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| ==MathTEST== | | ==MathTEST== |
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| | =sect33= |
| | ==sect333=== |
| | text111 |
| <math>\sin^2(x)+\cos(x)^2+e^{i \pi}+0</math> | | <math>\sin^2(x)+\cos(x)^2+e^{i \pi}+0</math> |
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| Mediawiki-Math:
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| <math>\sin(x)^2+\cos(x)^2+e^{i \pi}=0</math>
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| <math>\begin{align}
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| & \frac{d}{dt}\frac{\partial L(\bar{r},\bar{v},t)}{\partial {{v}_{k}}}=m{{{\ddot{x}}}_{k}}+q\left( \frac{\partial }{\partial t}{{A}_{k}}(\bar{r},t)+\frac{\partial {{A}_{k}}(\bar{r},t)}{\partial {{x}_{l}}}\frac{\partial {{x}_{l}}}{\partial t} \right)=m{{{\ddot{x}}}_{k}}+q\left( \frac{\partial }{\partial t}+\bar{v}\cdot \nabla \right){{A}_{k}}(\bar{r},t) \\
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| & \frac{\partial L(\bar{r},\bar{v},t)}{\partial {{x}_{k}}}=q\left[ \frac{\partial }{\partial {{x}_{k}}}\left( \bar{v}\bar{A} \right)-\frac{\partial }{\partial {{x}_{k}}}\Phi \right] \\
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| & \Rightarrow 0=\frac{d}{dt}\frac{\partial L(\bar{r},\bar{v},t)}{\partial {{v}_{k}}}-\frac{\partial L(\bar{r},\bar{v},t)}{\partial {{x}_{k}}}=m{{{\ddot{x}}}_{k}}+q\left( \frac{\partial }{\partial t}+\bar{v}\cdot \nabla \right){{A}_{k}}(\bar{r},t)-q\left[ \frac{\partial }{\partial {{x}_{k}}}\left( \bar{v}\bar{A} \right)-\frac{\partial }{\partial {{x}_{k}}}\Phi \right] \\
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| & =m{{{\ddot{x}}}_{k}}+q\frac{\partial }{\partial t}{{A}_{k}}(\bar{r},t)+q\left[ \left( \bar{v}\cdot \nabla \right){{A}_{k}}(\bar{r},t)-\frac{\partial }{\partial {{x}_{k}}}\left( \bar{v}\bar{A} \right) \right]+q\frac{\partial }{\partial {{x}_{k}}}\Phi \\
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| & \left[ \left( \bar{v}\cdot \nabla \right){{A}_{k}}(\bar{r},t)-\frac{\partial }{\partial {{x}_{k}}}\left( \bar{v}\bar{A} \right) \right]=-{{\left[ \bar{v}\times \left( \nabla \times \bar{A} \right) \right]}_{k}} \\
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| & \Rightarrow 0=m\ddot{\bar{r}}+q\frac{\partial }{\partial t}A(\bar{r},t)-q\left[ \bar{v}\times \left( \nabla \times \bar{A} \right) \right]+q\nabla \Phi =m\ddot{\bar{r}}+q\left[ \frac{\partial }{\partial t}A(\bar{r},t)+\nabla \Phi -\left[ \bar{v}\times \left( \nabla \times \bar{A} \right) \right] \right]
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| \end{align}</math>
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| <math>\underline{b}</math>
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| <math>\begin{align}a&+b\\\\c&+d\end{align}</math>
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| <math>\text{Magnetfeld}\quad </math>
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| <math>\underline{\nabla }</math>
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| <math>c+c*c^2+c+2c+8+ \cos^2x+y</math>
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| <math>
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| \begin{align} \text{Magnetfeld}
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| \quad \underline{B}&=\underline{\nabla }\times \underline{A} \\ \text{elektrisches Feld}\quad \underline{E}&=-\underline{\nabla }\phi -\frac{1}{c}{{\partial }_{t}}\underline{A} \\ \text{one or about spaces} \end{align}
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| </math>
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MathTEST
sect33
sect333=
text111
text222