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Russia Izhevsk
Section Mechanics
Title A Chaplygin sleigh with a moving point mass
Author(-s) Bizyaev I.A.a
Affiliations Udmurt State Universitya
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
UDC 517.925
MSC 37J60
DOI 10.20537/vm170408
Received 22 November 2017
Language Russian
Citation Bizyaev I.A. A Chaplygin sleigh with a moving point mass, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 4, pp. 583-589.
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