Introduction to Classical Mechanics · Problem 6.6

The Lagrangian method — Morin

Physics — Mechanics · noether-theorem-conserved-momentum

Problem

Consider the Lagrangian

L = \frac{m}{2}(5\dot{x}^2 - 2\dot{x}\dot{y} + 2\dot{y}^2) + C(2x - y)

. This

L

is invariant under the transformation

x \to x + \epsilon

and

y \to y + 2\epsilon

. Find the conserved momentum using Noether's theorem.