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The jacobi integral in nonholonomic mechanics

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Abstract

In this paper we discuss conditions for the existence of the Jacobi integral (that generalizes energy) in systems with inhomogeneous and nonholonomic constraints. As an example, we consider in detail the problem of motion of the Chaplygin sleigh on a rotating plane and the motion of a dynamically symmetric ball on a uniformly rotating surface. In addition, we discuss illustrative mechanical models based on the motion of a homogeneous ball on a rotating table and on the Beltrami surface.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700, Russia

    Alexey V. Borisov

  2. Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Alexey V. Borisov, Ivan. S. Mamaev & Ivan. A. Bizyaev

  3. M. T. Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069, Russia

    Ivan. S. Mamaev

  4. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Ivan. A. Bizyaev

Authors
  1. Alexey V. Borisov
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  2. Ivan. S. Mamaev
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  3. Ivan. A. Bizyaev
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Correspondence to Alexey V. Borisov.

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Borisov, A.V., Mamaev, I.S. & Bizyaev, I.A. The jacobi integral in nonholonomic mechanics. Regul. Chaot. Dyn. 20, 383–400 (2015). https://doi.org/10.1134/S1560354715030107

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  • DOI: https://doi.org/10.1134/S1560354715030107

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