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



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 3, Pages 103–113 (Mi vuu340)  

This article is cited in 2 scientific papers (total in 2 papers)

MECHANICS

On detachment conditions of a top on an absolutely rough support

A. P. Ivanova, N. D. Shuvalova, T. B. Ivanovab

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, Russia
b Department of Theoretical Physics, Udmurt State University, Izhevsk, Russia

Abstract: The classical problem about the motion of a heavy symmetric rigid body (top) with a fixed point on the horizontal plane is discussed. Due to the unilateral nature of the contact, detachments (jumps) are possible under certain conditions. We know two scenarios of detachment related to changing the sign of the normal reaction or the sign of the normal acceleration, and the mismatch of these conditions leads to a paradox. To determine the nature of paradoxes an example of the pendulum (rod) within the limitations of the real coefficient of friction was studied in detail. We showed that in the case of the first type of the paradox (detachment is impossible and contact is impossible) the body begins to slide on the support. In the case of the paradox of the second type (detachment is possible and contact is possible) contact is retained up to the sign change of the normal reaction, and then at the detachment the normal acceleration is non-zero.

Keywords: friction, Lagrange top, paradox, detachment.

Full text: PDF file (301 kB)
References: PDF file   HTML file
UDC: 531.36
MSC: 70F40
Received: 01.08.2012

Citation: A. P. Ivanov, N. D. Shuvalov, T. B. Ivanova, “On detachment conditions of a top on an absolutely rough support”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 3, 103–113

Citation in format AMSBIB
\Bibitem{IvaShuIva12}
\by A.~P.~Ivanov, N.~D.~Shuvalov, T.~B.~Ivanova
\paper On detachment conditions of a~top on an absolutely rough support
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 3
\pages 103--113
\mathnet{http://mi.mathnet.ru/vuu340}


Linking options:
  • http://mi.mathnet.ru/eng/vuu340
  • http://mi.mathnet.ru/eng/vuu/y2012/i3/p103

    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

    This publication is cited in the following articles:
    1. I. S. Mamaev, T. B. Ivanova, “Dinamika tverdogo tela, opirayuschegosya ostrym kraem na naklonnuyu ploskost, pri nalichii sukhogo treniya”, Nelineinaya dinam., 9:3 (2013), 567–593  mathnet
    2. Ivan S. Mamaev, Tatiana B. Ivanova, “The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction”, Regul. Chaotic Dyn., 19:1 (2014), 116–139  mathnet  crossref  mathscinet  zmath
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:161
    Full text:52
    References:35
    First page:1

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