16.9 : 오일러 운동 방정식

Consider a rigid body rotating with an angular velocity of ω in an inertial frame of reference.

Another rotating frame is attached to the body that moves with the body with an angular velocity of Ω.

The summation of the total moment is equal to the sum of the rate of change of angular momentum about the center of mass with respect to the rotating frame and the cross-product of the angular velocity of the object with its angular momentum.

When the angular velocity of the rotating axes is equal to the angular velocity of the body, then the moments and product of inertia with respect to rotating axes will be constant.

Recalling the scalar components of the angular momentum, the total moment equation can be expressed in scalar components.

If the rotating axes are chosen as principle axes of inertia, then the product of the inertia term vanishes, simplifying the scalar form of the total moment equation.

These are known as Euler's equations of motion for rotating bodies.