Vectors

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

The time derivative of a vector [math]\displaystyle{ \vec{\bf u} = u \vec{\bf e} }[/math], where [math]\displaystyle{ \| \vec{\bf e} \| = 1 }[/math], is:

[math]\displaystyle{ \left. \frac{d \vec{\bf u}}{dt} \right]_R = \dot{u} \vec{\bf e} + \vec{\bf\Omega}^\vec{\bf e}_R \times \vec{\bf u} }[/math]