Title: Alternative Lagrangians obtained by scalar deformations,
Abstract: We study non-conservative like SODEs admitting explicit Lagrangian
descriptions. Such systems are equivalent to the system of Lagrange equations
of some Lagrangian $L$, including a covariant force field which represents
non-conservative forces. We find necessary and sufficient conditions for the
existence of a differentiable function $\Phi:\mathbb{R}\rightarrow\mathbb{R}$
such that the initial system is equivalent to the system of Euler-Lagrange
equations of the deformed Lagrangian $\Phi(L)$. We give various examples of
such deformations.