Search academic texts

Information × Registration Number 0224U033603, (0123U103046) , R & D reports Title Constructive and qualitative methods for the study of nonlinear boundary value problems and their application to mechanical problems popup.stage_title Дослідження математичних моделей із використанням конструктивних та якісних методів Head Niesmielova Olha V., Доктор фізико-математичних наук Registration Date 31-12-2024 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description1 The aim of the work is to obtain constructive necessary and sufficient conditions for the existence and construction of effective algorithms for finding approximations to solutions of nonlinear boundary value problems, unsolved with respect to the derivative and differential-algebraic boundary value problems, as well as to obtain the conditions for asymptotic stability of rotation in a medium with resistance of a system of two elastically coupled Lagrange gyroscopes with an ideal fluid. popup.description2  The aim of the project was to obtain constructive necessary and sufficient conditions for the existence and construction of efficient algorithms for finding approximations to solutions of nonlinear boundary value problems unsolved with respect to the derivative and differential-algebraic boundary value problems, as well as to obtain conditions for the asymptotic stability of rotation in a medium with resistance of a system of two elastically coupled Lagrange gyroscopes with an ideal fluid. DIn this project, we study a variety of boundary value problems for systems of ordinary differential equations, differential-algebraic systems, matrix integro-differential systems, including boundary value problems unsolved with respect to the derivative. For the considered problems, the conditions of solvability were established and iterative schemes for constructing solutions, including accelerated convergence, were proposed. All the obtained results are demonstrated by examples. Also considered are the problems of stabilisation of unstable uniform rotation in a medium with drag of a ‘sleeping’ Lagrangian gyroscope with an ideal fluid using a second rotating gyroscope and the problem of stabilisation of uniform rotation in a medium with drag of a Lagrangian gyroscope on a suspension. The results of the project are the conditions for the asymptotic stability of uniform rotations in a medium with resistance of a system of two elastically coupled Lagrangian gyroscopes with an ideal fluid, as well as two Lagrangian gyroscopes with an ideal fluid on a suspension. The influence of the fluid, dissipation, mass and inertial characteristics of the suspension, and the elasticity of the joints on the stability conditions were evaluated. Product Description popup.authors Sviatenko Yaroslav I. popup.nrat_date 2024-12-31 Close