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Display information for equation id:math.1199.1174 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.1174)

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Ko- und Kontravariante Schreibweise der Relativitätstheorie Eq: math.2169.13

Hash: 3dfe06be669a37e46e6318a4efb588bd

TeX (original user input):

\begin{align}
& {{u}^{i}}:=\frac{d{{x}^{i}}}{ds}\Rightarrow {{u}^{i}}{{u}_{i}}=\frac{d{{x}^{i}}d{{x}_{i}}}{{{\left( ds \right)}^{2}}}=1 \\
& mit \\
& ds={{\left( d{{x}^{i}}d{{x}_{i}} \right)}^{\frac{1}{2}}}=c{{\left( 1-{{\beta }^{2}} \right)}^{\frac{1}{2}dt}}=\frac{c}{\gamma }dt \\
& \Rightarrow {{u}^{0}}=\gamma  \\
& {{u}^{\alpha }}=\frac{\gamma }{c}{{v}^{\alpha }} \\
& {{v}^{\alpha }}:=\frac{d{{x}^{\alpha }}}{dt} \\
& \beta :=\frac{v}{c} \\
& \gamma :=\frac{1}{\sqrt{1-{{\beta }^{2}}}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{u}^{i}}:={\frac {d{{x}^{i}}}{ds}}\Rightarrow {{u}^{i}}{{u}_{i}}={\frac {d{{x}^{i}}d{{x}_{i}}}{{\left(ds\right)}^{2}}}=1\\&mit\\&ds={{\left(d{{x}^{i}}d{{x}_{i}}\right)}^{\frac {1}{2}}}=c{{\left(1-{{\beta }^{2}}\right)}^{{\frac {1}{2}}dt}}={\frac {c}{\gamma }}dt\\&\Rightarrow {{u}^{0}}=\gamma \\&{{u}^{\alpha }}={\frac {\gamma }{c}}{{v}^{\alpha }}\\&{{v}^{\alpha }}:={\frac {d{{x}^{\alpha }}}{dt}}\\&\beta :={\frac {v}{c}}\\&\gamma :={\frac {1}{\sqrt {1-{{\beta }^{2}}}}}\\\end{aligned}}

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\begin{aligned} u^{i} : = \frac{d x^{i}}{d s} \Rightarrow u^{i} u_{i} = \frac{d x^{i} d x_{i}}{{(d s)}^{2}} = 1 \\ m i t \\ d s = {(d x^{i} d x_{i})}^{\frac{1}{2}} = c {(1 - β^{2})}^{\frac{1}{2} d t} = \frac{c}{γ} d t \\ \Rightarrow u^{0} = γ \\ u^{α} = \frac{γ}{c} v^{α} \\ v^{α} : = \frac{d x^{α}}{d t} \\ β : = \frac{v}{c} \\ γ : = \frac{1}{\sqrt{1 - β^{2}}} \end{aligned}

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