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Display information for equation id:math.1347.79 on revision:1347

* Page found: Mechanik des starren Körpers (eq math.1347.79)

Occurrences on the following pages:

Kinetische Energie und Trägheitstensor Eq: math.2016.74

Hash: 4e0b4b43cc66c6cb5497d32db3e9be9c

TeX (original user input):

\begin{align}
  & \rho (\bar{x})=\rho (r) \\
 & {{J}_{1}}={{J}_{2}}={{J}_{3}}=:J \\
 & 3J={{J}_{1}}+{{J}_{2}}+{{J}_{3}}=\int_{{}}^{{}}{{{d}^{3}}x}\rho (r)\left[ \left( {{x}_{2}}^{2}+{{x}_{3}}^{2} \right)+\left( {{x}_{1}}^{2}+{{x}_{3}}^{2} \right)+\left( {{x}_{1}}^{2}+{{x}_{2}}^{2} \right) \right]=\int_{{}}^{{}}{{{d}^{3}}x}\rho (r)2{{r}^{2}} \\
 & 3J=2\cdot 4\pi \int_{0}^{R}{dr{{r}^{4}}\rho (r)} \\
\end{align}

TeX (checked):

{\begin{aligned}&\rho ({\bar {x}})=\rho (r)\\&{{J}_{1}}={{J}_{2}}={{J}_{3}}=:J\\&3J={{J}_{1}}+{{J}_{2}}+{{J}_{3}}=\int _{}^{}{{{d}^{3}}x}\rho (r)\left[\left({{x}_{2}}^{2}+{{x}_{3}}^{2}\right)+\left({{x}_{1}}^{2}+{{x}_{3}}^{2}\right)+\left({{x}_{1}}^{2}+{{x}_{2}}^{2}\right)\right]=\int _{}^{}{{{d}^{3}}x}\rho (r)2{{r}^{2}}\\&3J=2\cdot 4\pi \int _{0}^{R}{dr{{r}^{4}}\rho (r)}\\\end{aligned}}

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\begin{matrix} ρ (\bar{x}) = ρ (r) \\ J_{1} = J_{2} = J_{3} = : J \\ 3 J = J_{1} + J_{2} + J_{3} = \int_{}^{} d^{3} x ρ (r) [({x_{2}}^{2} + {x_{3}}^{2}) + ({x_{1}}^{2} + {x_{3}}^{2}) + ({x_{1}}^{2} + {x_{2}}^{2})] = \int_{}^{} d^{3} x ρ (r) 2 r^{2} \\ 3 J = 2 \cdot 4 π \int_{0}^{R} d r r^{4} ρ (r) \end{matrix}

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Identifiers

$ρ$

$\bar{x}$

$ρ$

$r$

$J_{1}$

$J_{2}$

$J_{3}$

$J$

$J$

$J_{1}$

$J_{2}$

$J_{3}$

$x$

$ρ$

$r$

$x_{2}$

$x_{3}$

$x_{1}$

$x_{3}$

$x_{1}$

$x_{2}$

$x$

$ρ$

$r$

$r$

$J$

$π$

$R$

$r$

$r$

$ρ$

$r$

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