Global Invariant Manifolds in a Problem of Kalman-Bucy Filtering for Gyroscopic Systems

The effect of random inputs on the movement of systems of solid bodies was investigated by many authors, see, for example, [1]. The paper deals with the analysis of the equations of gyroscopic systems under the influence of random forces. The possibility of the replacement of the equations of motion by the corresponding precessional equations is investigated. This approach is widespread in mechanics and gives suitable results in numerous cases. But there are a great number of examples when the substitution of the original equations by the precessional ones leads to inaccurate or qualitatively incorrect results.