Geodesic
Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 4, pp. 615-629

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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.
Mots-clés : roller-racer, monodromy matrix
Keywords: nonholonomic constraints, vibrating plane, orbital stability. 
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     title = {Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_4_a7/}
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E. M. Artemova; A. A. Kilin; Yu. V. Korobeinikova. Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 4, pp. 615-629. http://geodesic.mathdoc.fr/item/VUU_2022_32_4_a7/