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Display information for equation id:math.870.9 on revision:870
* Page found: Hamiltonsches Prinzip (eq math.870.9)
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Hash: e4536e30a294f3b7edb7177b7063b0a8
TeX (original user input):
\begin{align}
\delta S\left[ q \right] & =S\left[ {{q}_{0}} \right]-\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{L\left( q+\delta q,\dot{q}+\delta \dot{q},t \right)dt} \\
& =S\left[ {{q}_{0}} \right]-\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( \underbrace{L}_{=S\left[ {{q}_{0}} \right]}+{{\partial }_{q}}L\delta q+{{\partial }_{{\dot{q}}}}L\delta \dot{q} \right)dt} \\
& =-\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{\partial }_{q}}L\delta q+{{\partial }_{{\dot{q}}}}L\delta \dot{q} \right)dt}
\end{align}
TeX (checked):
{\begin{aligned}\delta S\left[q\right]&=S\left[{{q}_{0}}\right]-\int \limits _{{t}_{1}}^{{t}_{2}}{L\left(q+\delta q,{\dot {q}}+\delta {\dot {q}},t\right)dt}\\&=S\left[{{q}_{0}}\right]-\int \limits _{{t}_{1}}^{{t}_{2}}{\left(\underbrace {L} _{=S\left[{{q}_{0}}\right]}+{{\partial }_{q}}L\delta q+{{\partial }_{\dot {q}}}L\delta {\dot {q}}\right)dt}\\&=-\int \limits _{{t}_{1}}^{{t}_{2}}{\left({{\partial }_{q}}L\delta q+{{\partial }_{\dot {q}}}L\delta {\dot {q}}\right)dt}\end{aligned}}
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