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Nonlinear physics and mechanics
The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint
A. A. Kilin, T. B. Ivanova Ural Mathematical Center, Udmurt State University
ul. Universitetskaya 1, Izhevsk, 426034 Russia
Аннотация:
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.
Ключевые слова:
nonholonomic constraint, first integral, integrability, reduction.
Поступила в редакцию: 25.10.2022 Принята в печать: 07.12.2022
Образец цитирования:
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd835 https://www.mathnet.ru/rus/nd/v19/i1/p3
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