Abstract:
This paper addresses the problem of a sphere with axisymmetric mass distribution rolling
on a horizontal plane. It is assumed that there is no slipping of the sphere as it rolls in the
direction of the projection of the symmetry axis onto the supporting plane. It is also assumed
that, in the direction perpendicular to the above-mentioned one, the sphere can slip relative to
the plane. Examples of realization of the above-mentioned nonholonomic constraint are given.
Equations of motion are obtained and their first integrals are found. It is shown that the system
under consideration admits a redundant set of first integrals, which makes it possible to perform
reduction to a system with one degree of freedom.
Keywords:
nonholonomic constraint, first integral, integrability, reduction.
Citation:
A. A. Kilin, T. B. Ivanova, “The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:1 (2023), 3–17
\Bibitem{KilIva23}
\by A. A. Kilin, T. B. Ivanova
\paper The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint
\jour Rus. J. Nonlin. Dyn.
\yr 2023
\vol 19
\issue 1
\pages 3--17
\mathnet{http://mi.mathnet.ru/nd835}
\crossref{https://doi.org/10.20537/nd221205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4573509}
Citation in format AMSBIB
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