Classical Dynamics of Particles and Systems · Problem 1-27

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · vector-calculus

Problem

\mathbf{r}

and

\dot{\mathbf{r}} = \mathbf{v}

are both explicit functions of time, show that

\frac{d}{dt}[\mathbf{r} \times (\mathbf{v} \times \mathbf{r})] = r^2\mathbf{a} + (\mathbf{r} \cdot \mathbf{v})\mathbf{v} - (v^2 + \mathbf{r} \cdot \mathbf{a})\mathbf{r}