Linear Acceleration

Equation $77$ from page=20

$$\frac{d}{dt}{\vec{v}}_p={\vec{a}}_b+({\vec{a}}_p{)}_b+\alpha \times {\vec{r}}_{p/b}+\vec{\omega }\times (\vec{\omega }\times {\vec{r}}_{p/b})+2\vec{\omega }\times ({\vec{v}}_p{)}_b$$

Where

• ${\vec{a}}_b$ represents the linear acceleration of the origin of the moving reference frame.
• $({\vec{a}}_p{)}_b$ represents the linear acceleration of the point $P$ relative to the coordinate axes of the moving reference frame.
• $\alpha \times {\vec{r}}_{p/b}$ is the linear acceleration of point P due to angular acceleration of the moving reference frame.
• $\vec{\omega }\times (\vec{\omega }\times {\vec{r}}_{p/b})$ is the centripetal acceleration.
• $2\vec{\omega }\times ({\vec{v}}_p{)}_b$ is the Coriolis acceleration of P.