Mathematics-Online lexicon: Mass, Center of Mass, Barycenter

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	Mathematics-Online lexicon:
	Mass, Center of Mass, Barycenter

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The mass of a solid

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 of The $\nu$ - th coordinate of the (geometric) barycenter of is

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

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automatically generated 8/ 4/2008