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This article is cited in 4 scientific papers (total in 4 papers)
Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint
Alexander A. Kilinab, Elena N. Pivovarovaa a Ural Mathematical Center, Udmurt State University,
ul. Universitetskaya 1, 426034 Izhevsk, Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS,
ul. S. Kovalevskoi 16, 620990 Ekaterinburg, Russia
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.
Keywords:
nonholonomic constraint, unbalanced disk, omnidisk, permanent rotations, periodic
solutions, stability, integrability, chaos, invariant manifolds, manifolds of fall.
Received: 12.10.2022 Accepted: 10.12.2022
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
Linking options:
https://www.mathnet.ru/eng/rcd1196 https://www.mathnet.ru/eng/rcd/v28/i1/p78
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Abstract page: | 85 | References: | 24 |
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