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Display information for equation id:math.1255.145 on revision:1255

* Page found: Das d'Alembertsche Prinzip (eq math.1255.145)

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Normalschwingungen Eq: math.1515.6

Hash: 6418c6854a50415ad01eed2eec7fa36c

TeX (original user input):

\begin{align}
  & {{{\vec{v}}}_{i}}=\sum\limits_{j}{{}}\left( \frac{\partial {{{\vec{r}}}_{i}}}{\partial {{q}_{j}}} \right){{{\dot{q}}}_{j}} \\
 & T=\frac{1}{2}\sum\limits_{i}{{{m}_{i}}}\left( \sum\limits_{j,k}{\left( \frac{\partial {{{\vec{r}}}_{i}}}{\partial {{q}_{j}}} \right)\left( \frac{\partial {{{\vec{r}}}_{i}}}{\partial {{q}_{j}}} \right)}{{{\dot{q}}}_{j}}{{{\dot{q}}}_{k}} \right)\ge 0 \\
 & T=\frac{1}{2}\sum\limits_{j,k}{{{T}_{jk}}}{{{\dot{q}}}_{j}}{{{\dot{q}}}_{k}} \\
 & {{T}_{jk}}={{T}_{kj}}\approx \sum\limits_{i}{{{m}_{i}}{{\left( \frac{\partial {{{\vec{r}}}_{i}}}{\partial {{q}_{j}}} \right)}_{0}}{{\left( \frac{\partial {{{\vec{r}}}_{i}}}{\partial {{q}_{j}}} \right)}_{0}}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\vec {v}}_{i}}=\sum \limits _{j}{}\left({\frac {\partial {{\vec {r}}_{i}}}{\partial {{q}_{j}}}}\right){{\dot {q}}_{j}}\\&T={\frac {1}{2}}\sum \limits _{i}{{m}_{i}}\left(\sum \limits _{j,k}{\left({\frac {\partial {{\vec {r}}_{i}}}{\partial {{q}_{j}}}}\right)\left({\frac {\partial {{\vec {r}}_{i}}}{\partial {{q}_{j}}}}\right)}{{\dot {q}}_{j}}{{\dot {q}}_{k}}\right)\geq 0\\&T={\frac {1}{2}}\sum \limits _{j,k}{{T}_{jk}}{{\dot {q}}_{j}}{{\dot {q}}_{k}}\\&{{T}_{jk}}={{T}_{kj}}\approx \sum \limits _{i}{{{m}_{i}}{{\left({\frac {\partial {{\vec {r}}_{i}}}{\partial {{q}_{j}}}}\right)}_{0}}{{\left({\frac {\partial {{\vec {r}}_{i}}}{\partial {{q}_{j}}}}\right)}_{0}}}\\\end{aligned}}

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MathML (6.203 KB / 594 B) :

\begin{aligned} {\vec{v}}_{i} = \sum_{j} (\frac{\partial {\vec{r}}_{i}}{\partial q_{j}}) {\dot{q}}_{j} \\ T = \frac{1}{2} \sum_{i} m_{i} (\sum_{j, k} (\frac{\partial {\vec{r}}_{i}}{\partial q_{j}}) (\frac{\partial {\vec{r}}_{i}}{\partial q_{j}}) {\dot{q}}_{j} {\dot{q}}_{k}) \geq 0 \\ T = \frac{1}{2} \sum_{j, k} T_{j k} {\dot{q}}_{j} {\dot{q}}_{k} \\ T_{j k} = T_{k j} \approx \sum_{i} m_{i} {(\frac{\partial {\vec{r}}_{i}}{\partial q_{j}})}_{0} {(\frac{\partial {\vec{r}}_{i}}{\partial q_{j}})}_{0} \end{aligned}

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Identifiers

${\vec{v}}_{i}$

$j$

${\vec{r}}_{i}$

$q_{j}$

${\dot{q}}_{j}$

$T$

$i$

$m_{i}$

$j$

$k$

${\vec{r}}_{i}$

$q_{j}$

${\vec{r}}_{i}$

$q_{j}$

${\dot{q}}_{j}$

${\dot{q}}_{k}$

$T$

$j$

$k$

$T_{j k}$

${\dot{q}}_{j}$

${\dot{q}}_{k}$

$T_{j k}$

$T_{k j}$

$i$

$m_{i}$

${\vec{r}}_{i}$

$q_{j}$

${\vec{r}}_{i}$

$q_{j}$

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