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



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






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


Regul. Chaotic Dyn., 2016, Volume 21, Issue 2, Pages 204–231 (Mi rcd75)  

Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations

Maria Przybylskaa, Stefan Rauch-Wojciechowskib

a Institute of Physics, University of Zielona Góra, Licealna 9, PL-65417, Zielona Góra, Poland
b Department of Mathematics, Linköping University, 581 83, Linköping, Sweden

Abstract: We present a qualitative analysis of the dynamics of a rolling and sliding disk in a horizontal plane. It is based on using three classes of asymptotic solutions: straight-line rolling, spinning about a vertical diameter and tumbling solutions. Their linear stability analysis is given and it is complemented with computer simulations of solutions starting in the vicinity of the asymptotic solutions. The results on asymptotic solutions and their linear stability apply also to an annulus and to a hoop.

Keywords: rigid body, nonholonomic mechanics, rolling disk, sliding disk

Funding Agency Grant Number
National Science Centre (Narodowe Centrum Nauki) DEC-2013/09/B/ST1/04130
M.P. has been supported by grant No. DEC-2013/09/B/ST1/04130 of the National Science Center of Poland, and M.P. and S.R. gracefully acknowledge support from the Department of Mathematics of Linköping University.


References: PDF file   HTML file

English version:
DOI: https://doi.org/10.1134/S1560354716020052

Bibliographic databases:

MSC: 37J60, 37J25, 70G45
Received: 27.10.2015
Accepted:15.02.2016
Language:

Citation: Maria Przybylska, Stefan Rauch-Wojciechowski, “Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations”, Regul. Chaotic Dyn., 21:2 (2016), 204–231

Citation in format AMSBIB
\Bibitem{PrzRau16}
\by Maria Przybylska, Stefan Rauch-Wojciechowski
\paper Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 204--231
\mathnet{http://mi.mathnet.ru/rcd75}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3486006}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000374286800005}


Linking options:
  • http://mi.mathnet.ru/eng/rcd75
  • http://mi.mathnet.ru/eng/rcd/v21/i2/p204

    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
  • Number of views:
    This page:79
    References:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019