Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Articles dans des revues à comité de lecture

Li(e)nearity
Leone R., Haas F.
ArXiv : arxiv:1612.04435 [PDF]

We demonstrate the fact that linearity is a meaningful symmetry in the sense of Lie and Noether. The role played by that `linearity symmetry' in the quadrature of linear ordinary second-order differential equations is reviewed, by the use of canonical coordinates and the identification of a Wronskian-like conserved quantity as Lie invariant. The Jacobi last multiplier associated with two independent linearity symmetries is applied to derive the Caldirola-Kanai Lagrangian from symmetry principles. Then the symmetry is recognized to be also a Noether one. Finally, the study is extended to higher-order linear ordinary differential equations, derivable or not from an action principle.



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