1.
Artemova E. M., Kilin A. A., Korobeinikova Y. V.
Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane
Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2022, vol. 32, no. 4, pp. 615-629
Abstract
pdf (513.14 Kb)
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 |
| Citation: |
Artemova E. M., Kilin A. A., Korobeinikova Y. V., Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane, Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2022, vol. 32, no. 4, pp. 615-629 |
| DOI: |
10.35634/vm220408 |
| Full text: |
pdf
(513.14 Kb)
|
Journal Info
| Impact-factor WoS (2022): |
0.500 |
| Impact-factor RSCI (2022): |
0.342 (Q3) |
| ISSN (print): |
1994-9197 |
| ISSN (online): |
2076-5959 |
| Site: |
http://vst.ics.org.ru |
