Asymptotic properties of the solutions of the equations of motion of gyroscopic systems

The motion of mechanical systems acted upon by gyroscopic and positional forces characterized by a large parameter in the corresponding equations of motion is considered. Periodic solutions of such equations were investigated earlier in 1, 2]. It is proved below that solutions of these equations exist, defined in an interval the length of which is a monotonically increasing unbounded function of the large parameter, and which transfer into the solutions of the corresponding degenerate systems as the large parameter approaches infinity. This function can be specified in more detail if additional assumptions are made regarding the properties of the system and the nature of the forces acting on it.