RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






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


Nelin. Dinam., 2017, Volume 13, Number 2, Pages 207–226 (Mi nd561)  

Original papers

On stability of motion of the Maxwell pendulum

A. P. Markeevab

a Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudny, Moscow Region, 141701, Russia
b A.Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: We investigate the stability of motion of the Maxwell pendulum in a uniform gravity field [1, 2]. The threads on which the axis and the disk of the pendulum have been suspended are assumed to be weightless and inextensible, and the characteristic linear size of the disk is assumed to be small compared to the lengths of threads. In the unperturbed motion the angle the threads make with the vertical is zero, and the disk moves along the vertical and rotates around its horizontal axis. The nonlinear problem of stability of this motion is solved with respect to small deviations of the threads from the vertical. By means of canonical transformations and the Poincaré section surface method, the problem is reduced to the study of stability of the fixed point of the area-preserving mapping of the plane into itself. In the space of dimensionless parameters of the problem, regions of stability and instability are found.

Keywords: stability, map, canonical transformations

Funding Agency Grant Number
Russian Science Foundation 14-21-00068


DOI: https://doi.org/10.20537/nd1702005

Full text: PDF file (374 kB)
References: PDF file   HTML file

UDC: 531.36, 531.53
MSC: 70H05, 70H15, 70E50
Received: 23.01.2017
Accepted:10.04.2017

Citation: A. P. Markeev, “On stability of motion of the Maxwell pendulum”, Nelin. Dinam., 13:2 (2017), 207–226

Citation in format AMSBIB
\Bibitem{Mar17}
\by A.~P.~Markeev
\paper On stability of motion of the Maxwell pendulum
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 2
\pages 207--226
\mathnet{http://mi.mathnet.ru/nd561}
\crossref{https://doi.org/10.20537/nd1702005}
\elib{http://elibrary.ru/item.asp?id=29443378}


Linking options:
  • http://mi.mathnet.ru/eng/nd561
  • http://mi.mathnet.ru/eng/nd/v13/i2/p207

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Нелинейная динамика
    Number of views:
    This page:170
    Full text:53
    References:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020