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Display information for equation id:math.1957.49 on revision:1957
* Page found: Kanonische Transformationen (eq math.1957.49)
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\begin{align}
& \delta \left\{ {{M}_{1}}(q({{t}_{2}}),Q({{t}_{2}}),{{t}_{2}})-{{M}_{1}}(q({{t}_{1}}),Q({{t}_{1}}),{{t}_{1}}) \right\}=\sum\limits_{k}{\left( \left. \frac{\partial {{M}_{1}}}{\partial {{q}_{k}}}\delta {{q}_{k}} \right|_{{{t}_{1}}}^{{{t}_{2}}}+\left. \frac{\partial {{M}_{1}}}{\partial {{Q}_{k}}}\delta {{Q}_{k}} \right|_{{{t}_{1}}}^{{{t}_{2}}} \right)} \\
& mit\left. \quad \frac{\partial {{M}_{1}}}{\partial {{q}_{k}}}\delta {{q}_{k}} \right|_{{{t}_{1}}}^{{{t}_{2}}}=0\quad und\quad \left. \frac{\partial {{M}_{1}}}{\partial {{Q}_{k}}}\delta {{Q}_{k}} \right|_{{{t}_{1}}}^{{{t}_{2}}}\ne 0 \\
\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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi>Q</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo>−</mo><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi>Q</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></munder><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msubsup><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><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></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><mi>δ</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><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></msubsup><mo>+</mo><msubsup><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><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></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><mi>δ</mi><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><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></msubsup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mi>i</mi><mi>t</mi><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mspace width="1em"></mspace><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></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><mi>δ</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><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></msubsup><mo>=</mo><mn>0</mn><mspace width="1em"></mspace><mi>u</mi><mi>n</mi><mi>d</mi><mspace width="1em"></mspace><msubsup><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><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></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><mi>δ</mi><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><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></msubsup><mo>≠</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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