Problems of complex systems analysis and modelling in mechanics

This research develops the Lyapunov stability theory methods for the problem of qualitative investigation of singular systems. General approach permits to elaborate the efficient methods of analysis in the complicated systems dynamics. The conditions are determined under which qualitative investigation of complex systems is reduced to the investigation of simplified systems for critical matrices cases. The stability theory methods give the possibility of the parameters values estimating, allow to construct the shortened systems (as the comparison systems), for which the reduction principle is justifiable in dynamics of complex systems. The obtained results enable to give strict solving of mathematical modelling problems; to receive the correct idealized models with the estimates of parameters, stability and attraction domains; to give the interesting applications in mechanics for gyrosystems, electromechanical systems, in the oscillation theory, etc