Problems of stability with respect to a part of variables

Mathematical models based on nonlinear differential equations for dynamic systems of classical mechanics and biophysics are considered. The research concentrates on these equations integration features, their solutions properties, stability and behavior nearby an equilibrium point. Factors which can change the solution stability such as a form of a problem definition, a choice of the generalized coordinates and equations describing the process, the presence of small periodic or random perturbation are taken into account in the research.