Ivan Polekhin (Candidate of Physics and Mathematics, Steklov Mathematical Institute RAS, Moscow Institute of Physics and Technology) will read a mini-course of lectures
鈥淣ew results on the dynamics of an inverted pendulum鈥�.
Lectures will be held daily
from 4 to 8 October 2021 at
18:10 at the Sobolev Institute of Mathematics (IM) SB RAS. On October 4, the lecture will be read in room 115 of the IM SB RAS, on October 5鈥�8 鈥� in room 417 of the IM SB RAS.
A course of five lectures will be devoted to the presentation of results on the dynamics of an inverted pendulum and similar systems obtained in recent years.
Course program:
- The movement of an inverted pendulum without falls in the presence of additional external influences that are not assumed to be small.
-
Forced oscillations of an inverted pendulum. Upper and lower solution method. Topological methods for studying forced vibrations.
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Forced vibrations of an inverted spherical pendulum and more general systems.
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Kapitsa-Whitney pendulum. A variational method for proving the existence of forced oscillations.
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A topological method for studying the global stabilizability of controlled systems with feedback.
In Lectures 1 and 5, the presentation will be very elementary (basic properties of ODEs, the concept of continuity). The rest of the lectures will require some knowledge of averaging theory, functional analysis and topology. However, the general ideas and wording of the statements can also be understood by first year students.
