Introduction to Classical Mechanics · Problem 6.4

The Lagrangian method — Morin

Physics — Mechanics · lagrangian-cylindrical-coordinates-conservation

Problem

Consider a potential that depends only on the distance to the

z

axis. In cylindrical coordinates, the Lagrangian is

L = \frac{1}{2}m(\dot{r}^2 + r^2\dot{\theta}^2 + \dot{z}^2) - V(r).

Identify the cyclic coordinates and the corresponding conserved quantities.