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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 4, Pages 583–589 (Mi vuu610)  

MECHANICS

A Chaplygin sleigh with a moving point mass

I. A. Bizyaev

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: Nonholonomic mechanical systems arise in the context of many problems of practical significance. A famous model in nonholonomic mechanics is the Chaplygin sleigh. The Chaplygin sleigh is a rigid body with a sharp weightless wheel in contact with the (supporting) surface. The sharp edge of the wheel prevents the wheel from sliding in the direction perpendicular to its plane. This paper is concerned with a Chaplygin sleigh with time-varying mass distribution, which arises due to the motion of a point in the direction transverse to the plane of the knife edge. Equations of motion are obtained from which a closed system of equations with time-periodic coefficients decouples. This system governs the evolution of the translational and angular velocities of the sleigh. It is shown that if the projection of the center of mass of the whole system onto the axis along the knife edge is zero, the translational velocity of the sleigh increases. The trajectory of the point of contact is, as a rule, unbounded.

Keywords: nonholonomic mechanics, chaplygin sleigh, acceleration, first integrals.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.2404.2017/4.6


DOI: https://doi.org/10.20537/vm170408

Full text: PDF file (314 kB)
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Document Type: Article
UDC: 517.925
Received: 22.11.2017

Citation: I. A. Bizyaev, “A Chaplygin sleigh with a moving point mass”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017), 583–589

Citation in format AMSBIB
\Bibitem{Biz17}
\by I.~A.~Bizyaev
\paper A Chaplygin sleigh with a moving point mass
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 4
\pages 583--589
\mathnet{http://mi.mathnet.ru/vuu610}
\crossref{https://doi.org/10.20537/vm170408}
\elib{http://elibrary.ru/item.asp?id=32248459}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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