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Nelin. Dinam., 2013, Volume 9, Number 4, Pages 721–754 (Mi nd417)  

This article is cited in 6 scientific papers (total in 6 papers)

The problem of drift and recurrence for the rolling Chaplygin ball

Alexey V. Borisovabcd, Alexander A. Kilinbcda, Ivan S. Mamaevdbca

a A. A. Blagonravov Mechanical Engineering Research Institute of RAS, Bardina str. 4, Moscow, 117334, Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia
c Laboratory of nonlinear analysis and the design of new types of vehicles, Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
d Institute of Computer Science

Abstract: We investigate the motion of the point of contact (absolute dynamics) in the integrable problem of the Chaplygin ball rolling on a plane. Although the velocity of the point of contact is a given vector function of variables of a reduced system, it is impossible to apply standard methods of the theory of integrable Hamiltonian systems due to the absence of an appropriate conformally Hamiltonian representation for an unreduced system. For a complete analysis we apply the standard analytical approach, due to Bohl and Weyl, and develop topological methods of investigation. In this way we obtain conditions for boundedness and unboundedness of the trajectories of the contact point.

Keywords: nonholonomic constraint, absolute dynamics, bifurcation diagram, bifurcation complex, drift, resonance, invariant torus.

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Document Type: Article
UDC: 531.8, 517.925
MSC: 37J60, 37J35, 70E18
Received: 04.10.2013
Revised: 02.12.2013

Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The problem of drift and recurrence for the rolling Chaplygin ball”, Nelin. Dinam., 9:4 (2013), 721–754

Citation in format AMSBIB
\by Alexey~V.~Borisov, Alexander~A.~Kilin, Ivan~S.~Mamaev
\paper The problem of drift and recurrence for the rolling Chaplygin ball
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 4
\pages 721--754

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    This publication is cited in the following articles:
    1. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “Regulyarnye i khaoticheskie attraktory v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 10:3 (2014), 361–380  mathnet
    2. A. A. Kilin, E. V. Vetchanin, “Upravlenie dvizheniem tverdogo tela v zhidkosti s pomoschyu dvukh podvizhnykh mass”, Nelineinaya dinam., 11:4 (2015), 633–645  mathnet
    3. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    4. A. V. Borisov, I. S. Mamaev, “Symmetries and reduction in nonholonomic mechanics”, 20, no. 5, 2015, 553–604  mathnet  crossref  isi
    5. I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250  mathnet  elib
    6. E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  crossref  mathscinet  isi  elib
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