Scientific seminar "Nonpotential dynamical systems and neural network technologies" (сhairs: prof. Savchin V.M., associate prof. Shorokhov S.G.)
On May 31 at 19:00 p.m. (Moscow time)
Speaker: Budochkina Svetlana, associate professor of S.M. Nikol’skii Mathematical Institute.
Topic: "Direct and inverse problems of mechanics of non-potential systems with an infinite number of degrees of freedom".
The talk is devoted to the presentation of the results of the investigation of motion of non-potential systems with an infinite number of degrees of freedom, which, on the one hand, is a further development of classical mechanics, and on the other — allows us, as a very special case, to investigate the motion of systems with a finite number of degrees of freedom. So, the purpose of the talk is also to construct a unified theory of finite-dimensional and infinite-dimensional systems. The connecting link in this direction is the operator approach, on the basis of which general methods for investigation of different classes of equations of motion have been developed.
The achievement of these goals is carried out by solving the following main tasks:
- Construction of Hamiltonian actions for equations of motion of non-potential systems with an infinite number of degrees of freedom using Eulerian and non-Eulerian classes of functionals;
- Representation of equations of motion of non-potential systems with an infinite number of degrees of freedom in the form of classical and non-classical Hamiltonian equations;
- Obtaining formulas for finding integrals of the equations of motion of non-potential systems with an infinite number of degrees of freedom by using invariance properties of the equations of motion and the corresponding Hamiltonian actions.