- #26

- 351

- 99

Let ##\boldsymbol e_1 \boldsymbol e_2 \boldsymbol e_3## be a basis of an inertial frame and let

##\boldsymbol u_1\boldsymbol u_2\boldsymbol u_3## be a basis of a body-fixed frame.

We can present ##\boldsymbol \omega## in two forms

$$\boldsymbol \omega=\omega^i\boldsymbol e_i=\Omega^i\boldsymbol u_i.$$

Introduce a notation

$$\boldsymbol {\dot\omega}=\dot\omega^i\boldsymbol e_i,\quad \frac{\delta\boldsymbol \omega}{\delta t}=\dot\Omega^i\boldsymbol u_i.$$

THEOREM. $$\boldsymbol {\dot\omega}=\frac{\delta\boldsymbol \omega}{\delta t}.$$