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Display information for equation id:math.1345.14 on revision:1345

* Page found: Mechanik des starren Körpers (eq math.1345.14)

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Hash: bde4a8889079b87198b02256b755fd69

TeX (original user input):

\begin{align}
  & \sum\limits_{i=1}^{n}{{{m}_{i}}}=M \\ 
 & \bar{V}\cdot \sum\limits_{i=1}^{n}{{{m}_{i}}}\left( \bar{\omega }\times {{{\bar{x}}}^{(i)}} \right)=\left( \bar{V}\times \bar{\omega } \right)\sum\limits_{i=1}^{n}{{{m}_{i}}}{{{\bar{x}}}^{(i)}}=0,da\sum\limits_{i=1}^{n}{{{m}_{i}}}{{{\bar{x}}}^{(i)}}=0 \\ 
 & {{\left( \bar{\omega }\times {{{\bar{x}}}^{(i)}} \right)}^{2}}={{\omega }^{2}}{{x}^{2}}{{\sin }^{2}}\alpha ={{\omega }^{2}}{{x}^{2}}(1-{{\cos }^{2}}\alpha )={{\omega }^{2}}{{x}^{2}}-{{\left( \bar{\omega }\cdot \bar{x} \right)}^{2}}=\sum\limits_{m=1}^{3}{\sum\limits_{n=1}^{3}{{}}{{\omega }^{m}}\left[ {{x}^{2}}{{\delta }_{mn}}-{{x}_{m}}{{x}_{n}} \right]}{{\omega }^{n}} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&\sum \limits _{i=1}^{n}{{m}_{i}}=M\\&{\bar {V}}\cdot \sum \limits _{i=1}^{n}{{m}_{i}}\left({\bar {\omega }}\times {{\bar {x}}^{(i)}}\right)=\left({\bar {V}}\times {\bar {\omega }}\right)\sum \limits _{i=1}^{n}{{m}_{i}}{{\bar {x}}^{(i)}}=0,da\sum \limits _{i=1}^{n}{{m}_{i}}{{\bar {x}}^{(i)}}=0\\&{{\left({\bar {\omega }}\times {{\bar {x}}^{(i)}}\right)}^{2}}={{\omega }^{2}}{{x}^{2}}{{\sin }^{2}}\alpha ={{\omega }^{2}}{{x}^{2}}(1-{{\cos }^{2}}\alpha )={{\omega }^{2}}{{x}^{2}}-{{\left({\bar {\omega }}\cdot {\bar {x}}\right)}^{2}}=\sum \limits _{m=1}^{3}{\sum \limits _{n=1}^{3}{}{{\omega }^{m}}\left[{{x}^{2}}{{\delta }_{mn}}-{{x}_{m}}{{x}_{n}}\right]}{{\omega }^{n}}\\\end{aligned}}

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MathML (5.981 KB / 657 B) :

\begin{aligned} \sum_{i = 1}^{n} m_{i} = M \\ \bar{V} \cdot \sum_{i = 1}^{n} m_{i} (\bar{ω} \times {\bar{x}}^{(i)}) = (\bar{V} \times \bar{ω}) \sum_{i = 1}^{n} m_{i} {\bar{x}}^{(i)} = 0, d a \sum_{i = 1}^{n} m_{i} {\bar{x}}^{(i)} = 0 \\ {(\bar{ω} \times {\bar{x}}^{(i)})}^{2} = ω^{2} x^{2} \sin^{2} α = ω^{2} x^{2} (1 - \cos^{2} α) = ω^{2} x^{2} - {(\bar{ω} \cdot \bar{x})}^{2} = \sum_{m = 1}^{3} \sum_{n = 1}^{3} ω^{m} [x^{2} δ_{m n} - x_{m} x_{n}] ω^{n} \end{aligned}

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Identifiers

$i$

$n$

$m_{i}$

$M$

$\bar{V}$

$i$

$n$

$m_{i}$

$\bar{ω}$

$\bar{x}$

$i$

$\bar{V}$

$\bar{ω}$

$i$

$n$

$m_{i}$

$\bar{x}$

$i$

$d$

$a$

$i$

$n$

$m_{i}$

$\bar{x}$

$i$

$\bar{ω}$

$\bar{x}$

$i$

$ω$

$x$

$α$

$ω$

$x$

$α$

$ω$

$x$

$\bar{ω}$

$\bar{x}$

$m$

$n$

$ω$

$m$

$x$

$δ_{m n}$

$x_{m}$

$x_{n}$

$ω$

$n$

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