Classical Mechanics (Kibble & Berkshire) · Problem 1.14

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

Physics — Mechanics · differentiation-of-vectors

Problem

\boldsymbol{r}(t) = (3t^2 - 4)\boldsymbol{i} + t^3 \boldsymbol{j} + (t+3)\boldsymbol{k}

, where

\{\boldsymbol{i}, \boldsymbol{j}, \boldsymbol{k}\}

is a constant standard basis, find

\dot{\boldsymbol{r}}

and

\ddot{\boldsymbol{r}}

. Deduce the time derivative of

\boldsymbol{r}\times\dot{\boldsymbol{r}}