The Stäckel theorem in the Lagrangian formalism and the use of local times




Stäckel's theorem, Lagrangian formulation, fictitious time.


We show that the conditions for the separability of the Hamilton-Jacobi equation given by the Stäckel theorem imply that, making use of 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.


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How to Cite

G. F. Torres del Castillo, “The Stäckel theorem in the Lagrangian formalism and the use of local times”, Rev. Mex. Fís., vol. 67, no. 3 May-Jun, pp. 447–451, May 2021.



07 Gravitation, Mathematical Physics and Field Theory