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Display information for equation id:math.1322.65 on revision:1322
* Page found: Das Hamiltonsche Prinzip (eq math.1322.65)
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Hash: 9e37230d2e78ded564ad478dbd659f89
TeX (original user input):
\begin{align}
& \bar{E}\acute{\ }(\bar{q},t)=-\nabla \Phi \acute{\ }(\bar{q},t)-\frac{\partial }{\partial t}\bar{A}\acute{\ }(\bar{q},t)=-\nabla \left( \Phi (\bar{q},t)-\frac{\partial }{\partial t}\chi (\bar{q},t) \right)-\frac{\partial }{\partial t}\left( \bar{A}(\bar{q},t)+\nabla \chi (\bar{q},t) \right)=\bar{E}(\bar{q},t) \\
& \bar{B}\acute{\ }(\bar{q},t)=\nabla \times \bar{A}\acute{\ }(\bar{q},t)=\nabla \times \left( \bar{A}(\bar{q},t)+\nabla \chi (\bar{q},t) \right)=\bar{B}(\bar{q},t) \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {E}}{\acute {\ }}({\bar {q}},t)=-\nabla \Phi {\acute {\ }}({\bar {q}},t)-{\frac {\partial }{\partial t}}{\bar {A}}{\acute {\ }}({\bar {q}},t)=-\nabla \left(\Phi ({\bar {q}},t)-{\frac {\partial }{\partial t}}\chi ({\bar {q}},t)\right)-{\frac {\partial }{\partial t}}\left({\bar {A}}({\bar {q}},t)+\nabla \chi ({\bar {q}},t)\right)={\bar {E}}({\bar {q}},t)\\&{\bar {B}}{\acute {\ }}({\bar {q}},t)=\nabla \times {\bar {A}}{\acute {\ }}({\bar {q}},t)=\nabla \times \left({\bar {A}}({\bar {q}},t)+\nabla \chi ({\bar {q}},t)\right)={\bar {B}}({\bar {q}},t)\\\end{aligned}}
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<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"><mover><mi>E</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mi>Φ</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mover><mi>A</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>Φ</mi><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>χ</mi><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>A</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mi mathvariant="normal">∇</mi><mi>χ</mi><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><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"><mover><mi>B</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mover><mi>A</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∇</mi><mo stretchy="false">×</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>A</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mi mathvariant="normal">∇</mi><mi>χ</mi><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mover><mi>B</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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