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Russia Izhevsk
Year
2022
Volume
32
Issue
4
Pages
615-629
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Section Mechanics
Title Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane
Author(-s) Artemova E.M.a, Kilin A.A.ab, Korobeinikova Yu.V.b
Affiliations Udmurt State Universitya, Izhevsk State Technical Universityb
Abstract This paper addresses the problem of a roller-racer rolling on an oscillating plane. Equations of motion of the roller-racer in the form of a system of four nonautonomous differential equations are obtained. Two families of particular solutions are found which correspond to rectilinear motions of the roller-racer along and perpendicular to the plane's oscillations. Numerical estimates are given for the multipliers of solutions corresponding to the motion of the robot along the oscillations. Also, a special case is presented in which it is possible to obtain analytic expressions of the multipliers. In this case, it is shown that the motion along oscillations of a “folded” roller-racer is linearly orbitally stable as it moves with its joint ahead, and that all other motions are unstable. It is shown that, in a linear approximation, the family corresponding to the motion of the robot is perpendicular to the plane's oscillations, that is, it is unstable.
Keywords roller-racer, nonholonomic constraints, vibrating plane, monodromy matrix, orbital stability
UDC 517.933, 517.938
MSC 37J60, 34D20
DOI 10.35634/vm220408
Received 17 October 2022
Language Russian
Citation Artemova E.M., Kilin A.A., Korobeinikova Yu.V. Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 4, pp. 615-629.
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