https://doi.org/10.1140/epjb/s10051-023-00615-x
Regular Article - Statistical and Nonlinear Physics
Dynamics of the generalized penny-model on the rotating plane
1
Department of Mechanics, Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina, 8, 119991, Moscow, Russian Federation
2
Department of Actuarial and Financial Mathematics, I. N. Ulianov Chuvash State University, Moskovskii pr., 15, 428015, Cheboksary, Chuvash Republic, Russian Federation
Received:
9
June
2023
Accepted:
23
October
2023
Published online:
4
December
2023
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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
