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For problems like this where the coordinate system itself is rotating, the moment equations are
(5)
⎲⎳Mx
= Ixω̇x − IyΩzωy + IzΩyωz
⎲⎳My
= Iyω̇y − IzΩxωz + IxΩzωx
⎲⎳Mz
= Izω̇z − IxΩyωx + IyΩxωy
The above equations are simplified greatly when it is recognized that the following are equal to zero: ωz, Ωx, Ωz, ωẋ, ωẏ, ωż. With these simplifications, the moment equations become:
(6)
⎲⎳Mx
= 0
⎲⎳My
= 0
⎲⎳Mz
= − IxΩyωx
= − 91, 875Nm
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