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Display information for equation id:math.1411.41 on revision:1411

* Page found: Symmetrien und Erhaltungsgrößen (eq math.1411.41)

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Räumliche Translationsinvarianz Eq: math.1938.28

Hash: e58bb5725c074f530aca1064ae867e07

TeX (original user input):

\begin{align}
  & {{I}_{x}}=\frac{\partial L}{\partial {{{\dot{\bar{r}}}}_{1}}}{{{\bar{e}}}_{x}}+\frac{\partial L}{\partial {{{\dot{\bar{r}}}}_{2}}}{{{\bar{e}}}_{x}}=\frac{\partial L}{\partial {{{\dot{x}}}_{1}}}+\frac{\partial L}{\partial {{{\dot{x}}}_{2}}}={{m}_{1}}{{{\dot{x}}}_{1}}+{{m}_{2}}{{{\dot{x}}}_{2}}={{P}_{x}}=const \\
 & {{I}_{y}}=\frac{\partial L}{\partial {{{\dot{\bar{r}}}}_{1}}}{{{\bar{e}}}_{y}}+\frac{\partial L}{\partial {{{\dot{\bar{r}}}}_{2}}}{{{\bar{e}}}_{y}}=\frac{\partial L}{\partial {{{\dot{y}}}_{1}}}+\frac{\partial L}{\partial {{{\dot{y}}}_{2}}}={{m}_{1}}{{{\dot{y}}}_{1}}+{{m}_{2}}{{{\dot{y}}}_{2}}={{P}_{y}}=const \\
 & {{I}_{z}}=\frac{\partial L}{\partial {{{\dot{\bar{r}}}}_{1}}}{{{\bar{e}}}_{z}}+\frac{\partial L}{\partial {{{\dot{\bar{r}}}}_{2}}}{{{\bar{e}}}_{z}}=\frac{\partial L}{\partial {{{\dot{z}}}_{1}}}+\frac{\partial L}{\partial {{{\dot{z}}}_{2}}}={{m}_{1}}{{{\dot{z}}}_{1}}+{{m}_{2}}{{{\dot{z}}}_{2}}={{P}_{z}}=const \\
\end{align}

TeX (checked):

{\begin{aligned}&{{I}_{x}}={\frac {\partial L}{\partial {{\dot {\bar {r}}}_{1}}}}{{\bar {e}}_{x}}+{\frac {\partial L}{\partial {{\dot {\bar {r}}}_{2}}}}{{\bar {e}}_{x}}={\frac {\partial L}{\partial {{\dot {x}}_{1}}}}+{\frac {\partial L}{\partial {{\dot {x}}_{2}}}}={{m}_{1}}{{\dot {x}}_{1}}+{{m}_{2}}{{\dot {x}}_{2}}={{P}_{x}}=const\\&{{I}_{y}}={\frac {\partial L}{\partial {{\dot {\bar {r}}}_{1}}}}{{\bar {e}}_{y}}+{\frac {\partial L}{\partial {{\dot {\bar {r}}}_{2}}}}{{\bar {e}}_{y}}={\frac {\partial L}{\partial {{\dot {y}}_{1}}}}+{\frac {\partial L}{\partial {{\dot {y}}_{2}}}}={{m}_{1}}{{\dot {y}}_{1}}+{{m}_{2}}{{\dot {y}}_{2}}={{P}_{y}}=const\\&{{I}_{z}}={\frac {\partial L}{\partial {{\dot {\bar {r}}}_{1}}}}{{\bar {e}}_{z}}+{\frac {\partial L}{\partial {{\dot {\bar {r}}}_{2}}}}{{\bar {e}}_{z}}={\frac {\partial L}{\partial {{\dot {z}}_{1}}}}+{\frac {\partial L}{\partial {{\dot {z}}_{2}}}}={{m}_{1}}{{\dot {z}}_{1}}+{{m}_{2}}{{\dot {z}}_{2}}={{P}_{z}}=const\\\end{aligned}}

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\begin{aligned} I_{x} = \frac{\partial L}{\partial {\dot{\bar{r}}}_{1}} {\bar{e}}_{x} + \frac{\partial L}{\partial {\dot{\bar{r}}}_{2}} {\bar{e}}_{x} = \frac{\partial L}{\partial {\dot{x}}_{1}} + \frac{\partial L}{\partial {\dot{x}}_{2}} = m_{1} {\dot{x}}_{1} + m_{2} {\dot{x}}_{2} = P_{x} = c o n s t \\ I_{y} = \frac{\partial L}{\partial {\dot{\bar{r}}}_{1}} {\bar{e}}_{y} + \frac{\partial L}{\partial {\dot{\bar{r}}}_{2}} {\bar{e}}_{y} = \frac{\partial L}{\partial {\dot{y}}_{1}} + \frac{\partial L}{\partial {\dot{y}}_{2}} = m_{1} {\dot{y}}_{1} + m_{2} {\dot{y}}_{2} = P_{y} = c o n s t \\ I_{z} = \frac{\partial L}{\partial {\dot{\bar{r}}}_{1}} {\bar{e}}_{z} + \frac{\partial L}{\partial {\dot{\bar{r}}}_{2}} {\bar{e}}_{z} = \frac{\partial L}{\partial {\dot{z}}_{1}} + \frac{\partial L}{\partial {\dot{z}}_{2}} = m_{1} {\dot{z}}_{1} + m_{2} {\dot{z}}_{2} = P_{z} = c o n s t \end{aligned}

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Identifiers

$I_{x}$

$L$

${\dot{\bar{r}}}_{1}$

${\bar{e}}_{x}$

$L$

${\dot{\bar{r}}}_{2}$

${\bar{e}}_{x}$

$L$

${\dot{x}}_{1}$

$L$

${\dot{x}}_{2}$

$m_{1}$

${\dot{x}}_{1}$

$m_{2}$

${\dot{x}}_{2}$

$P_{x}$

$c$

$o$

$n$

$s$

$t$

$I_{y}$

$L$

${\dot{\bar{r}}}_{1}$

${\bar{e}}_{y}$

$L$

${\dot{\bar{r}}}_{2}$

${\bar{e}}_{y}$

$L$

${\dot{y}}_{1}$

$L$

${\dot{y}}_{2}$

$m_{1}$

${\dot{y}}_{1}$

$m_{2}$

${\dot{y}}_{2}$

$P_{y}$

$c$

$o$

$n$

$s$

$t$

$I_{z}$

$L$

${\dot{\bar{r}}}_{1}$

${\bar{e}}_{z}$

$L$

${\dot{\bar{r}}}_{2}$

${\bar{e}}_{z}$

$L$

${\dot{z}}_{1}$

$L$

${\dot{z}}_{2}$

$m_{1}$

${\dot{z}}_{1}$

$m_{2}$

${\dot{z}}_{2}$

$P_{z}$

$c$

$o$

$n$

$s$

$t$

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