Question Number 31566 by ajfour last updated on 10/Mar/18
Commented by ajfour last updated on 10/Mar/18
$${Frame}\:{XYZ}\:{is}\:{fixed}.\:{Frame}\:{xyz} \\ $$$${rotates}\:{with}\:{angular}\:{velocity}\:\Omega. \\ $$$${Relate}\:{acceleration}\:{of}\:{particle}\: \\ $$$${in}\:{fixed}\:{frame}\:{to}\:{that}\:{in}\:{rotating} \\ $$$${frame}. \\ $$
Answered by ajfour last updated on 11/Mar/18
$$\bar {{v}}_{{P}} =\:\left(\bar {{v}}_{{P}} \right)_{{xyz}} +\bar {\Omega}×\bar {{r}} \\ $$$$\bar {{a}}_{{P}} \:=\:\left(\bar {{a}}_{{P}} \right)_{{xyz}} +\bar {\Omega}×\left(\bar {{v}}_{{P}} \right)_{{xyz}} +\frac{{d}\bar {\Omega}}{{dt}}×\bar {{r}}+ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\bar {\Omega}×\left(\bar {{v}}_{{P}} \right)_{{xyz}} +\bar {\Omega}×\left(\bar {\Omega}×\bar {{r}}\right) \\ $$