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

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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

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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