Grants

Project Lead: Pivovarova Elena Nikolaevna

Fund: Russian Science Foundation

Project Number: 26-71-00090

Implementation period: 2026-2028

Annotation:
This project is dedicated to investigating the dynamics of rigid bodies subject to non-integrable constraints. The project aims to study two problems in non-holonomic mechanics that trace back to the classical results of Routh and Chaplygin. The first problem involves finding particular solutions and analyzing the stability of the motion of a homogeneous sphere on a Beltrami surface (a surface of revolution). The second problem concerns finding particular solutions and analyzing their stability for a system of two spheres: one sphere rolls along a horizontal plane, while the second rolls over the first.

Project Lead: Artemova Elizaveta Markovna

Fund: Russian Science Foundation

Project Number: 26-71-00049

Implementation period: 2026-2028

Annotation:
The project aims to investigate the motion of a solid body in a fluid, a topic of significant relevance to applications in theoretical mechanics and hydromechanics. This project proposes the development of an alternative mathematical model based on the theory of body motion in an ideal (incompressible) fluid with the artificial addition of an attached point vortex. This model is expected to replicate the effect of a stable vortex structure near a rigid body, as observed in viscous flows, but within a simpler analytical framework.

Project Lead: Bizyaev Ivan Alexeyevich

Fund: Russian Science Foundation

Project Number: 26-71-10116

Implementation period: 2026-2029

Annotation:
This project aims to develop fundamental research methods in the field of nonholonomic mechanics and their application to describing the dynamics of real mechanical systems that are implemented in practice and have potential for practical application.This project plans to develop new methods for analyzing nonholonomic systems. Furthermore, the project includes solving a number of complex, non-trivial problems in nonholonomic mechanics, which require the integrated application of qualitative analysis methods. Work within the project will be carried out in two main directions. The first direction is the development of general methods for studying systems with nonholonomic constraints. The second direction of the project is related to the study of specific dynamical systems describing the dynamics of assemblies of bodies with rolling elements.

Project Lead: Mamaev Ivan Sergeevich

Fund: Russian Science Foundation

Project Number: 25-11-00305

Implementation period: 2025-2027

Annotation:
This project plans to conduct comprehensive research aimed at developing and analyzing the motion of robotic systems. These studies include the development of designs and the creation of full-scale samples of mobile robots, the construction of mathematical models of motion that allow studying their dynamics, and solving control problems of the systems under consideration. In addition, conducting theoretical studies of the dynamics and controllability of robots will allow developing recommendations for optimizing the design parameters and control parameters. The scientific novelty of the research lies in the development of control algorithms for the considered designs of robotic systems (omniwheel, spherical, screwless underwater), using the results of the study of dynamic models describing their motion, taking into account the features of the external environment. In addition, the considered designs of robotic systems are new and have advantages in maneuverability, cross-country ability, controllability compared to existing models of mobile robots.

Project Lead: Kilin Alexander Alexandrovich

Fund: Ministry of Science and Higher Education of the Russian Federation

Project Number:

Implementation period: 2020-2027

Annotation:
Within the Ural Mathematical Center, the research direction “Regular and Chaotic Dynamics” is being developed. This area is devoted to the study of Dynamical Systems Theory (including the theory of integrability, chaos, and Celestial Mechanics, as well as rigid body dynamics). It represents one of the central fields of modern mathematics and maintains strong connections with other branches of mathematics, as well as with problems in mechanics, physics, biology, economics, and other disciplines. The relevance of these studies is determined by the possibility of applying the developed mathematical approaches to numerous physical problems, including those arising in the theory of nonholonomic systems, classical problems of vortex dynamics and the motion of bodies in fluids, as well as in celestial mechanics and related areas.

Project Lead: Kilin Alexander Alexandrovich

Fund: Ministry of Science and Higher Education of the Russian Federation

Project Number: FEWS-2025-0004

Implementation period: 2025-2027

Annotation:
The project is devoted to investigating theoretical and experimental aspects of mechanical systems with rolling elements, described by nonlinear dynamical systems with non-integrable constraints. The tasks formulated within the project are interdisciplinary in nature, and their solution requires joint research in such fields as theoretical mechanics, dynamical systems theory, control theory, and robotics. The theoretical results obtained will be applied in specific engineering developments, namely in the design and development of control algorithms for mobile spherical robots.

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.

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.

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.

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.

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.

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.

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.