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Display information for equation id:math.1905.8 on revision:1905

* Page found: Eichtransformation der Lagrangefunktion (eq math.1905.8)

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Eichtransformation der Lagrangefunktion Eq: math.1905.8

Hash: 0cd0494e7538684b6ad6e7f3348249cf

TeX (original user input):

\begin{align}
  & \frac{\partial L}{\partial {{{\dot{q}}}_{k}}}=m{{{\dot{q}}}_{k}}+e{{A}_{k}} \\
 & \frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}=m{{{\ddot{q}}}_{k}}+e\frac{d}{dt}{{A}_{k}}(\bar{q}(t),t) \\
 & \frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}=m{{{\ddot{q}}}_{k}}+e\left( \frac{\partial }{\partial t}{{A}_{k}}+\sum\limits_{l}{\frac{\partial {{A}_{k}}}{\partial {{q}_{l}}}{{{\dot{q}}}_{l}}} \right) \\
 & \frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}=m{{{\ddot{q}}}_{k}}+e\left( \frac{\partial }{\partial t}{{A}_{k}}+\left( \dot{\bar{q}}\cdot \nabla  \right){{A}_{k}} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}=m{{\dot {q}}_{k}}+e{{A}_{k}}\\&{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}=m{{\ddot {q}}_{k}}+e{\frac {d}{dt}}{{A}_{k}}({\bar {q}}(t),t)\\&{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}=m{{\ddot {q}}_{k}}+e\left({\frac {\partial }{\partial t}}{{A}_{k}}+\sum \limits _{l}{{\frac {\partial {{A}_{k}}}{\partial {{q}_{l}}}}{{\dot {q}}_{l}}}\right)\\&{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}=m{{\ddot {q}}_{k}}+e\left({\frac {\partial }{\partial t}}{{A}_{k}}+\left({\dot {\bar {q}}}\cdot \nabla \right){{A}_{k}}\right)\\\end{aligned}}

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MathML (5.997 KB / 578 B) :

\begin{aligned} \frac{\partial L}{\partial {\dot{q}}_{k}} = m {\dot{q}}_{k} + e A_{k} \\ \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}} = m {\ddot{q}}_{k} + e \frac{d}{d t} A_{k} (\bar{q} (t), t) \\ \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}} = m {\ddot{q}}_{k} + e (\frac{\partial}{\partial t} A_{k} + \sum_{l} \frac{\partial A_{k}}{\partial q_{l}} {\dot{q}}_{l}) \\ \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}} = m {\ddot{q}}_{k} + e (\frac{\partial}{\partial t} A_{k} + (\dot{\bar{q}} \cdot \nabla) A_{k}) \end{aligned}

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Identifiers

$L$

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

$m$

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

$e$

$A_{k}$

$d$

$d$

$t$

$L$

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

$m$

${\ddot{q}}_{k}$

$e$

$d$

$d$

$t$

$A_{k}$

$\bar{q}$

$t$

$t$

$d$

$d$

$t$

$L$

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

$m$

${\ddot{q}}_{k}$

$e$

$t$

$A_{k}$

$l$

$A_{k}$

$q_{l}$

${\dot{q}}_{l}$

$d$

$d$

$t$

$L$

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

$m$

${\ddot{q}}_{k}$

$e$

$t$

$A_{k}$

$\dot{\bar{q}}$

$A_{k}$

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