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Nelin. Dinam., 2009, Volume 5, Number 3, Pages 345–356 (Mi nd97)  

This article is cited in 8 scientific papers (total in 9 papers)

Chaplygin's ball with a gyrostat: singular solutions

A. Yu. Moskvin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper deals with the rolling motion of a balanced, dynamically asymmetric ball with a gyrostat on a horizontal rough plane. To investigate the dynamical behavior of the system and find singular solutions, the bifurcation diagram of the momentum map and the bifurcation complex are constructed. The singular solutions are described and their stability is examined. It is shown that the addition of a gyrostat can turn stable singular solutions into unstable ones and vice versa.

Keywords: bifurcational complex, Chapligin ball, stability, nonholonomic system.

Full text: PDF file (461 kB)

Document Type: Article
UDC: 531.133.1
MSC: 37N15
Received: 18.06.2009

Citation: A. Yu. Moskvin, “Chaplygin's ball with a gyrostat: singular solutions”, Nelin. Dinam., 5:3 (2009), 345–356

Citation in format AMSBIB
\Bibitem{Mos09}
\by A.~Yu.~Moskvin
\paper Chaplygin's ball with a gyrostat: singular solutions
\jour Nelin. Dinam.
\yr 2009
\vol 5
\issue 3
\pages 345--356
\mathnet{http://mi.mathnet.ru/nd97}
\elib{http://elibrary.ru/item.asp?id=12851470}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. Yu. Moskvin, “Rezinovyi shar na ploskosti: kriticheskie resheniya”, Nelineinaya dinam., 6:2 (2010), 345–358  mathnet
    3. A. V. Borisov, I. S. Mamaev, “Otvet na zamechaniya A. T. Fomenko”, Nelineinaya dinam., 6:4 (2010), 893–895  mathnet
    4. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov”, Nelineinaya dinam., 8:2 (2012), 289–307  mathnet
    5. Rozenblat G.M., “The Choice of Physically Realizable Parameters When Studying the Dynamics of Spherical and Ellipsoidal Rigid Bodies”, Dokl. Phys., 60:9 (2015), 412–418  crossref  isi
    6. Rozenblat G.M., “On the Choice of Physically Realizable Parameters When Studying the Dynamics of Spherical and Ellipsoidal Rigid Bodies”, Mech. Sol., 51:4 (2016), 415–423  crossref  isi
    7. A. I. Zhila, “Chaplygin's ball with a rotor: Non-degeneracy of singular points”, Moscow University Mathematics Bulletin, 71:2 (2016), 45–54  mathnet  crossref  mathscinet  isi  elib
    8. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. A. I. Zhila, “Comparison of the system “Chaplygin ball with a rotor” and the Zhukovskii system from the rough Liouville equivalence point of view”, Moscow University Mathematics Bulletin, 72:6 (2017), 245–250  mathnet  crossref  mathscinet  isi
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