In a paper, eq 24 I am reading, the author mentions the equation of rigid body motion which is written as the sum of translational motion of the centre of mass, $x_G(t)$ and a rotational term about an axis through the centre of mass, viz,
$$w(t,x)=w_G(t)+R(t)\times(x-x_G(t)),$$ where $w$ is the velocity field and $w_G$ the velocity of the centre of mass and $R$, is the angular velocity(?).
Then they proceed to differentiate the equation to obtain the equation
I do not understand how the third term in this equation is obtained and what it signifies. Should the third term not be $R(t)\times w(t,x)$?