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Display information for equation id:math.1446.118 on revision:1446

* Page found: Relativistische Formulierung der Elektrodynamik (eq math.1446.118)

Occurrences on the following pages:

Relativistisches Hamiltonprinzip Eq: math.2176.21

Hash: 673a83adeeb6650fb29e89055701d3f7

TeX (original user input):

\begin{align}
& \frac{d}{dt}{{p}^{1}}=q\left( {{E}^{1}}+{{v}^{2}}{{B}^{3}}-{{v}^{3}}{{B}^{2}} \right) \\
& =q\left( {{F}^{10}}+{{F}^{21}}\frac{1}{c}{{v}^{2}}-{{F}^{13}}\frac{1}{c}{{v}^{3}} \right) \\
& =\frac{q}{\gamma }\left( {{F}^{10}}\gamma +{{F}^{21}}\frac{\gamma }{c}{{v}^{2}}-{{F}^{13}}\frac{\gamma }{c}{{v}^{3}} \right)=\frac{q}{\gamma }{{F}^{1\mu }}{{u}_{\mu }} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {d}{dt}}{{p}^{1}}=q\left({{E}^{1}}+{{v}^{2}}{{B}^{3}}-{{v}^{3}}{{B}^{2}}\right)\\&=q\left({{F}^{10}}+{{F}^{21}}{\frac {1}{c}}{{v}^{2}}-{{F}^{13}}{\frac {1}{c}}{{v}^{3}}\right)\\&={\frac {q}{\gamma }}\left({{F}^{10}}\gamma +{{F}^{21}}{\frac {\gamma }{c}}{{v}^{2}}-{{F}^{13}}{\frac {\gamma }{c}}{{v}^{3}}\right)={\frac {q}{\gamma }}{{F}^{1\mu }}{{u}_{\mu }}\\\end{aligned}}

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MathML (3.624 KB / 477 B) :

\begin{aligned} \frac{d}{d t} p^{1} = q (E^{1} + v^{2} B^{3} - v^{3} B^{2}) \\ = q (F^{10} + F^{21} \frac{1}{c} v^{2} - F^{13} \frac{1}{c} v^{3}) \\ = \frac{q}{γ} (F^{10} γ + F^{21} \frac{γ}{c} v^{2} - F^{13} \frac{γ}{c} v^{3}) = \frac{q}{γ} F^{1 μ} u_{μ} \end{aligned}

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Identifiers

$d$

$d$

$t$

$p$

$q$

$E$

$v$

$B$

$v$

$B$

$q$

$F$

$F$

$c$

$v$

$F$

$c$

$v$

$q$

$γ$

$F$

$γ$

$F$

$γ$

$c$

$v$

$F$

$γ$

$c$

$v$

$q$

$γ$

$F$

$μ$

$u_{μ}$

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