Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 2, Pages 356–361
DOI: https://doi.org/10.21638/11701/spbu01.2020.217
(Mi vspua196)
 

This article is cited in 1 scientific paper (total in 1 paper)

MECHANICS

The transgression effect in the problem of motion of an almost holonomic pendulum

A. S. Kuleshov, I. I. Ulyatovskaya

Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119234, Russian Federation
Full-text PDF (295 kB) Citations (1)
Abstract: In 1986, Ya. V. Tatarinov presented the basis of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that when the value of this parameter is zero, the constraints of such a system become integrable, i. e. in this case we have a family of holonomic systems depending on several arbitrary integration constants. We will assume that these holonomic systems are integrable hamiltonian systems. When the small parameter is not zero, the methods of perturbation theory can be used to represent, to a first approximation, the motion of the system with nonzero parameter values, as a combination of the motion of a slightly modified holonomic system with slowly varying previous integration constants (transgression effect). In this paper, we describe the transgression effect in the problem of motion of an almost holonomic pendulum.
Keywords: weakly nonholonomic systems, almost holonomic pendulum, transgression.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00140
20-01-00637
The work is supported by Russian Foundation for Basic Research (grants 19-01-00140, 20-01-00637).
Received: 18.11.2019
Revised: 11.12.2019
Accepted: 12.12.2019
Document Type: Article
UDC: 517.928+531.53
MSC: 70F25, 70K60, 70K70
Language: Russian
Citation: A. S. Kuleshov, I. I. Ulyatovskaya, “The transgression effect in the problem of motion of an almost holonomic pendulum”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:2 (2020), 356–361
Citation in format AMSBIB
\Bibitem{KulUly20}
\by A.~S.~Kuleshov, I.~I.~Ulyatovskaya
\paper The transgression effect in the problem of motion of an almost holonomic pendulum
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 2
\pages 356--361
\mathnet{http://mi.mathnet.ru/vspua196}
\crossref{https://doi.org/10.21638/11701/spbu01.2020.217}
Linking options:
  • https://www.mathnet.ru/eng/vspua196
  • https://www.mathnet.ru/eng/vspua/v7/i2/p356
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
    Statistics & downloads:
    Abstract page:45
    Full-text PDF :9
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024