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Display information for equation id:math.1199.1266 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.1266)

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Relativistisches Hamiltonprinzip Eq: math.2176.8

Hash: e8dbce51b4c7d7f84a314d28bca6d3d2

TeX (original user input):

\begin{align}
& \delta \left( ds \right)=\delta {{\left( d{{x}^{\mu }}d{{x}_{\mu }} \right)}^{\frac{1}{2}}}=\frac{1}{2}\frac{\left( d\delta {{x}^{\mu }} \right)d{{x}_{\mu }}+d{{x}^{\mu }}\left( d\delta {{x}_{\mu }} \right)}{ds} \\
& \left( d\delta {{x}^{\mu }} \right)d{{x}_{\mu }}=d{{x}^{\mu }}\left( d\delta {{x}_{\mu }} \right) \\
& =\frac{d{{x}^{\mu }}}{ds}\left( d\delta {{x}_{\mu }} \right)={{u}^{\mu }}\left( d\delta {{x}_{\mu }} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&\delta \left(ds\right)=\delta {{\left(d{{x}^{\mu }}d{{x}_{\mu }}\right)}^{\frac {1}{2}}}={\frac {1}{2}}{\frac {\left(d\delta {{x}^{\mu }}\right)d{{x}_{\mu }}+d{{x}^{\mu }}\left(d\delta {{x}_{\mu }}\right)}{ds}}\\&\left(d\delta {{x}^{\mu }}\right)d{{x}_{\mu }}=d{{x}^{\mu }}\left(d\delta {{x}_{\mu }}\right)\\&={\frac {d{{x}^{\mu }}}{ds}}\left(d\delta {{x}_{\mu }}\right)={{u}^{\mu }}\left(d\delta {{x}_{\mu }}\right)\\\end{aligned}}

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MathML (3.524 KB / 439 B) :

\begin{aligned} δ (d s) = δ {(d x^{μ} d x_{μ})}^{\frac{1}{2}} = \frac{1}{2} \frac{(d δ x^{μ}) d x_{μ} + d x^{μ} (d δ x_{μ})}{d s} \\ (d δ x^{μ}) d x_{μ} = d x^{μ} (d δ x_{μ}) \\ = \frac{d x^{μ}}{d s} (d δ x_{μ}) = u^{μ} (d δ x_{μ}) \end{aligned}

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Identifiers

$δ$

$d$

$s$

$δ$

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$μ$

$d$

$x_{μ}$

$d$

$δ$

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$μ$

$d$

$x_{μ}$

$d$

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$μ$

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$x_{μ}$

$d$

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$d$

$δ$

$x$

$μ$

$d$

$x_{μ}$

$d$

$x$

$μ$

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$δ$

$x_{μ}$

$d$

$x$

$μ$

$d$

$s$

$d$

$δ$

$x_{μ}$

$u$

$μ$

$d$

$δ$

$x_{μ}$

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