Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane
Author:
Artemova E.M.1,
Kilin A.A.1,
Korobeinikova Yu.V.2
Affiliation:
1. Udmurt State University
2. Kalashnikov Izhevsk State Technical University
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.
Funder
Ministry of Science and Higher Education of the Russian Federation
Publisher
Udmurt State University
Subject
Fluid Flow and Transfer Processes,General Mathematics,General Computer Science