Stationary Action Principle for Vehicle System with Damping

The aim of this note is to show possible consequences of the principle of stationary action formulated for non-conservative systems. As an example, linear models of vibratory system with damping and with one and two degrees of freedom are considered. This kind of models are frequently used to describe road and rail vehicles. There are vibrations induced by road profile. The appropriate action functional is proposed with the Lagrangian density containing: the kinetic and potential energies as well as dissipative one. Possible variations of generalized coordinates are introduced together with a noncommutative rule between operations of taking variations of the coordinates and their time derivatives. The stationarity of the action functional leads to the Euler-Lagrange equations.