Question Number 27986 by ajfour last updated on 18/Jan/18
$${Prove}\:{that}\:{the}\:{angular}\:{momentum} \\ $$$$\bar {\boldsymbol{{H}}}_{{G}} \:{of}\:{a}\:{rigid}\:{body}\:{about}\:{its}\:{mass} \\ $$$${center}\:{is}\:{given}\:{by}\:: \\ $$$${H}_{{x}} =\bar {{I}}_{{x}} \omega_{{x}} −\bar {{I}}_{{xy}} \omega_{{y}} −\bar {{I}}_{{xz}} \omega_{{z}} \\ $$$${H}_{{y}} =−\bar {{I}}_{{yx}} \omega_{{x}} +\bar {{I}}_{{y}} \omega_{{y}} −\bar {{I}}_{{yz}} \omega_{{z}} \\ $$$${H}_{{z}} =−\bar {{I}}_{{zx}} \omega_{{x}} −\bar {{I}}_{{zy}} \omega_{{y}} +\bar {{I}}_{{z}} \omega_{{z}} \\ $$$$\:\:\:\:{where}\:\:\bar {{I}}_{{x}} =\int\left({y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right){dm} \\ $$$$\:\:\:\:\:\:\bar {{I}}_{{xy}} =\int{xy}\:{dm}\:…{and}\:{so}\:{on}.. \\ $$
Commented by ajfour last updated on 22/Mar/19
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