“…In the future, by developing the application of TAU methods in this matter, it is possible to study the dynamic system stability analytically, for example, according to the Hurwitz criterion, with stability areas construction according to certain parameters. It is possible to optimize the system parameters to obtain the best transient response, for example, by integral estimates, using computer simulation, artificial intelligence [48], using multi-criteria analysis [49], prediction of a new form of the cutting tool on base of machinability tests [50], using Petri nets for modeling and performance evaluation of discrete event systems [51], using a numerical analysis of the stress-strain [52] or other. The numerical solution to the differential Equation (1) can be used for simulation of the tool holder working process in various modes for various parameters, various new materials too [53].…”