Loading [MathJax]/jax/output/SVG/config.js
Regular and Chaotic Dynamics
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


Regular and Chaotic Dynamics, 2013, Volume 18, Issue 5, Pages 490–496
DOI: https://doi.org/10.1134/S156035471305002X
(Mi rcd133)
 

This article is cited in 11 scientific papers (total in 11 papers)

The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity

Alexey V. Borisovabc, Ivan S. Mamaevcba

a Institute of Computer Science; Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b A. A. Blagonravov Mechanical Engineering Research Institute of RAS, ul. Bardina 4, Moscow, 117334 Russia
c Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
Citations (11)
References:
Abstract: We consider the problem of rolling of a ball with an ellipsoidal cavity filled with an ideal fluid, which executes a uniform vortex motion, on an absolutely rough plane. We point out the case of existence of an invariant measure and show that there is a particular case of integrability under conditions of axial symmetry.
Keywords: vortex motion, nonholonomic constraint, Chaplygin ball, invariant measure, integrability, rigid body, ideal fluid.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation NSh-2519.2012.1
1.1248.2011
1.7734.2013
14.A37.21.1935
This work was carried out at the Udmurt State University and was supported by Grant of the President of the Russian Federation for Support of Leading Scientific Schools NSh-2519.2012.1 “Dynamical Systems of Classical Mechanics and Control Problems”, Analytic Departmental Target Program “Development of Scientific Potential of Higher Schools” (1.1248.2011), Analytic Depart-mental Target Program “Development of Scientific Potential of Higher Schools” (1.7734.2013), Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (Agreement №14.A37.21.1935).
Received: 25.11.2011
Accepted: 18.01.2012
Bibliographic databases:
Document Type: Article
MSC: 70E18, 76B47
Language: English
Citation: Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity”, Regul. Chaotic Dyn., 18:5 (2013), 490–496
Citation in format AMSBIB
\Bibitem{BorMam13}
\by Alexey V. Borisov, Ivan S. Mamaev
\paper The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 5
\pages 490--496
\mathnet{http://mi.mathnet.ru/rcd133}
\crossref{https://doi.org/10.1134/S156035471305002X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3117257}
\zmath{https://zbmath.org/?q=an:1286.70008}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000325810200002}
Linking options:
  • https://www.mathnet.ru/eng/rcd133
  • https://www.mathnet.ru/eng/rcd/v18/i5/p490
  • This publication is cited in the following 11 articles:
    1. Vladimir Dragović, Fariba Khoshnasib-Zeinabad, “Topology of the isoenergy manifolds of the Kirchhoff rigid body case on e(3)”, Topology and its Applications, 311 (2022), 107955  crossref
    2. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582  mathnet  crossref  mathscinet
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi Integral in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:3 (2015), 383–400  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    4. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
    5. Alexander P. Ivanov, “On the Control of a Robot Ball Using Two Omniwheels”, Regul. Chaotic Dyn., 20:4 (2015), 441–448  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    6. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    7. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    8. Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    9. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  mathnet  crossref  mathscinet  zmath
    10. Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “Special Solutions of a High-order Equation for Waves in a Liquid with Gas Bubbles”, Regul. Chaotic Dyn., 19:5 (2014), 576–585  mathnet  crossref  mathscinet  zmath
    11. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:229
    References:58
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025