Stability theory methods and mechanics singular systems

The work is devoted to the elaboration of analysis methods in complex system dynamics. A generalized approach, based on Lyapunov´s methods and Chetaev´s ideas, considering from unified views all mechanical systems as singular ones, makes it possible to obtain a reduction principle in general qualitative analysis, to elaborate the technology of modelling in mechanics. With the method, combining the stability methods and perturbation methods, the critical cases are considered, when unperturbed systems are on the boundary of stability areas. This approach gives the possibility of estimating the values of parameters, which justify the reduction principle. It enables one to obtain simplified mechanical mathematical models to substantiate introduced idealization. This allows one to solve the problem of comparison system construction and to determine the domains of their acceptability. In mechanics applications (for gyrosystems, stabilization systems, electromechanical systems, etc.) the technique gives an effective algorithm at the engineering level for modelling problems and idealization that permits one to obtain the strict substantiation of idealized models (known and new: inertialess model, precession model, limit model, Aristotle´s model, etc.)