Grants
Applications of methods of the theory of dynamical systems in problems of hydrodynamics, celestial mechanics and gravitation
Project Lead: Bizyaev Ivan Alexeyevich
Fund: Ministry of Science and Higher Education of Russia
Project Number: FEWS-2024-0007
Implementation period: 2024-2026
Annotation:
The project is devoted to the study of dynamical systems arising in problems of hydrodynamics and gravitation theory. Solving these problems requires the use of modern methods of qualitative and numerical analysis of systems of differential equations.
Investigation of rigid body dynamics in the presence of nonintegrable constraints
Project Lead: Pivovarova Elena Nikolaevna
Fund: Russian Science Foundation
Project Number: 23-71-01045
Implementation period: 2023 - 2025
Annotation:
The project is devoted to investigating the dynamics of rigid bodies on a plane in the presence of nonintegrable constraints. Research in this direction is motivated by the results obtained, which can be applied to model the motion of mobile robots with a rigid external shell. This projects provides for the study of rigid bodies using the model of rubber body motion and for a detailed study of the dynamics of an ellipsoid od revolution on a horizontal plane. The project also provides for analysis of the dynamics of a truncated ellipsoid – an ellipsoid of revolution that is symmetrically truncated on both sides by planes so that the cuts form round disks.
Modern methods of the theory of dynamical systems, control theory and topology in problems of mechanics, robotics and mathematical physics
Project Lead: Kilin Alexander Alexandrovich
Fund: Ministry of Science and Higher Education of Russia
Project Number: FEWS-2020-0009
Implementation period: 2020-2024
Annotation:
The project is dedicated to conducting complex theoretical and experimental studies of mechanical systems with rolling elements, described by nonlinear dynamic systems with non-integrable constraints, as well as to the study of problems of mathematical physics.
Qualitative and numerical analysis of dynamical systems arising in mechanics problems concerning systems with rolling and in robotics problems
Project Lead: Bizyaev Ivan Alexeyevich
Fund: Russian Science Foundation
Project Number: 21-71-10039
Implementation period: 2021-2024
Annotation:
The project is aimed at investigating a number of nonholonomic mechanics and robotics problems that are of much current interest for applications. In this project it is planned to study the dynamics of mobile wheeled systems, both statically stable (multilink wheeled vehicle) and statically unstable (monocycles, bicycles) and also to study the dynamics of model systems of nonholonomic mechanics and systems with friction.
Dynamics and control of the motion of rigid bodies in a fluid in the presence of singularities of the fluid flow
Project Lead: Mamaev Ivan Sergeevich
Fund: Russian Science Foundation
Project Number: 22-21-00836
Implementation period: 2022-2023
Annotation:
The project is concerned with investigating the problems of rigid bodies moving in a fluid, which are of much current interest for applications, using modern methods of dynamical systems theory. In particular, the project addresses two main problems.
Search and study of side effects in the problem of nonholonomic mechanics
Project Lead: Kilin Alexander Alexandrovich
Fund: Russian Science Foundation
Project Number: 22-21-00797
Implementation period: 2022-2023
Annotation:
The project is concerned with investigating nonholonomic mechanics problems, which are of much current interest from the fundamental and applied point of view, using modern methods of dynamical systems theory and stability theory. This project is aimed at searching for and studying various dynamical effects in a number of new problems of nonholonomic mechanics.
Research on the dynamics and stabilization of mobile spherical robots on a vibrating surface
Project Lead: Pivovarova Elena Nikolaevna
Fund: Russian Science Foundation
Project Number: 20-71-00053
Implementation period: 2020-2022
Annotation:
The main purpose of the work is to investigate the dynamics and stabilization of mechanical systems describing the motion of spherical robots under the action of external factors, which are of great interest in the context of mobile robotics. This project is aimed at investigating the dynamics and stabilization of two models of spherical robots controlled by changing the intrinsic gyrostatic momentum.