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Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics

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Abstract

We show that the Suslov nonholonomic rigid body problem studied in by Fedorov and Kozlov (Am. Math. Soc. Transl. Ser. 2 168:141–171, 1995), Jovanović (Reg. Chaot. Dyn. 8(1):125–132, 2005), and Zenkov and Bloch (J. Geom. Phys. 34(2):121–136, 2000) can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Moscow Lomonosov University, Moscow, 119 899, Russia

    Yuri N. Fedorov

  2. Departament de Matemàtica I, Universitat Politecnica de Catalunya, Barcelona, E-08028, Spain

    Yuri N. Fedorov

  3. Mathematical Institute SANU, Kneza Mihaila 35, 11000, Belgrade, Serbia

    Božidar Jovanović

Authors
  1. Yuri N. Fedorov
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  2. Božidar Jovanović
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Correspondence to Yuri N. Fedorov.

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Fedorov, Y.N., Jovanović, B. Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics. Lett Math Phys 76, 215–230 (2006). https://doi.org/10.1007/s11005-006-0069-3

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  • DOI: https://doi.org/10.1007/s11005-006-0069-3

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