Methods of stability theory in systems analysis and modelling

The work is devoted to the analysis method for complicated systems dynamics. A generalized approach based on the Lyapunov´s methods, from common attitudes of mechanical systems, permits to receive the reduction principle in general qualitative analysis and to elaborate the technology of modelling in mechanics. Using the method, combined with 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 values of parameter estimation which justify the reduction principle. It enables one to adapt the simplified mechanical-mathematics models, and allows one to solve the problem of comparison systems construction and to determine the domains of their acceptability. In the applications to mechanical systems, the technique gives an effective engineering algorithm for the modelling problems