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Display information for equation id:math.1898.3 on revision:1898

* Page found: Das hamiltonsche Wirkungsprinzip (eq math.1898.3)

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Hash: d0270c87e86ffee120ae55832276e8f5

TeX (original user input):

\begin{align}
  & \delta W=0 \\
 & \delta W=\delta \int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}F=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1}^{f}{{}}\left\{ \frac{\partial L}{\partial {{q}_{k}}}\delta {{q}_{k}}(t)+\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}\frac{d}{dt}\delta {{q}_{k}}(t) \right\} \\
 & \delta W=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1}^{f}{{}}\left\{ \frac{\partial L}{\partial {{q}_{k}}}-\frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}} \right\}\delta {{q}_{k}}(t)=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&\delta W=0\\&\delta W=\delta \int \limits _{{t}_{1}}^{{t}_{2}}{dt}F=\int \limits _{{t}_{1}}^{{t}_{2}}{dt}\sum \limits _{k=1}^{f}{}\left\{{\frac {\partial L}{\partial {{q}_{k}}}}\delta {{q}_{k}}(t)+{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}{\frac {d}{dt}}\delta {{q}_{k}}(t)\right\}\\&\delta W=\int \limits _{{t}_{1}}^{{t}_{2}}{dt}\sum \limits _{k=1}^{f}{}\left\{{\frac {\partial L}{\partial {{q}_{k}}}}-{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}\right\}\delta {{q}_{k}}(t)=0\\\end{aligned}}

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MathML (48.758 KB / 4.95 KB) :

δ W = 0 δ W = δ t 1 t 2 𝑑 t F = t 1 t 2 𝑑 t k = 1 f { L q k δ q k ( t ) + L q ˙ k d d t δ q k ( t ) } δ W = t 1 t 2 𝑑 t k = 1 f { L q k - d d t L q ˙ k } δ q k ( t ) = 0 missing-subexpression 𝛿 𝑊 0 missing-subexpression 𝛿 𝑊 𝛿 superscript subscript subscript 𝑡 1 subscript 𝑡 2 differential-d 𝑡 𝐹 superscript subscript subscript 𝑡 1 subscript 𝑡 2 differential-d 𝑡 superscript subscript 𝑘 1 𝑓 𝐿 subscript 𝑞 𝑘 𝛿 subscript 𝑞 𝑘 𝑡 𝐿 subscript ˙ 𝑞 𝑘 𝑑 𝑑 𝑡 𝛿 subscript 𝑞 𝑘 𝑡 missing-subexpression 𝛿 𝑊 superscript subscript subscript 𝑡 1 subscript 𝑡 2 differential-d 𝑡 superscript subscript 𝑘 1 𝑓 𝐿 subscript 𝑞 𝑘 𝑑 𝑑 𝑡 𝐿 subscript ˙ 𝑞 𝑘 𝛿 subscript 𝑞 𝑘 𝑡 0 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\delta W=0\\ &\displaystyle\delta W=\delta\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}F=\int% \limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1}^{f}{{}}\left\{\frac{% \partial L}{\partial{{q}_{k}}}\delta{{q}_{k}}(t)+\frac{\partial L}{\partial{{{% \dot{q}}}_{k}}}\frac{d}{dt}\delta{{q}_{k}}(t)\right\}\\ &\displaystyle\delta W=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1% }^{f}{{}}\left\{\frac{\partial L}{\partial{{q}_{k}}}-\frac{d}{dt}\frac{% \partial L}{\partial{{{\dot{q}}}_{k}}}\right\}\delta{{q}_{k}}(t)=0\\ \end{aligned}}}

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MathML (4.598 KB / 555 B) :

δW=0δW=δt1t2dtF=t1t2dtk=1f{Lqkδqk(t)+Lq˙kddtδqk(t)}δW=t1t2dtk=1f{LqkddtLq˙k}δqk(t)=0

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