Abstract:
This work is devoted to the study of the dynamics of the Chaplygin ball with variable moments of inertia, which occur due to the motion of pairs of internal material points, and internal rotors. The components of the inertia tensor and the gyrostatic momentum are periodic functions. In general, the problem is nonintegrable. In a special case, the relationship of the problem under consideration with the Liouville problem with changing parameters is shown. The case of the Chaplygin ball moving from rest is considered separately. Poincaré maps are constructed, strange attractors are found, and the stages of the origin of strange attractors are shown. Also, the trajectories of contact points are constructed to confirm the chaotic dynamics of the ball. A chart of dynamical regimes is constructed in a separate case for analyzing the nature of strange attractors.
The work was supported by RFBR grant 18-29-10051 mk and was carried out at MIPT under project
5-100 for state support for leading universities of the Russian Federation.
\Bibitem{BorMik20}
\by A. V. Borisov, E. A. Mikishanina
\paper Dynamics of the Chaplygin Ball with Variable Parameters
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 3
\pages 453--462
\mathnet{http://mi.mathnet.ru/nd721}
\crossref{https://doi.org/10.20537/nd200304}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4159467}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85095433170}
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This publication is cited in the following 5 articles:
E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Mech. Solids, 59:1 (2024), 127
E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, no. 1, 230
Evgeniya A. Mikishanina, “Dynamics of the generalized penny-model on the rotating plane”, Eur. Phys. J. B, 96 (2023), 15–8
E. A. Mikishanina, “Rolling motion dynamics of a spherical robot with a pendulum actuator controlled by the Bilimovich servo-constraint”, Theoret. and Math. Phys., 211:2 (2022), 679–691
E. A. Mikishanina, “Dinamika kacheniya diska s naklonnoi skolzyaschei oporoi”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2021, no. 3, 45–56
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