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Display information for equation id:math.1410.113 on revision:1410

* Page found: Symmetrien und Erhaltungsgrößen (eq math.1410.113)

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TeX (original user input):

\begin{align}
  & \sum\limits_{k=1}^{N}{\left( \frac{\partial T}{\partial \left( \lambda {{{\dot{q}}}_{k}} \right)} \right)\left( \frac{\partial \left( \lambda {{{\dot{q}}}_{k}} \right)}{\partial \lambda } \right)}\left| _{\lambda =1} \right.=2\lambda T\left| _{\lambda =1} \right.\Leftrightarrow \sum\limits_{k=1}^{N}{\left( \frac{\partial T}{\partial \left( {{{\dot{q}}}_{k}} \right)} \right){{{\dot{q}}}_{k}}}=2T \\ 
 & \left( \frac{\partial \left( \lambda {{{\dot{q}}}_{k}} \right)}{\partial \lambda } \right)={{{\dot{q}}}_{k}} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&\sum \limits _{k=1}^{N}{\left({\frac {\partial T}{\partial \left(\lambda {{\dot {q}}_{k}}\right)}}\right)\left({\frac {\partial \left(\lambda {{\dot {q}}_{k}}\right)}{\partial \lambda }}\right)}\left|_{\lambda =1}\right.=2\lambda T\left|_{\lambda =1}\right.\Leftrightarrow \sum \limits _{k=1}^{N}{\left({\frac {\partial T}{\partial \left({{\dot {q}}_{k}}\right)}}\right){{\dot {q}}_{k}}}=2T\\&\left({\frac {\partial \left(\lambda {{\dot {q}}_{k}}\right)}{\partial \lambda }}\right)={{\dot {q}}_{k}}\\\end{aligned}}

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MathML (4.501 KB / 525 B) :

\begin{aligned} \sum_{k = 1}^{N} (\frac{\partial T}{\partial (λ {\dot{q}}_{k})}) (\frac{\partial (λ {\dot{q}}_{k})}{\partial λ}) | λ = 1 = 2 λ T | λ = 1 \Leftrightarrow \sum_{k = 1}^{N} (\frac{\partial T}{\partial ({\dot{q}}_{k})}) {\dot{q}}_{k} = 2 T \\ (\frac{\partial (λ {\dot{q}}_{k})}{\partial λ}) = {\dot{q}}_{k} \end{aligned}

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Identifiers

$k$

$N$

$T$

$λ$

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

$λ$

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

$λ$

$λ$

$λ$

$T$

$λ$

$k$

$N$

$T$

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

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

$T$

$λ$

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

$λ$

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

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