Vectors

This is a vector [math]\displaystyle{ \vec{\bf u} }[/math].

The time derivative of a vector [math]\displaystyle{ \vec{\bf u} }[/math] with respect to a reference frame [math]\displaystyle{ R }[/math] is

[math]\displaystyle{ \left. \frac{d \vec{\bf u}}{dt} \right]_\text{R} = \left. \frac{d \vec{\bf u}}{dt} \right]_\text{REL} + \vec{\bf\Omega}^\text{REL}_\text{R} \times \vec{\bf u} }[/math]