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Display information for equation id:math.1951.18 on revision:1951
* Page found: Legendre- Transformation und Hamiltonfunktion (eq math.1951.18)
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Hash: b333822123edee688b2c0812701aff1c
TeX (original user input):
\begin{align}
& L({{q}_{1}},...,{{q}_{f}},{{{\dot{q}}}_{1}},...,{{{\dot{q}}}_{f}},t) \\
& {{p}_{k}}:=\frac{\partial L}{\partial {{{\dot{q}}}_{k}}} \\
& H({{q}_{1}},...,{{q}_{f}},{{p}_{1}},...,{{p}_{f}},t)=\sum\limits_{k=1}^{f}{{{{\dot{q}}}_{k}}{{p}_{k}}-L} \\
\end{align}
TeX (checked):
{\begin{aligned}&L({{q}_{1}},...,{{q}_{f}},{{\dot {q}}_{1}},...,{{\dot {q}}_{f}},t)\\&{{p}_{k}}:={\frac {\partial L}{\partial {{\dot {q}}_{k}}}}\\&H({{q}_{1}},...,{{q}_{f}},{{p}_{1}},...,{{p}_{f}},t)=\sum \limits _{k=1}^{f}{{{\dot {q}}_{k}}{{p}_{k}}-L}\\\end{aligned}}
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MathML (2.396 KB / 450 B) :
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>L</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mi>...</mi><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>,</mo><msub><mover><mi>q</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mi>...</mi><mo>,</mo><msub><mover><mi>q</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">:=</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><mover><mi>q</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>H</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mi>...</mi><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mi>...</mi><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo stretchy="false">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><msub><mover><mi>q</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">−</mo><mi>L</mi></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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