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Information × Registration Number 0212U000650, 0107U004101 , R & D reports Title Variational and decompositional methods for contructing applied models of dynamics for nonlinear systems popup.stage_title Head Samoilenko Anatolii Mikhailovych, Registration Date 12-03-2012 Organization International mathemetical center of National academy of sciences of Ukraine popup.description2 A universal complex approach to the statement and the study of a wide circle of problems of the mechanics of nonlinear continual systems is developed. The approach is based on the use of the variation principles of mechanics for the formulation of starting problems and on the conception of the separation of motions in mechanical systems (the simultaneous use of the methods of spatial and amplitude decompositions). The advantage of this approach is the correct statement of mathematical problems and a possibility to automatically obtain the dynamical boundary conditions and the forces of interaction between the components of a system. For objects different by the character of their mathematical description (the Eulerian or Lagrangian description of a motion of the continual components of a system in the form of boundary-value problems with partial differential equations and the description of the dynamics of motion of a solid body with the use of a system of ordinary differential equations), an algorithm of description of the unique scheme of formulation of a mathematical model in the form of a nonlinear system of ordinary differential equations for the amplitude parameters of motion of a system is constructed. The efficiency of the proposed approach is demonstrated by the example of the study of a group of problems of the nonlinear dynamics of a joint motion of a fluid with free surface and a reservoir with cylindrical shape. The relevant recommendations for using the obtained results are given. The detailed scientific report, including the "numerical experiments" (the method of Academician A.A. Samarskii) describing the experimental data obtained by physicists in contemporary real experiments, is carried out. Product Description popup.authors Бєлов Юрій Анатолійович Бойчук Тамара Павлівна Буцан Георгій Петрович Губська Вікторія Володимирівна Дзюбенко Герман Анатолійович Заволока Юлія Анатоліївна Ковальчук Богдан Петрович Лимарченко Олег Степанович Марціянова Людмила Валентинівна Мейнарович Євген Володимирович Митропольський Юрій Олексійович Трушина Світлана Павлівна popup.nrat_date 2020-04-02 Close