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Display information for equation id:math.1926.22 on revision:1926
* Page found: Zeitliche Translationsinvarianz (eq math.1926.22)
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Hash: b02f16c536b69e27890484cf6deea900
TeX (original user input):
0=\delta \int\limits_{\tau 1}^{\tau 2}{{}}\bar{L}d\tau =\delta \int\limits_{t1}^{t2}{{}}Ldt\Leftrightarrow \frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}-\frac{\partial L}{\partial {{q}_{k}}}=0
TeX (checked):
0=\delta \int \limits _{\tau 1}^{\tau 2}{}{\bar {L}}d\tau =\delta \int \limits _{t1}^{t2}{}Ldt\Leftrightarrow {\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}-{\frac {\partial L}{\partial {{q}_{k}}}}=0
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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"><mn>0</mn><mo>=</mo><mi>δ</mi><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>τ</mi><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>τ</mi><mn>2</mn></mrow></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mi>d</mi><mi>τ</mi><mo>=</mo><mi>δ</mi><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mn>2</mn></mrow></mrow></munderover><mi>L</mi><mi>d</mi><mi>t</mi><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>L</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>L</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mn>0</mn></mstyle></mrow></math>
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