Abstract:
The problem of the rolling of a disk on a plane is considered under the assumption
that there is no slipping in the direction parallel to the horizontal diameter of the disk and
that the center of mass does not move in the horizontal direction. This problem is reduced to
investigating a system of three first-order differential equations. It is shown that the reduced
system is reversible relative to involution of codimension one and admits a two-parameter family
of fixed points. The linear stability of these fixed points is analyzed. Using numerical simulation,
the nonintegrability of the problem is shown. It is proved that the reduced system admits, even
in the nonintegrable case, a two-parameter family of periodic solutions. A number of dynamical
effects due to the existence of involution of codimension one and to the degeneracy of the fixed
points of the reduced system are found.
Citation:
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
\Bibitem{KilPiv23}
\by Alexander A. Kilin, Elena N. Pivovarova
\paper Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 1
\pages 78--106
\mathnet{http://mi.mathnet.ru/rcd1196}
\crossref{https://doi.org/10.1134/S1560354723010069}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4559070}
Linking options:
https://www.mathnet.ru/eng/rcd1196
https://www.mathnet.ru/eng/rcd/v28/i1/p78
This publication is cited in the following 4 articles:
A. G. Agúndez, D. García-Vallejo, E. Freire, “Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints”, Nonlinear Dyn, 112:4 (2024), 2453
Ivan Yu. Polekhin, “On the dynamics and integrability of the Ziegler pendulum”, Nonlinear Dyn, 112:9 (2024), 6847
Simon Sailer, Remco I. Leine, NODYCON Conference Proceedings Series, Advances in Nonlinear Dynamics, Volume I, 2024, 605
A. A. Kilin, T. B. Ivanova, “The Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:4 (2023), 533–543
Citation in format AMSBIB
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