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Dynamics of the generalized penny-model on the rotating plane

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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.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: No data associated in the manuscript.]

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Funding

This work was supported by the Russian Science Foundation (Project no. 19-71-30012) https://rscf.ru/en/project/19-71-30012/.

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Authors and Affiliations

  1. Department of Mechanics, Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina, 8, Moscow, 119991, Russian Federation

    Evgeniya A. Mikishanina

  2. Department of Actuarial and Financial Mathematics, I. N. Ulianov Chuvash State University, Moskovskii pr., 15, Cheboksary, 428015, Chuvash Republic, Russian Federation

    Evgeniya A. Mikishanina

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Correspondence to Evgeniya A. Mikishanina.

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Mikishanina, E.A. Dynamics of the generalized penny-model on the rotating plane. Eur. Phys. J. B 96, 157 (2023). https://doi.org/10.1140/epjb/s10051-023-00615-x

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