# Euler's equation of the rigid body's dynamics - Vector form with rigid body's angular acceleration

I have the following Euler's equations (9.23) ($$\omega$$ is the rigid body's angular velocity, $$\Omega$$ is the angular velocity of the reference frame whose origin is fixed on the rigid body and whose axes are not fixed on rigid body):

I don't understand how rewrite it inserting the expression 9.24 for the angular acceleration.

$$M_{3 \times 1}=I_{3 \times 3} \alpha_{3 \times 1}$$
Here $$M$$ is the vector torque, $$I$$ is the moment of inertia tensor and $$\alpha$$ is the angular acceleration vector. Simplifying $$\alpha$$ will give the required equations.