Introduction to Classical Mechanics · Problem 6.3

The Lagrangian method — Morin

Physics — Mechanics · lagrangian-linear-momentum-conservation

Problem

Consider a ball thrown through the air. In the full three dimensions, the Lagrangian is

L = \frac{1}{2}m(\dot{x}^2 + \dot{y}^2 + \dot{z}^2) - mgz.

Identify the cyclic coordinates and the corresponding conserved momenta.