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Information × Registration Number 0221U103777, 0116U003108 , R & D reports Title Researches of mathematical models in problems of dynamics of control and observation popup.stage_title Head Novytskyi Viktor V, Registration Date 25-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The aim of this work is to create and develop promising mathematical methods for studying the problems of the dynamics of mechanical systems and to identify their parameters. Discrete and continuous linear almost conservative systems are considered. Using the direct product of matrices, as well as the decomposition into power series, a new approach to finding an adaptive optimal controller was found. The model of a controlled object in the form of a system with perturbed obliquely symmetric nondegenerate matrix of coefficients is investigated. An adaptive identification algorithm has been developed to determine unknown system parameters. The problem of determining the orientation of a solid with a known estimate of the parameters of the Rodrigo-Hamilton vector at a given time and measurements of projections on a body-related coordinate system of a vector whose orientation is known in the navigation coordinate system is considered. Precise solutions of the problem of determining the assessment of orientation are obtained, which provides a minimum of the corresponding quality functional. The nonlinear oscillations of the mechanical system “reservoir with liquid with a free surface” under the action of a horizontal force that changes according to the harmonic law have been studied. We used the modal principle, which allows the system to provide the required qualitative characteristics in perturbations, and the variational principle of the least Gaussian coercion. The elliptic bounded and general problems of three bodies are considered for the first time from a single point of view, and thus the general key conditions that ensure Lagrange stability are distinguished for them. The obtained theorems on Lagrange stability, including the spatial elliptic bounded problem of three bodies, when, as is known, the Jacobi integral does not exist. Product Description popup.authors popup.nrat_date 2021-02-25 Close