In Park and Lynch's "Modern Robotics" textbook (Section 8.2.1), they give the following derivation for the velocity and acceleration of a point $p_i$ with respect to a fixed body frame $\{b\}$, with the origin of $\{b\}$ at the center of mass of the moving body:

I don't follow the derivation. Typically in introductory dynamics textbooks, the coriolis acceleration of a point in a moving reference frame is given as $2\omega \times v_{rel}$, where $v_{rel}$ is the velocity of the point relative to the moving reference. However, in "Modern Robotics", the point $p_i$ is rigidly fixed to the body and so there is no relative velocity which would give rise to the coriolis acceleration. Also, even if I'm mistaken above, it is not clear to me why the coriolis acceleration term in Park/Lynch is off by a factor of 2 relative to the typical coriolis acceleration term.