  This paper is a preliminary work to address the problem of dynamical systems
with parameters varying in time. An idea to predict their behaviour is
proposed. These systems are called \emph{transient systems}, and are
distinguished from \emph{steady systems}, in which parameters are constant. In
particular, in steady systems the excitation is either constant (e.g. nought)
or periodic with amplitude, frequency and phase angle which do not vary in
time. We apply our method to systems which are subjected to a transient
excitation, which is neither constant nor periodic. The effect of switching-off
and full-transient forces is investigated. The former can be representative of
switching-off procedures in machines; the latter can represent earthquake
vibrations, wind gusts, etc. acting on a mechanical system. This class of
transient systems can be seen as the evolution of an ordinary steady system
into another ordinary steady system, for both of which the classical theory of
dynamical systems holds. The evolution from a steady system to the other is
driven by a transient force, which is regarded as a map between the two steady
systems.
