The Stäckel theorem in the Lagrangian formalism and the use of local times
DOI:
https://doi.org/10.31349/RevMexFis.67.447Keywords:
Stäckel's theorem, Lagrangian formulation, fictitious time.Abstract
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.References
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A.M. Perelomov, {it Integrable Systems of Classical Mechanics and Lie Algebras}, Vol. I (Birkh"auser, Basel, 1990). doi.org/10.1007/978-3-0348-9257-5
G.F. Torres del Castillo, The use of fictitious time in Lagrangian mechanics, {it Rev. Mex. F'is. E} (submitted).
G.F. Torres del Castillo, {it An Introduction to Hamiltonian Mechanics} (Springer, Cham, 2018). doi.org/10.1007/978-3-319-95225-3
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Copyright (c) 2021 Gerardo Francisco Torres del Castillo
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