Given a basic Lagrangian, how would I determine invariant quantities? My hunch says it would be quantities that do not depend on position or time? Saying that, perhaps using the Lagrange equation to solve for equations of motion and along the way whatever terms disappear would be my invariant quantities? This seems like a harsh oversimplification, but I can not tell? Any help understanding the invariant quantities would be appreciated. I don't want to solve the actual problem here so to speak, but rather understand the theory. I did solve a problem a few weeks back showing that electromagnetic force was invariant under a gauge transformation, but this seems to be a different concept?