Local time in Lagrangian mechanics

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.19.020209

Keywords:

Lagrangian formulation; local time; Hamiltonian formulation; Schr\

Abstract

We show that under the replacement of the time by a local time in the Lagrange equations, the form of the equations is maintained if the Lagrangian does not depend explicitly on the time. We also study the corresponding modifications in the Hamilton equations and in the Hamilton--Jacobi equation.

References

G.F. Torres del Castillo, An Introduction to Hamiltonian Mechanics (Springer, Cham, 2018). https://doi.org/10.1007/978-3-319-95225-3.

L.A. Pars, A Treatise on Analytical Dynamics (Wiley, New York, 1965; reprinted by Ox Bow Press, 1979). https://doi.org/10.2307/3612016.

D.T. Greenwood, Classical Dynamics (Prentice-Hall, Englewood Cliffs, New Jersey, 1977; reprinted by Dover, 1997), Sec. 2-3.

A.M. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras, Vol. I (Birkhäuser, Basel, 1990), Sect. 2.3. https://doi.org/10.1007/978-3-0348-9257-5.

G.F. Torres del Castillo, The use of fictitious time in Lagrangian mechanics, Rev. Mex. Fıs. E 18 (2021) 020201. https://doi.org/10.31349/RevMexFisE.18.020201.

G.F. Torres del Castillo, The Stäckel theorem in the Lagrangian formalism and the use of local times, Rev. Mex. Fıs. 67 (2021) 447. https://doi.org/10.31349/RevMexFis.67.447.

D.C. Khandekar, S.V. Lawande, and K.V. Bhagwat, PathIntegral Methods and their Applications (World Scientific, Singapore, 1993), Sec. 5.2. https://doi.org/10.1142/1332.

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Published

2022-07-01

How to Cite

[1]
G. F. Torres del Castillo, “Local time in Lagrangian mechanics”, Rev. Mex. Fis. E, vol. 19, no. 2 Jul-Dec, pp. 020209 1–, Jul. 2022.

Issue

Vol. 19 No. 2 Jul-Dec (2022): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2022 Gerardo Francisco Torres del Castillo

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Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.