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ART-Skript Eq: math.1110.110

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TeX (original user input):

\begin{align}
  & md_{\tau }^{2}{{x}^{\mu }}=m{{d}_{\tau }}\left( {{d}_{\tau }}{{x}^{\mu }} \right)=m{{d}_{\tau }}\left( \partial {{'}_{\alpha }}{{x}^{\mu }}{{\partial }_{\tau }}x{{'}^{\alpha }} \right)=0 \\
 & =m\left( \partial '_{\alpha \beta }^{2}{{x}^{\mu }}{{\partial }_{\tau }}x{{'}^{\alpha }}{{\partial }_{\tau }}x{{'}^{\beta }}+\partial {{'}_{\alpha }}{{x}^{\mu }}d_{\tau }^{2}x{{'}^{\alpha }} \right)=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&md_{\tau }^{2}{{x}^{\mu }}=m{{d}_{\tau }}\left({{d}_{\tau }}{{x}^{\mu }}\right)=m{{d}_{\tau }}\left(\partial {{'}_{\alpha }}{{x}^{\mu }}{{\partial }_{\tau }}x{{'}^{\alpha }}\right)=0\\&=m\left(\partial '_{\alpha \beta }^{2}{{x}^{\mu }}{{\partial }_{\tau }}x{{'}^{\alpha }}{{\partial }_{\tau }}x{{'}^{\beta }}+\partial {{'}_{\alpha }}{{x}^{\mu }}d_{\tau }^{2}x{{'}^{\alpha }}\right)=0\\\end{aligned}}

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MathML (2.739 KB / 413 B) :

\begin{aligned} m d_{τ}^{2} x^{μ} = m d_{τ} (d_{τ} x^{μ}) = m d_{τ} (\partial'_{α} x^{μ} \partial_{τ} x'^{α}) = 0 \\ = m (\partial'_{α β}^{2} x^{μ} \partial_{τ} x'^{α} \partial_{τ} x'^{β} + \partial'_{α} x^{μ} d_{τ}^{2} x'^{α}) = 0 \end{aligned}

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$m$

$d$

$τ$

$x$

$μ$

$m$

$d_{τ}$

$d_{τ}$

$x$

$μ$

$m$

$d_{τ}$

$α$

$x$

$μ$

$τ$

$x$

$α$

$m$

$α$

$β$

$x$

$μ$

$τ$

$x$

$α$

$τ$

$x$

$β$

$α$

$x$

$μ$

$d$

$τ$

$x$

$α$

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