Hamiltonians and Lagrangians of non-autonomous one-dimensional mechanical systems

G.F. Torres del Castillo, I. Rubalcava García

Abstract


It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allows us to obtain previously known results such as the infinite number of Hamiltonians in the autonomous case and the Helmholtz condition for the existence of a Lagrangian.

Keywords


Non-autonomous systems; Hamilton equations; Lagrangians

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REVISTA MEXICANA DE FÍSICA, year 67, issue 1, January-February 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf, e-mail: rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 4, 2021.

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