Stability analysis of equilibrium positions of nonlinear mechanical systems by means of decomposition
One of the main problems arising in the stability analysis of mechanical systems is that the mathemaical model investigated is described by a nonlinear system of differential equations with high dimensionality and a large number of parameters Since a direct analysis of such models is difficult, the most natural and fruitful approach is based on the idea of decomposition, 1 e, the separation of the complex system into several simpler subsystems of lower dimensionality, the separate investigation of these systems and the substantiated transfer of obtained conclusions and results to the original system This approach is widely and successfully used in modern theory of stability and control In the present paper, mechanical systems, influenced by dissipative, gyroscopic and essentially nonlinear positional forces are studied By the use of a decomposition method and the Lyapunov direct method, the conditions are obtained under which a stability analysis of an equilibrium position for the original system with the dimension 2n can be reduced to the stability analysis of equilibrium positions for two auxiliary isolated subsystems with the dimension n each Moreover, the problem of influence of nonconservative forces on the equilibrium position stability is investigated