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Display information for equation id:math.860.8 on revision:860
* Page found: Hamiltonsches Prinzip (eq math.860.8)
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\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}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>δ</mi><mi>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mi>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>−</mo><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>L</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>q</mi><mo>+</mo><mi>δ</mi><mi>q</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mo>+</mo><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mi>t</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mi>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>−</mo><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><munder><mrow data-mjx-texclass="OP"><munder><mi>L</mi><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>=</mo><mi>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow></mrow></mrow></munder><mo>+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mi>L</mi><mi>δ</mi><mi>q</mi><mo>+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mrow></msub><mi>L</mi><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mi>t</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mo>−</mo><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mi>L</mi><mi>δ</mi><mi>q</mi><mo>+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mrow></msub><mi>L</mi><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mi>t</mi></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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