Introduction to Classical Mechanics · Problem 7.1

Angular momentum, Part I (Constant L) — Morin

Physics — Mechanics · central-forces-effective-potential

Problem

Exponential spiral * Given

L

, find the

V(r)

that leads to a spiral path of the form

r = r_0 e^{a\theta}

. Choose

E

to be zero. Hint: Obtain an expression for

\dot{r}

that contains no

\theta

's, and then use Eq. (7.9).