The use of fictitious time in Lagrangian mechanics




Lagrangian formulation, fictitious time, Kepler problem, Liouville systems


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.


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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.

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

G.F. Torres del Castillo, {it An Introduction to Hamiltonian Mechanics} (Springer, Cham, 2018).

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How to Cite

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.