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Display information for equation id:math.2176.26 on revision:2176
* Page found: Relativistisches Hamiltonprinzip (eq math.2176.26)
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Hash: d217c537cb32f92b357196ac4c2cb069
TeX (original user input):
\begin{align}
& \frac{d}{ds}\frac{E}{c}=\frac{\gamma }{{{c}^{2}}}\frac{dE}{dt}=\frac{q}{c}\left( {{F}^{01}}{{u}_{1}}+{{F}^{02}}{{u}_{2}}+{{F}^{03}}{{u}_{3}} \right)= \\
& =\frac{q\gamma }{{{c}^{2}}}\left( -{{E}^{1}}{{v}_{1}}-{{E}^{2}}{{v}_{2}}-{{E}^{3}}{{v}_{3}} \right)=\frac{q\gamma }{{{c}^{2}}}\left( {{E}^{1}}{{v}^{1}}+{{E}^{2}}{{v}^{2}}+{{E}^{3}}{{v}^{3}} \right) \\
& \frac{dE}{dt}=q\bar{E}\cdot \bar{v} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\frac {d}{ds}}{\frac {E}{c}}={\frac {\gamma }{{c}^{2}}}{\frac {dE}{dt}}={\frac {q}{c}}\left({{F}^{01}}{{u}_{1}}+{{F}^{02}}{{u}_{2}}+{{F}^{03}}{{u}_{3}}\right)=\\&={\frac {q\gamma }{{c}^{2}}}\left(-{{E}^{1}}{{v}_{1}}-{{E}^{2}}{{v}_{2}}-{{E}^{3}}{{v}_{3}}\right)={\frac {q\gamma }{{c}^{2}}}\left({{E}^{1}}{{v}^{1}}+{{E}^{2}}{{v}^{2}}+{{E}^{3}}{{v}^{3}}\right)\\&{\frac {dE}{dt}}=q{\bar {E}}\cdot {\bar {v}}\\\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"><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>s</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>γ</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>E</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>01</mn></mrow></msup><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>02</mn></mrow></msup><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">+</mo><msup><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>03</mn></mrow></msup><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>q</mi><mi>γ</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo stretchy="false">−</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>q</mi><mi>γ</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>E</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mi>q</mi><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">⋅</mo><mover><mi>v</mi><mo>¯</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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