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I am scratching my head on a very basic formula whose meaning escapes my intuition. On basically all texts of mechanics the following result is derived:

Suppose that a rigid body is moving with respect to a fixed reference system $O(x_1,x_2,x_3)$ and let $\omega$ be the vector of his angular velocity. We can retrieve the components of $\omega$ as a function of Euler's angles $\varphi,\theta,\psi$ and their time derivatives, on the body fixed reference frame axes $\Omega(\xi_1,\xi_2,\xi_3)$ as:

$$\omega_{\xi_1}=\dot{\theta}cos\varphi+\dot{\psi}sin\theta sin\varphi$$ $$\omega_{\xi_2}=-\dot{\theta}sin\varphi+\dot{\psi}sin\theta cos\varphi$$ $$\omega_{\xi_3}=\dot{\varphi}+\dot{\psi}cos\theta$$

Now my dumb question is: how can we have non null angular velocity components $\omega_{\xi_1}$,$\omega_{\xi_2}$,$\omega_{\xi_3}$ with respect to the body fixed reference frame if such frame is, by definition, rotating together with the body? Please explain this like I were five years old as I am in the horrendous situation in which I understood the math procedure to retrieve a formula but I cannot grasp its meaning!

Thanks in advance

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