Alexey Davydov
Current position:
Head of the Chair of the Dynamical System Theory, Lomonosov Moscow State University, Moscow, Russia;
Head of Chair of the Mathematics, National University of Science and Technology MISiS (part time), Moscow, Russia.
Main research areas:
singularity theory, structural stability of dynamical systems, mathematical control theory, optimization and parametric optimization
Previous positions:
1982-1990: assistant professor (1982-1984) and associated professor (1984-1990), Vladimir State University, Russia;
1990-1993: research fellow (doctorant), Steklov Mathematical Institute RAS;
1994-2006: Full Professor, Vladimir State University, Russia;
2006-2014: Head of the Chair of the Functional Analysis and its Applications, Vladimir State University, Russia (2014-2016 – part time);
2016-2020: Leading Researcher, National University of Science and Technology MISiS, Moscow, Russia;
2016-2020: Head of Chair, National University of Science and Technology MISiS, Moscow, Russia;
2014-2016; 2016-2020, part time; 2021 – now: Head of the Chair of the Dynamical System Theory, Lomonosov Moscow State University, Moscow, Russia.
Education:
Master Thesis in Mathematics (1979) and PhD in Mathematics and Physics (1982), Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Russia;
Doctor of Science in Mathematics and Physics (1993), Steklov Mathematical Institute RAS.
Editorial board member/associate editor:
«Journal of Dynamical and Control Systems» (since 1995) and of «Izvestia:Mathematics» (since 2010) .
Awards:
Moscow Mathematical Society awards a young mathematician for his/her outstanding work in the field (1986);
MAIK/INTERPERIODICA award (2002).
Publications:
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Davydov A. A., Plakhov A.
Dynamics of a Pendulum in a Rarefied Flow
2024, vol. 29, no. 1, pp. 134-142
Abstract
We consider the dynamics of a rod on the plane in a flow of non-interacting point
particles moving at a fixed speed. When colliding with the rod, the particles are reflected
elastically and then leave the plane of motion of the rod and do not interact with it. A thin
unbending weightless “knitting needle” is fastened to the massive rod. The needle is attached
to an anchor point and can rotate freely about it. The particles do not interact with the needle.
The equations of dynamics are obtained, which are piecewise analytic: the phase space is divided
into four regions where the analytic formulas are different. There are two fixed points of the
system, corresponding to the position of the rod parallel to the flow velocity, with the anchor
point at the front and the back. It is found that the former point is topologically a stable focus,
and the latter is topologically a saddle. A qualitative description of the phase portrait of the
system is obtained.
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