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Display information for equation id:math.1122.17 on revision:1122

* Page found: Euler-Lagrange-Gleichungen (eq math.1122.17)

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\begin{align}
  & \delta S\left[ q \right]=-\left[ {{\partial }_{{\dot{q}}}}L\delta q \right]_{{{t}_{1}}}^{{{t}_{2}}}-\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{\partial }_{q}}L\delta q-{{d}_{t}}\left( {{\partial }_{{\dot{q}}}}L \right)\delta q \right)dt} \\
 & =\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{d}_{t}}{{\partial }_{{\dot{q}}}}-{{\partial }_{q}} \right)L\delta qdt}
\end{align}

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δ ⁢ S ⁢ [ q ] = - [ ∂ q ˙ ⁡ L ⁢ δ ⁢ q ] t 1 t 2 - ∫ t 1 t 2 ( ∂ q ⁡ L ⁢ δ ⁢ q - d t ⁢ ( ∂ q ˙ ⁡ L ) ⁢ δ ⁢ q ) ⁢ 𝑑 t = ∫ t 1 t 2 ( d t ⁢ ∂ q ˙ - ∂ q ) ⁢ L ⁢ δ ⁢ q ⁢ 𝑑 t missing-subexpression 𝛿 𝑆 delimited-[] 𝑞 superscript subscript delimited-[] subscript ˙ 𝑞 𝐿 𝛿 𝑞 subscript 𝑡 1 subscript 𝑡 2 superscript subscript subscript 𝑡 1 subscript 𝑡 2 subscript 𝑞 𝐿 𝛿 𝑞 subscript 𝑑 𝑡 subscript ˙ 𝑞 𝐿 𝛿 𝑞 differential-d 𝑡 missing-subexpression absent superscript subscript subscript 𝑡 1 subscript 𝑡 2 subscript 𝑑 𝑡 subscript ˙ 𝑞 subscript 𝑞 𝐿 𝛿 𝑞 differential-d 𝑡 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\delta S\left[q% \right]=-\left[{{\partial}_{{\dot{q}}}}L\delta q\right]_{{{t}_{1}}}^{{{t}_{2}}% }-\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left({{\partial}_{q}}L\delta q-{{d}_{t}% }\left({{\partial}_{{\dot{q}}}}L\right)\delta q\right)dt}\\ &\displaystyle=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left({{d}_{t}}{{\partial}_% {{\dot{q}}}}-{{\partial}_{q}}\right)L\delta qdt}\end{aligned}}}

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δS[q]=−[∂q˙Lδq]t1t2−∫t1t2(∂qLδq−dt(∂q˙L)δq)dt=∫t1t2(dt∂q˙−∂q)Lδqdt

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