Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane

This paper addresses the problem of a roller-racer rolling on an oscillating plane. Equations motion in form system four nonautonomous differential equations are obtained. Two families particular solutions found which correspond to rectilinear motions along and perpendicular plane's oscillations. Numerical estimates given for multipliers corresponding robot Also, special case is presented it possible obtain analytic expressions multipliers. In this case, shown that oscillations “folded” linearly orbitally stable as moves with its joint ahead, all other unstable. It that, linear approximation, family oscillations, is,