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On the Noether's Theorem

P. Lam-Estrada, J. Lopez-Bonilla, R. López-Vázquez


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.

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