# Dynamics of an Unbalanced Disk with a Single Nonholonomic Constraint

*2023, Volume 28, Number 1, pp. 78-106*

Author(s):

**Kilin A. A., Pivovarova E. N.**

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.

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