The Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint
Received 02 November 2023; accepted 10 December 2023; published 11 December 2023
2023, Vol. 19, no. 4, pp. 533-543
Author(s): Kilin A. A., Ivanova T. B.
This paper investigates the problem of a sphere with axisymmetric mass distribution rolling
on a horizontal plane. It is assumed that the sphere can slip in the direction of the projection of
the symmetry axis onto the supporting plane. Equations of motion are obtained and their first
integrals are found. It is shown that in the general case the system considered is nonintegrable
and does not admit an invariant measure with smooth density. Some particular cases of the
existence of an additional integral of motion are found and analyzed. In addition, the limiting
case in which the system is integrable by the Euler – Jacobi theorem is established.
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