On the motion of Chaplygin's sledge
type: Item
instance of: scholarly article
title: On the motion of Chaplygin's sledge
zbMATH Open document ID: 0664.70019
DOI: 10.1016/0021-8928(87)90079-7
author: N. K. Moshchuk
published in: Journal of Applied Mathematics and Mechanics
publication date: 1987-01-01T00:00:00Z
review text: The plane motion of Chaplygin's sledge is studied. In his original studies of this non-holonomic system, Chaplygin assumed that the support plane is horizontal, and used a reduction factor to reduce the problem to the study of a Hamiltonian system with two degrees of freedom and one cyclical coordinate (i.e., a completely Liouville integrable system). A smooth reversible replacement of the phase variables is used below for the reduction. The motion is studied in detail by the methods of Hamiltonian mechanics, and the motion on an inclined plane is studied by the averaging method.
Mathematics Subject Classification ID: 70F25
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 4087106
zbMATH Keywords: Chaplygin's sledge
zbMATH Keywords: non-holonomic system
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: completely Liouville integrable system
zbMATH Keywords: smooth reversible replacement
MaRDI profile type: Publication
full work available at URL: 0021-8928(87)90079-7
OpenAlex ID: W1976089397
cites work: Der Schlitten
cites work: Q5558515
cites work: Reducing the equations of motion of certain nonholonomic Chaplygin systems to Lagrangian and Hamiltonian form
cites work: Q3829094
cites work: AVERAGING IN SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
description: scientific article; zbMATH DE number 4087106