P. Lam-Estrada, José Luis Lopez-Bonilla, R. López-Vázquez, Lanczos Approach to Noether’s Theorem, BSMaSS Volume 11, The Bulletin of Society for Mathematical Services and Standards (Volume 11)
https://www.scipress.com/BSMaSS.11.1
Abstract:
    If the action A=∫<sub>t</sub><sub>1</sub><sup>t2</sup>L(q,q,t)dt is invariant under the infinitesimal transformation t˜=t+ετ(q,t), q˜=q<sub>r</sub>+εζ<sub>r</sub>(q,t), r-1,...,n with ε=constant≤1, then the Noether’s theorem permits to construct the corresponding conserved quantity. The Lanczos method accepts that ε=q<sub>n+1 </sub>is a new degree of freedom, thus the Euler-Lagrange equation for this new variable gives the Noether’s constant of motion.
Keywords:
    Invariance of the Action, Noether’s Theorem, Variational Lanczos Technique