Classical Mechanics (Kibble & Berkshire) · Problem 1.15

Velocity, acceleration and scalar angular velocity — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · differentiation-of-vectors

Problem

The vector

\boldsymbol{v}

is a function of the time

t

and

\boldsymbol{k}

is a constant vector. Find the time derivatives of (i)

|\boldsymbol{v}|^2

, (ii)

(\boldsymbol{v} \cdot \boldsymbol{k})\boldsymbol{v}

, (iii)

\left[\boldsymbol{v},\, \dot{\boldsymbol{v}},\, \boldsymbol{k}\right]