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Revista mexicana de física E

Print version ISSN 1870-3542

Rev. mex. fís. E vol.59 n.2 México Jul./Dec. 2013




Variational symmetries of Lagrangians


G.F. Torres del Castillo*, C. Andrade Mirón**, and R.I. Bravo Rojas**


* Departamento de Física Matemática, Instituto de Ciencias Universidad Autónoma de Puebla, 72570 Puebla, Pue., México.

* Facultad de Ciencias Físico Matemáticas Universidad Autónoma de Puebla, Apartado postal 165, 72001 Puebla, Pue., México.


Received 25 June 2013
Accepted 8 November 2013



We present an elementary derivation of the equation for the infinitesimal generators of variational symmetries of a Lagrangian for a system with a finite number of degrees of freedom. We also give a simple proof of the existence of an infinite number of Lagrangians for a given second-order ordinary differential equation.

Keywords: Lagrangians; symmetries; constants of motion; ordinary differential equations.



Presentamos una derivación elemental de la ecuación para los generadores infinitesimales de simetrías variacionales de una lagrangiana para un sistema con un número finito de grados de libertad. Damos tambien una prueba simple de la existencia de un número infinito de lagrangianas para una ecuación diferencial ordinaria de segundo orden dada.

Descriptores: Lagrangianas; simetrías; constantes de movimiento; ecuaciones diferenciales ordinarias.

PACS: 45.20.Jj; 02.30.Hq; 02.20.Sv





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