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Display information for equation id:math.1309.12 on revision:1309

* Page found: Grundbegriffe der Mechanik (eq math.1309.12)

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Grundbegriffe der Mechanik Eq: math.1320.12

Hash: d0f1c8681f0639894b792b3ed85eabf0

TeX (original user input):

\begin{align}
  & {{{\vec{F}}}^{(12)}}={{m}^{(1)}}\frac{d}{{{(dt)}^{{}}}}{{{\vec{v}}}^{(1)}}={{m}^{(1)}}{{{\vec{a}}}^{(1)}} \\
 & {{{\vec{F}}}^{(21)}}={{m}^{(2)}}\frac{d}{{{(dt)}^{{}}}}{{{\vec{v}}}^{(2)}}={{m}^{(2)}}{{{\vec{a}}}^{(2)}} \\
 & \to \frac{d}{dt}\left( {{m}^{(1)}}{{{\vec{v}}}^{(1)}}+{{m}^{(2)}}{{{\vec{v}}}^{(2)}} \right)=0 \\
 & \to \frac{d}{dt}\left( {{{\vec{p}}}^{(1)}}+{{{\vec{p}}}^{(2)}} \right)=0 \\
 & \to {{{\vec{p}}}^{(1)}}+{{{\vec{p}}}^{(2)}}=const \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\vec {F}}^{(12)}}={{m}^{(1)}}{\frac {d}{{(dt)}^{}}}{{\vec {v}}^{(1)}}={{m}^{(1)}}{{\vec {a}}^{(1)}}\\&{{\vec {F}}^{(21)}}={{m}^{(2)}}{\frac {d}{{(dt)}^{}}}{{\vec {v}}^{(2)}}={{m}^{(2)}}{{\vec {a}}^{(2)}}\\&\to {\frac {d}{dt}}\left({{m}^{(1)}}{{\vec {v}}^{(1)}}+{{m}^{(2)}}{{\vec {v}}^{(2)}}\right)=0\\&\to {\frac {d}{dt}}\left({{\vec {p}}^{(1)}}+{{\vec {p}}^{(2)}}\right)=0\\&\to {{\vec {p}}^{(1)}}+{{\vec {p}}^{(2)}}=const\\\end{aligned}}

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\begin{aligned} {\vec{F}}^{(12)} = m^{(1)} \frac{d}{{(d t)}^{}} {\vec{v}}^{(1)} = m^{(1)} {\vec{a}}^{(1)} \\ {\vec{F}}^{(21)} = m^{(2)} \frac{d}{{(d t)}^{}} {\vec{v}}^{(2)} = m^{(2)} {\vec{a}}^{(2)} \\ \to \frac{d}{d t} (m^{(1)} {\vec{v}}^{(1)} + m^{(2)} {\vec{v}}^{(2)}) = 0 \\ \to \frac{d}{d t} ({\vec{p}}^{(1)} + {\vec{p}}^{(2)}) = 0 \\ \to {\vec{p}}^{(1)} + {\vec{p}}^{(2)} = c o n s t \end{aligned}

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Identifiers

$\vec{F}$

$m$

$d$

$d$

$t$

$\vec{v}$

$m$

$\vec{a}$

$\vec{F}$

$m$

$d$

$d$

$t$

$\vec{v}$

$m$

$\vec{a}$

$d$

$d$

$t$

$m$

$\vec{v}$

$m$

$\vec{v}$

$d$

$d$

$t$

$\vec{p}$

$\vec{p}$

$\vec{p}$

$\vec{p}$

$c$

$o$

$n$

$s$

$t$

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