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Display information for equation id:math.2176.11 on revision:2176

* Page found: Relativistisches Hamiltonprinzip (eq math.2176.11)

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Relativistisches Hamiltonprinzip Eq: math.2176.11

Hash: 688c40ea0917776e4ee28abe98d455cb

TeX (original user input):

\begin{align}
& \int_{1}^{2}{{}}-{{m}_{0}}c{{u}^{\mu }}d\left( \delta {{x}_{\mu }} \right)=\left[ -{{m}_{0}}c{{u}^{\mu }}\left( \delta {{x}_{\mu }} \right) \right]_{1}^{2}+\int_{1}^{2}{{}}{{m}_{0}}cd{{u}^{\mu }}\left( \delta {{x}_{\mu }} \right) \\
& \left[ -{{m}_{0}}c{{u}^{\mu }}\left( \delta {{x}_{\mu }} \right) \right]_{1}^{2}=0,weil\delta {{x}_{\mu }}_{1}^{2}=0 \\
& \Rightarrow \int_{1}^{2}{{}}-{{m}_{0}}c{{u}^{\mu }}d\left( \delta {{x}_{\mu }} \right)=\int_{1}^{2}{{}}{{m}_{0}}cd{{u}^{\mu }}\left( \delta {{x}_{\mu }} \right)=\int_{1}^{2}{{}}{{m}_{0}}c\frac{d{{u}^{\mu }}}{ds}\left( \delta {{x}_{\mu }} \right)ds \\
\end{align}

TeX (checked):

{\begin{aligned}&\int _{1}^{2}{}-{{m}_{0}}c{{u}^{\mu }}d\left(\delta {{x}_{\mu }}\right)=\left[-{{m}_{0}}c{{u}^{\mu }}\left(\delta {{x}_{\mu }}\right)\right]_{1}^{2}+\int _{1}^{2}{}{{m}_{0}}cd{{u}^{\mu }}\left(\delta {{x}_{\mu }}\right)\\&\left[-{{m}_{0}}c{{u}^{\mu }}\left(\delta {{x}_{\mu }}\right)\right]_{1}^{2}=0,weil\delta {{x}_{\mu }}_{1}^{2}=0\\&\Rightarrow \int _{1}^{2}{}-{{m}_{0}}c{{u}^{\mu }}d\left(\delta {{x}_{\mu }}\right)=\int _{1}^{2}{}{{m}_{0}}cd{{u}^{\mu }}\left(\delta {{x}_{\mu }}\right)=\int _{1}^{2}{}{{m}_{0}}c{\frac {d{{u}^{\mu }}}{ds}}\left(\delta {{x}_{\mu }}\right)ds\\\end{aligned}}

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\begin{matrix} \int_{1}^{2} - m_{0} c u^{μ} d (δ x_{μ}) = {[- m_{0} c u^{μ} (δ x_{μ})]}_{1}^{2} + \int_{1}^{2} m_{0} c d u^{μ} (δ x_{μ}) \\ {[- m_{0} c u^{μ} (δ x_{μ})]}_{1}^{2} = 0, w e i l δ {x_{μ}}_{1}^{2} = 0 \\ \Rightarrow \int_{1}^{2} - m_{0} c u^{μ} d (δ x_{μ}) = \int_{1}^{2} m_{0} c d u^{μ} (δ x_{μ}) = \int_{1}^{2} m_{0} c \frac{d u^{μ}}{d s} (δ x_{μ}) d s \end{matrix}

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Identifiers

$m_{0}$

$c$

$u$

$μ$

$δ$

$x_{μ}$

$m_{0}$

$c$

$u$

$μ$

$δ$

$x_{μ}$

$m_{0}$

$c$

$u$

$μ$

$δ$

$x_{μ}$

$m_{0}$

$c$

$u$

$μ$

$δ$

$x_{μ}$

$w$

$e$

$i$

$l$

$δ$

$x_{μ}$

$m_{0}$

$c$

$u$

$μ$

$δ$

$x_{μ}$

$m_{0}$

$c$

$u$

$μ$

$δ$

$x_{μ}$

$m_{0}$

$c$

$u$

$μ$

$d$

$s$

$δ$

$x_{μ}$

$d$

$s$

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