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Display information for equation id:math.1802.18 on revision:1802
* Page found: Kovariante Schreibweise der Relativitätstheorie (eq math.1802.18)
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Hash: 62664497193c7fd6a0dfd76bc78e50a2
TeX (original user input):
\begin{align}
& {{u}^{i}}:=\frac{d{{x}^{i}}}{ds} \\
& ds={{\left( d{{x}^{i}}d{{x}_{i}} \right)}^{\frac{1}{2}}}={{\left( {{c}^{2}}d{{t}^{2}}-{{\left( d\bar{r} \right)}^{2}} \right)}^{\frac{1}{2}}}=c{{\left[ 1-{{\left( \frac{1}{c}\frac{d\bar{r}}{dt} \right)}^{2}} \right]}^{\frac{1}{2}}}dt \\
& ds:={{\left( 1-{{\beta }^{2}} \right)}^{\frac{1}{2}}}dt=\frac{c}{\gamma }dt \\
\end{align}
TeX (checked):
{\begin{aligned}&{{u}^{i}}:={\frac {d{{x}^{i}}}{ds}}\\&ds={{\left(d{{x}^{i}}d{{x}_{i}}\right)}^{\frac {1}{2}}}={{\left({{c}^{2}}d{{t}^{2}}-{{\left(d{\bar {r}}\right)}^{2}}\right)}^{\frac {1}{2}}}=c{{\left[1-{{\left({\frac {1}{c}}{\frac {d{\bar {r}}}{dt}}\right)}^{2}}\right]}^{\frac {1}{2}}}dt\\&ds:={{\left(1-{{\beta }^{2}}\right)}^{\frac {1}{2}}}dt={\frac {c}{\gamma }}dt\\\end{aligned}}
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