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., 2010, Volume 6, Number 4, Pages 907–912 (Mi nd15)  

This article is cited in 4 scientific papers (total in 5 papers)

Comments. Discussion. Critique

Comparative analysis of friction models in dynamics of a ball on a plane

A. P. Ivanov

Moscow Institute of Physics and Technology

Abstract: Comparative analysis of the dynamics of a homogeneous ball on a plane with dry friction is conducted for two conjectures: 1) single contact point (non-holonomic statement); 2) the normal load is distributed in the circle spot of contact with radius $\varepsilon$. It is assumed that for given active forces and coefficient of friction the non-slip motion is possible. The expression for load distribution function $\phi$ at the contact spot (second statement) is arbitrary, with general mild restrictions, which ensure correctness of the passage to the limit. It is shown that for $\varepsilon\to 0$ the trajectory of the ball with contact spot approaches the trajectory of the ball with single contact point. Previously similar result was obtained by Fufaev [1] in the case $\phi=\mathrm{const}$. The possibility of approximation of reactions of non-holonomic constraints by means of forces of viscous friction was proved [2], [3], as well as by means of forces of dry friction with infinitely large coefficient of friction [4].

Keywords: systems with rolling motion, dry friction.

Full text: PDF file (150 kB)
References: PDF file   HTML file
UDC: 531.01
MSC: 70Е18
Received: 22.12.2010

Citation: A. P. Ivanov, “Comparative analysis of friction models in dynamics of a ball on a plane”, Nelin. Dinam., 6:4 (2010), 907–912

Citation in format AMSBIB
\Bibitem{Iva10}
\by A.~P.~Ivanov
\paper Comparative analysis of friction models in dynamics of a ball on a plane
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 907--912
\mathnet{http://mi.mathnet.ru/nd15}


Linking options:
  • http://mi.mathnet.ru/eng/nd15
  • http://mi.mathnet.ru/eng/nd/v6/i4/p907

    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. V. F. Zhuravlev, “Ponyatie svyazi v analiticheskoi mekhanike”, Nelineinaya dinam., 8:4 (2012), 853–860  mathnet
    2. A. V. Borisov, I. S. Mamaev, “Notes on new friction models and nonholonomic mechanics”, Phys. Usp., 58:12 (2015), 1220–1222  mathnet  crossref  crossref  adsnasa  isi  elib
    3. Alexey V. Borisov, Yury L. Karavaev, Ivan S. Mamaev, Nadezhda N. Erdakova, Tatyana B. Ivanova, Valery V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541  mathnet  crossref  mathscinet  zmath
    4. Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810  mathnet  crossref
    5. Zobova A.A., “A Review of Models of Distributed Dry Friction”, Pmm-J. Appl. Math. Mech., 80:2 (2016), 141–148  crossref  isi
  • Нелинейная динамика
    Number of views:
    This page:198
    Full text:63
    References:35
    First page:1

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