2∂qj∂tr¯i∂∂qjv→i=∂∂qj{∑k=1(∂r¯i∂qk)q˙k+∂∂tr¯i}=∑k=1(∂2r¯i∂qk∂qj)q˙k+∂2∂qj∂tr¯i
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data-mjx-texclass="ORD"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>v</mi><mo>→</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo 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data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></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"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mi>&#x2202;</mi><msub><mi>q</mi><mrow 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Calculated based on the variables occurring on the entire Das d'Alembertsche Prinzip page

Identifiers

  • d
  • d
  • t
  • r¯i
  • qj
  • k
  • r¯i
  • qk
  • qj
  • q˙k
  • qj
  • t
  • r¯i
  • qj
  • v→i
  • qj
  • k
  • r¯i
  • qk
  • q˙k
  • t
  • r¯i
  • k
  • r¯i
  • qk
  • qj
  • q˙k
  • qj
  • t
  • r¯i

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