|
This article is cited in 4 scientific papers (total in 4 papers)
Regular Papers
A Particular Integrable Case in the Nonautonomous Problem
of a Chaplygin Sphere Rolling on a Vibrating Plane
Alexander A. Kilin, Elena N. Pivovarova Ural Mathematical Center, Udmurt State University
ul. Universitetskaya 1, Izhevsk, 426034 Russia
Abstract:
In this paper we investigate the motion of a Chaplygin sphere rolling without slipping on a plane performing horizontal periodic oscillations. We show that in the system under consideration the projections of the angular momentum onto the axes of the fixed coordinate system remain unchanged. The investigation of the reduced system on a fixed level set of first integrals reduces to analyzing a three-dimensional period advance map on $SO(3)$. The analysis of this map suggests that in the general case the problem considered is nonintegrable. We find partial solutions to the system which are a generalization of permanent rotations and correspond to nonuniform rotations about a body- and space-fixed axis. We also find a particular integrable case which, after time is rescaled, reduces to the classical Chaplygin sphere rolling problem on the zero level set of the area integral.
Keywords:
Chaplygin sphere, rolling motion, nonholonomic constraint, nonautonomous dynamical
system, periodic oscillations, permanent rotations, integrable case, period advance map.
Received: 15.03.2021 Accepted: 11.11.2021
Citation:
Alexander A. Kilin, Elena N. Pivovarova, “A Particular Integrable Case in the Nonautonomous Problem
of a Chaplygin Sphere Rolling on a Vibrating Plane”, Regul. Chaotic Dyn., 26:6 (2021), 775–786
Linking options:
https://www.mathnet.ru/eng/rcd1146 https://www.mathnet.ru/eng/rcd/v26/i6/p775
|
Statistics & downloads: |
Abstract page: | 107 | References: | 26 |
|