On the motion of Chaplygin's sphere on a horizontal plane
type: Item
instance of: scholarly article
title: On the motion of Chaplygin's sphere on a horizontal plane
zbMATH Open document ID: 0579.70002
DOI: 10.1016/0021-8928(83)90108-9
author: N. K. Moshchuk
published in: Journal of Applied Mathematics and Mechanics
publication date: 1983-01-01T00:00:00Z
review text: The motion of Chaplygin's sphere, a heavy sphere on a fixed horizontal plane, is considered. It is assumed that the centre of mass of the sphere coincides with its geometric centre, and its principal central moments of inertia are different. In the unperturbed problem the sphere on an absolute smooth plane performs Euler-Poinsot motion about its centre, which moves rectilinearly and uniformly. In the case of low viscous or dry friction the perturbed motion of the sphere is investigated using the method of averaging. It is shown that the sphere tends to rotate about the axis of the largest principal central moment of inertia and the slip velocity approaches zero exponentially. In the case of dry friction and almost equal moments of inertia of the sphere, the system of averaged equations is fully integrable.
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 70E20
Mathematics Subject Classification ID: 70F25
zbMATH DE Number: 3928376
zbMATH Keywords: perturbation method
zbMATH Keywords: averaging method
zbMATH Keywords: low viscous friction
zbMATH Keywords: heavy sphere on a fixed horizontal plane
zbMATH Keywords: Euler-Poinsot motion
zbMATH Keywords: dry friction
zbMATH Keywords: slip velocity
MaRDI profile type: Publication
full work available at URL: 0021-8928(83)90108-9
OpenAlex ID: W2094969538
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description: scientific article; zbMATH DE number 3928376