Prove that the angular momentum H_G ^� of a rigid body about its mass center is given by : H_x =I_x ^� ω_x −I_(xy) ^� ω_y −I_(xz) ^� ω_z H_y =−I_(yx) ^� ω_x +I_y ^� ω_y −I_(yz) ^� ω_z H_z =−I_(zx) ^� ω_x −I_(zy) ^� ω_y +I_z ^� ω_z where I_x ^� =∫(y^2 +z^2 )dm I


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Question Number 27986 by ajfour last updated on 18/Jan/18

$P r o v e t h a t t h e a n g u l a r m o m e n t u m$ ${\bar{H}}_{G} o f a r i g i d b o d y a b o u t i t s m a s s$ $c e n t e r i s g i v e n b y :$ $H_{x} = {\bar{I}}_{x} ω_{x} - {\bar{I}}_{x y} ω_{y} - {\bar{I}}_{x z} ω_{z}$ $H_{y} = - {\bar{I}}_{y x} ω_{x} + {\bar{I}}_{y} ω_{y} - {\bar{I}}_{y z} ω_{z}$ $H_{z} = - {\bar{I}}_{z x} ω_{x} - {\bar{I}}_{z y} ω_{y} + {\bar{I}}_{z} ω_{z}$ $w h e r e {\bar{I}}_{x} = \int (y^{2} + z^{2}) d m$ ${\bar{I}}_{x y} = \int x y d m . . . a n d s o o n . .$
Commented by ajfour last updated on 22/Mar/19

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