Finite element models are usually presented as relations between lumped forces and discrete displacements. Mostly finite element models are found by the elaboration of the method of the virtual work - which is a special case of the Galerkin's variational principle -. By application of Galerkin's variational principle to time dependent problems, considering elements bordered by ge()metry and time b()undaries, we obtain relations between lumped impulses and discrete displacements. The analogy with respect to static models which formulates relati()ns between lumped forces and discrete displacements is striking. Models are formulated using linear and quadratic displacement fields with respect to time. Free model parameters are used to manipulate numerical stability, accuracy and numerical damping.
These numerical tools are used for the numerical simulation ()f a m()ving vehicle at a rail track structure. The analysis sh()ws the natural way ()f m()delling a moving structure (the train) with respect to a fixed supporting structure (the rail track).