Resumen

TORRES DEL CASTILLO, G. F.. The Stäckel theorem in the Lagrangian formalism and the use of local times. Rev. mex. fis. [online]. 2021, vol.67, n.3, pp.447-451.  Epub 21-Feb-2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.67.447.

We show that the conditions for the separability of the Hamilton-Jacobi equation given by the Stäckel theorem imply that, using the elementary Lagrangian formalism, one can find n functionally independent constants of motion, where 𝑛 is the number of degrees of freedom. We also show that this result can be linked to the fact that the Lagrangian for a system of this class is related to the sum of n one-dimensional Lagrangians, if one makes use of multiple local times.

Palabras llave : Stäckel’s theorem; Lagrangian formulation; fictitious time.

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