Geodesic
The Integrable Problem of the Rolling Motion
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 3-17

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ND_2023_19_1_a0,
     author = {A. A. Kilin and T. B. Ivanova},
     title = {The {Integrable} {Problem} of the {Rolling} {Motion}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2023_19_1_a0/}
}
TY  - JOUR
AU  - A. A. Kilin
AU  - T. B. Ivanova
TI  - The Integrable Problem of the Rolling Motion
JO  - Russian journal of nonlinear dynamics
PY  - 2023
SP  - 3
EP  - 17
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2023_19_1_a0/
LA  - en
ID  - ND_2023_19_1_a0
ER  - 
%0 Journal Article
%A A. A. Kilin
%A T. B. Ivanova
%T The Integrable Problem of the Rolling Motion
%J Russian journal of nonlinear dynamics
%D 2023
%P 3-17
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2023_19_1_a0/
%G en
%F ND_2023_19_1_a0
A. A. Kilin; T. B. Ivanova. The Integrable Problem of the Rolling Motion. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/ND_2023_19_1_a0/