On the Noether's Theorem

Abstract

If the action S = integral is invariant under the infinitesimal transformation t+e f(q,t), q + e g(q,t), r = 1,...,n, with e =constant <<1, then the Noether's theorem permits to construct the corresponding conserved quantity. The Lanczos approach employs to e as a new degree of freedom, thus the Euler-Lagrange equation for this new variable gives the Noether's constant of motion.