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Regular and Chaotic Dynamics, 2002, Volume 7, Issue 1, Pages 73–80
DOI: https://doi.org/10.1070/RD2002v007n01ABEH000197 (Mi rcd804) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Nonholonomic Systems

Non-Integrability of the Suslov Problem

A. J. Maciejewskia, M. Przybylskab

a Institute of Astronomy, University of Zielona Góra, Lubuska 2, 65-265 Zielona Góra, Poland
b Toruń Centre for Astronomy, Nicholaus Copernicus University, Gagarina 11, 87–100 Toruń, Poland
Citations (12)
DOI: https://doi.org/10.1070/RD2002v007n01ABEH000197
Abstract: In this paper we study integrability of the classical Suslov problem. We prove that in a version of this problem introduced by V.V. Kozlov the problem is integrable only in one known case. We consider also a generalisation of Kozlov version and prove that the system is not integrable. Our proofs are based on the Morales–Ramis theory.
Received: 28.01.2002
Bibliographic databases:
Document Type: Personalia
MSC: 70E18, 70E40
Language: English
Citation: A. J. Maciejewski, M. Przybylska, “Non-Integrability of the Suslov Problem”, Regul. Chaotic Dyn., 7:1 (2002), 73–80
Citation in format AMSBIB
\Bibitem{MacPrz02}
\by A. J. Maciejewski, M.~Przybylska
\paper Non-Integrability of the Suslov Problem
\jour Regul. Chaotic Dyn.
\yr 2002
\vol 7
\issue 1
\pages 73--80
\mathnet{http://mi.mathnet.ru/rcd804}
\crossref{https://doi.org/10.1070/RD2002v007n01ABEH000197}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1900056}
\zmath{https://zbmath.org/?q=an:1013.70007}
Linking options:
  • https://www.mathnet.ru/eng/rcd804
  • https://www.mathnet.ru/eng/rcd/v7/i1/p73
    • This publication is cited in the following 12 articles:
    1. Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106  mathnet  crossref  mathscinet
    2. Jaume Llibre, Rafael Ramírez, Valentín Ramírez, Dynamics through First-Order Differential Equations in the Configuration Space, 2023, 33  crossref
    3. Boris S. Bardin, Alexander S. Kuleshov, “Application of the Kovacic algorithm for the investigation of motion of a heavy rigid body with a fixed point in the Hess case”, Z Angew Math Mech, 102:11 (2022)  crossref
    4. Bizyaev I.A. Mamaev I.S., “Dynamics of the Nonholonomic Suslov Problem Under Periodic Control: Unbounded Speedup and Strange Attractors”, J. Phys. A-Math. Theor., 53:18 (2020), 185701  crossref  mathscinet  isi  scopus
    5. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The Hess–Appelrot system and its nonholonomic analogs”, Proc. Steklov Inst. Math., 294 (2016), 252–275  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. Jaume Llibre, Rafael Ramírez, Natalia Sadovskaia, “Integrability of the constrained rigid body”, Nonlinear Dyn, 73:4 (2013), 2273  crossref
    7. Wenlei Li, Shaoyun Shi, “Galoisian obstruction to the integrability of general dynamical systems”, Journal of Differential Equations, 252:10 (2012), 5518  crossref
    8. Adam Mahdi, Claudia Valls, “Analytic non-integrability of the Suslov problem”, Journal of Mathematical Physics, 53:12 (2012)  crossref
    9. ANDRZEJ J. MACIEJEWSKI, MARIA PRZYBYLSKA, “DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY”, Int. J. Geom. Methods Mod. Phys., 06:08 (2009), 1357  crossref
    10. Andrzej J Maciejewski, Maria Przybylska, Jacques-Arthur Weil, “Non-integrability of the generalized spring-pendulum problem”, J. Phys. A: Math. Gen., 37:7 (2004), 2579  crossref
    11. Andrzej J. Maciejewski, Maria Przybylska, “Nonintegrability of the Suslov problem”, Journal of Mathematical Physics, 45:3 (2004), 1065  crossref
    12. Andrzej J. Maciejewski, Maria Przybylska, “Non-integrability of ABC flow”, Physics Letters A, 303:4 (2002), 265  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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