Classical Dynamics of Particles and Systems · Problem 1-33

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · vector-calculus-integration

Problem

Show that

\int\left(\frac{\dot{\mathbf{r}}}{r} - \frac{\mathbf{r}\dot{r}}{r^2}\right)dt = \frac{\mathbf{r}}{r} + \mathbf{C}

where

\mathbf{C}

is a constant vector.