Symmetries of the Lagrange equations and equivalent Lagrangians

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Abstract
The theoretical basis justifying the possibility of associating equivalent Lagrangians with (t,q) symmetries of Lagrangian systems of differential equations is given. The proof is based on well-known results and leads to a technique for finding equivalent Lagrangians that it is quite simple and more general than another recently proposed technique, since it is valid for systems of more than one differential equation and for both discrete and continuous families of symmetries.