Virtual cutting system simulations developed using mathematical modelling allow us to consider the relationship between the CNC program, machine actuator trajectories and elastic deformations, as well as the laws guiding trajectory transformation into output processing characteristics. The transformations of these trajectories are defined by a system of nonlinear higher-order differential equations that are difficult to analyse. Another related issue is the difficulty involved in determining the variation patterns in the actuator servomotor dynamics driven by the cutting process. The paper proposes a general approach to analysing a controlled dynamic cutting system based on the asymptotic properties of nonlinear differential equations containing small parameters for derivatives. We focus on drive properties being dynamically determined by their interaction with the cutting process. The paper presents drive properties as functions of elastic matrices pertaining to subsystems representing the tool and the workpiece interacting via the cutting process, said functions derived by mathematical simulation.