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Display information for equation id:math.1889.39 on revision:1889
* Page found: Variationsprinzipien (eq math.1889.39)
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\delta f=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt\delta F(x,\dot{x})}=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt\left\{ \frac{\partial F}{\partial x}\delta x+\frac{\partial F}{\partial \dot{x}}\delta \dot{x} \right\}=}\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt\left\{ \frac{\partial F}{\partial x}+\frac{d}{dt}\frac{\partial F}{\partial \dot{x}} \right\}\delta x(t)}
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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"><mi>δ</mi><mi>f</mi><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>d</mi><mi>t</mi><mi>δ</mi><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>˙</mo></mover></mrow></mrow><mo stretchy="false">)</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>d</mi><mi>t</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mi>δ</mi><mi>x</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>˙</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>˙</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo>=</mo></mrow><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>d</mi><mi>t</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>˙</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">}</mo></mrow><mi>δ</mi><mi>x</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mstyle></mrow></math>
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