#### Euler's Equations for Rotations in the Body-Fixed Frame

Suppose now that the body-fixed frame is rotating in the space-fixed frame with angular velocity . Then the total torque on the rigid body becomes [270]Similarly, the total external forces on the center of mass become

*cf.*Eq.(B.15))

*Euler's equations:*

^{B.29}Since these equations are in the body-fixed frame, is the mass moment of inertia about principal axis , and is the angular velocity about principal axis .

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