![]() In the body-fixed coordinate frame, the equations of motion of a rigid body can be expressed as: I i is the principal moments of inertia about principal axis ‘ ω i’ and i is the angular velocity about the principal axis ‘i’. The body axis is chosen to be the principal axis such that: Transformed, the equation can be written as: The above equation is in the space-fixed inertial frame and needs to be transformed into the body-fixed frame. ![]() ![]() In this section, we will express the rotational motion of a rigid body in a body-fixed frame, ignoring the translational motion for simplicity.Īccording to Newton’s second law, the external torque N can be expressed as the following, where L is the angular momentum: It is simpler to calculate the equations of motion of the rigid body in a body-fixed principal frame.
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