Nonlinear physics and mechanics

On the Motion of the Chaplygin Sleigh Along a Horizontal Plane with Friction in the Asymmetric Case

A. Y. Shamin

Federal State Institution Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Nakhimovsky prosp. 36, building 1, 117218, Moscow, Russia

Abstract: This paper addresses the problem of the motion of the Chaplygin sleigh, a rigid body moving with three points in contact with a horizontal plane. One of them is equipped with a knife edge along which there is no slipping. Special attention is given to the case where dry friction is present at one of the points of support without the knife edge. The equations of motion of the body are written, the normal reactions are calculated, and the behavior of the phase curves in the neighborhood of an equilibrium point, depending on the geometric and mass characteristics of the body, is investigated by the method of introducing a small parameter.

Keywords: dry friction, Chaplygin sleigh.

MSC: 70F25, 70F40

Received: 19.12.2021
Accepted: 16.04.2022

Language: English

DOI: 10.20537/nd220207

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