If the action A=∫_{t}_{1}^{t2}L(q,q,t)dt is invariant under the infinitesimal transformation t˜=t+ετ(q,t), q˜=q_{r}+εζ_{r}(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_{n+1 }is a new degree of freedom, thus the Euler-Lagrange equation for this new variable gives the Noether’s constant of motion.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 11)

Pages:

1-3

DOI:

10.18052/www.scipress.com/BSMaSS.11.1

Citation:

P. Lam-Estrada et al., "Lanczos Approach to Noether’s Theorem", The Bulletin of Society for Mathematical Services and Standards, Vol. 11, pp. 1-3, 2014

Online since:

Sep 2014

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License