The paper deals with the development of mathematical backgrounds to transform dynamical system into the generalized time domain. This transformation allows to change the trajectory of the dynamical system's motion and gives to dynamical system new properties and features. One of such features is the possibility to form motion trajectories with identical anterior and posterior fronts. This feature gives us the possibility to improve system performance and accuracy and we consider system motion in direct and inverse time to ensure it. We study different time domains and define transformation functions to perform the transition from the one time domain into another one. As a result of our studies, we define generalized transformation factor and patterns in its determining, which usage makes it possible to rewrite the differential equation of the considered dynamical system into desired time domain without applying any transformation routines and defining any transformation functions. The implementation of our approach brings us to consider variable structure dynamical system which has an identical start and stop trajectories.