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Dynamics of the generalized penny-model on the rotating plane

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  • Evgeniya A. Mikishanina

    (Steklov Mathematical Institute of Russian Academy of Sciences
    I. N. Ulianov Chuvash State University)

Abstract

We consider a nonholonomic generalized penny-model on the rotating plane. The generalized penny-model is the model of an inhomogeneous balanced sphere rolling without slipping and articulated with a weightless sliding support that prevents the rotating of the sphere in a certain direction. The sliding of the support along the rotating plane is ideal. The equations of motion, based on the D’Alembert-Lagrange principle, are constructed. At fixed levels of the first integrals, we reduce the original system of equations of motion to an autonomous system of four differential equations admitting the integral of energy. In the case of dynamic symmetry, the reduced system is linear. Its solution can be obtained analytically. In the dynamically nonsymmetric model, we investigate the reduced problem using a two-dimensional or three-dimensional Poincaré map preserving the phase volume (we have the standard invariant measure). There are chaotic modes in the system. The results are illustrated graphically. Graphical abstract

Suggested Citation

  • Evgeniya A. Mikishanina, 2023. "Dynamics of the generalized penny-model on the rotating plane," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(12), pages 1-8, December.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:12:d:10.1140_epjb_s10051-023-00615-x
    DOI: 10.1140/epjb/s10051-023-00615-x
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