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Klassisch- mechanische Gleichgewichtsverteilungen Eq: math.2524.17

Klassisch- mechanische Gleichgewichtsverteilungen Eq: math.2524.19

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TeX (original user input):

\begin{align}

& \frac{\partial \rho \left( \xi ,t \right)}{\partial t}+div\left( \rho \dot{\xi } \right)=\frac{\partial \rho \left( \xi ,t \right)}{\partial t}+\sum\limits_{k=1}^{3N}{{}}\left( \frac{\partial \rho \left( \xi ,t \right)}{\partial {{q}_{k}}}{{{\dot{q}}}_{k}}+\frac{\partial \rho \left( \xi ,t \right)}{\partial {{p}_{k}}}{{{\dot{p}}}_{k}} \right)+\rho div\dot{\xi } \\

& \rho div\dot{\xi }=0 \\

& \Rightarrow \frac{\partial \rho \left( \xi ,t \right)}{\partial t}+div\left( \rho \dot{\xi } \right)=\frac{\partial \rho \left( \xi ,t \right)}{\partial t}+\sum\limits_{k=1}^{3N}{{}}\left( \frac{\partial \rho \left( \xi ,t \right)}{\partial {{q}_{k}}}{{{\dot{q}}}_{k}}+\frac{\partial \rho \left( \xi ,t \right)}{\partial {{p}_{k}}}{{{\dot{p}}}_{k}} \right)=\frac{d\rho \left( \xi ,t \right)}{dt}=0 \\

\end{align}

TeX (checked):

{\begin{aligned}&{\frac {\partial \rho \left(\xi ,t\right)}{\partial t}}+div\left(\rho {\dot {\xi }}\right)={\frac {\partial \rho \left(\xi ,t\right)}{\partial t}}+\sum \limits _{k=1}^{3N}{}\left({\frac {\partial \rho \left(\xi ,t\right)}{\partial {{q}_{k}}}}{{\dot {q}}_{k}}+{\frac {\partial \rho \left(\xi ,t\right)}{\partial {{p}_{k}}}}{{\dot {p}}_{k}}\right)+\rho div{\dot {\xi }}\\&\rho div{\dot {\xi }}=0\\&\Rightarrow {\frac {\partial \rho \left(\xi ,t\right)}{\partial t}}+div\left(\rho {\dot {\xi }}\right)={\frac {\partial \rho \left(\xi ,t\right)}{\partial t}}+\sum \limits _{k=1}^{3N}{}\left({\frac {\partial \rho \left(\xi ,t\right)}{\partial {{q}_{k}}}}{{\dot {q}}_{k}}+{\frac {\partial \rho \left(\xi ,t\right)}{\partial {{p}_{k}}}}{{\dot {p}}_{k}}\right)={\frac {d\rho \left(\xi ,t\right)}{dt}}=0\\\end{aligned}}

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\begin{aligned} \frac{\partial ρ (ξ, t)}{\partial t} + d i v (ρ \dot{ξ}) = \frac{\partial ρ (ξ, t)}{\partial t} + \sum_{k = 1}^{3 N} (\frac{\partial ρ (ξ, t)}{\partial q_{k}} {\dot{q}}_{k} + \frac{\partial ρ (ξ, t)}{\partial p_{k}} {\dot{p}}_{k}) + ρ d i v \dot{ξ} \\ ρ d i v \dot{ξ} = 0 \\ \Rightarrow \frac{\partial ρ (ξ, t)}{\partial t} + d i v (ρ \dot{ξ}) = \frac{\partial ρ (ξ, t)}{\partial t} + \sum_{k = 1}^{3 N} (\frac{\partial ρ (ξ, t)}{\partial q_{k}} {\dot{q}}_{k} + \frac{\partial ρ (ξ, t)}{\partial p_{k}} {\dot{p}}_{k}) = \frac{d ρ (ξ, t)}{d t} = 0 \end{aligned}

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Identifiers

$ρ$

$ξ$

$t$

$t$

$d$

$i$

$v$

$ρ$

$\dot{ξ}$

$ρ$

$ξ$

$t$

$t$

$k$

$N$

$ρ$

$ξ$

$t$

$q_{k}$

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

$ρ$

$ξ$

$t$

$p_{k}$

${\dot{p}}_{k}$

$ρ$

$d$

$i$

$v$

$\dot{ξ}$

$ρ$

$d$

$i$

$v$

$\dot{ξ}$

$ρ$

$ξ$

$t$

$t$

$d$

$i$

$v$

$ρ$

$\dot{ξ}$

$ρ$

$ξ$

$t$

$t$

$k$

$N$

$ρ$

$ξ$

$t$

$q_{k}$

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

$ρ$

$ξ$

$t$

$p_{k}$

${\dot{p}}_{k}$

$d$

$ρ$

$ξ$

$t$

$d$

$t$

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