滚轮赛车在振动平面上直线运动的轨道稳定性研究

E. Artemova, A. Kilin, Yu.V. Korobeinikova
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引用次数: 0

摘要

本文研究了滚轮在振动平面上的滚动问题。得到了滚轮赛车的运动方程,其形式为四个非自治微分方程组。找到了两类特解,它们对应于滚轮沿和垂直于平面振动的直线运动。给出了机器人沿振动方向运动的乘子解的数值估计。此外,还提出了一种特殊情况,在这种情况下,可以得到乘数的解析表达式。在这种情况下,它显示了一个“折叠的”滚轮赛车沿振荡运动是线性轨道稳定的,因为它的关节向前移动,而所有其他运动都是不稳定的。结果表明,在线性近似下,机器人运动所对应的族垂直于平面振荡,即不稳定。
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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 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.
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CiteScore
1.20
自引率
40.00%
发文量
27
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