Pryz A. Decomposition and mechanical analogies of linear dynamical systems

The dissertation research is devoted to the decomposition and construction of mechanical analogies in linear dynamic systems of even order. A generalization of the theorem about a mechanical analogy for the system of governance. It is shown that after application of the transformation as a result of decomposition of the original system into two, only one of them has a mechanical analogy. We compute the order of the matrix analogy without their direct construction. Consider the linear impulsive system and the construction of its terms received a mechanical analogy. We found a class of systems for which such a construction is possible. An analogy of mechanical equations of motion of the gyroscopic precession of the system, making it possible to establish analytical matrix relations between the matrices of gyroscopic forces in the full system and by its precession equations. Investigate the property of the transformation matrix to the Frobenius canonical form, we have constructed the algorithm of decomposition of a product of elementary matrices. The results obtained may move without significant changes in the linear time-varying systems in the form of Frobenius. Obtained necessary and sufficient conditions for the decomposition of the matrix of the mechanical analogy of the Frobenius matrix product. We show the application of the theory of mechanical analogies to the Research of stability of the mechanical system. Most of the theoretical results is illustrated by numerical examples.