Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Articles dans des revues à comité de lecture

Classical Noether theory with application to the linearly damped particle
Leone R., Gourieux T.
Eur. J. Phys. 36 (2015) 065022
DOI : 10.1088/0143-0807/36/6/065022
ArXiv : arxiv:1412.7523 [PDF]

This paper is devoted to the search for conservation laws in the unidimensional problem of a particle submitted to both a potential and a linear dissipation. After a review of Noether's theory and its relation to first integrals we analyse the variational point symmetries of the Lagrangian introduced by Bateman, Caldirola and Kanai. We find all the time-independent potentials allowing such symmetries. Then, we develop a symmetry-based transformation of Lagrangians into autonomous others, and apply it to our problem. To be complete, we enlarge the study to Lie point symmetries which we associate logically to Noether ones. Finally, we show that any first integral of the problem amounts to a local expression of the Bateman-Caldirola-Kanai action in the phase space, along the solution curves.



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