The use of fictitious time in Lagrangian mechanics

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.18.020201

Keywords:

Lagrangian formulation, fictitious time, Kepler problem, Liouville systems

Abstract

We present some examples in the elementary Lagrangian formulation of classical mechanics where the introduction of a parameter in place of the time (sometimes called fictitious time or local time) decouples the equations of motion.

References

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

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

A.M. Perelomov, {it Integrable Systems of Classical Mechanics and Lie Algebras}, Vol. I (Birkh"auser, Basel, 1990), Sect. 2.3. doi.org/10.1007/978-3-0348-9257-5

D.C. Khandekar, S.V. Lawande, and K.V. Bhagwat, {it Path-Integral Methods and their Applications} (World Scientific, Singapore, 1993), Sec. 5.2. doi.org/10.1142/1332

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

H. Goldstein, {it Classical Mechanics}, 2nd ed., (Addison-Wesley, Reading, MA, 1980).

M.G. Calkin, {it Lagrangian and Hamiltonian Mechanics} (World Scientific, Singapore, 1996). doi.org/10.1142/3111

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Published

2021-07-02

How to Cite

[1]
G. F. Torres del Castillo, “The use of fictitious time in Lagrangian mechanics”, Rev. Mex. Fis. E, vol. 18, no. 2 Jul-Dec, pp. 020201 1–, Jul. 2021.

Issue

Vol. 18 No. 2 Jul-Dec (2021): Revista Mexicana de Física E

Section

02 Education in Physics

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Copyright (c) 2021 Gerardo Francisco Torres del Castillo

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