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Mathematics-Online lexicon:

Mass, Center of Mass, Barycenter


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The mass of a solid $ K$ with density $ \varrho(x),\,x\in K$ is

$\displaystyle m = \int\limits_K \varrho(x)\,dK
$

The $ \nu$ - th coordinate of the center of mass is

$\displaystyle s_\nu = m^{-1}\int\limits_K x_\nu\varrho(x)\,dK \ .
$

In the special case when $ \varrho(x) = 1$ the first integral yields the volume $ V$ of $ K .$ The $ \nu$ - th coordinate of the (geometric) barycenter of $ K$ is

$\displaystyle s_\nu = V^{-1}\int\limits_K x_\nu \,dK \ .
$

()

Examples:


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  automatically generated 8/ 4/2008