Lagrangian descriptions of dissipative systems: a review
In this paper, we review classical and recent results on the Lagrangian description of dissipative systems. After hav-
ing recalled Rayleigh extension of Lagrangian formalism to equations of motion with dissipative forces, we describe
Helmholtz conditions, which represent necessary and sufficient conditions for the existence of a Lagrangian function for
a system of differential equations. These conditions are presented in different formalisms, some of them published in the
last decades. In particular, we state the necessary and sufficient conditions in terms of multiplier factors, discussing the
conditions for the existence of equivalent Lagrangians for the same system of differential equations. Some examples are
discussed, to show the application of the techniques described in the theorems stated in this paper.