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Display information for equation id:math.2524.19 on revision:2524

* Page found: Klassisch- mechanische Gleichgewichtsverteilungen (eq math.2524.19)

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Klassisch- mechanische Gleichgewichtsverteilungen Eq: math.2524.17

Klassisch- mechanische Gleichgewichtsverteilungen Eq: math.2524.19

Hash: 2daa165afeadfb2782b96849660c4cca

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\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}

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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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