平面库伦摩擦系统的动力学分析

Dynamic Analysis of Planar Coulomb Friction System

摘要: 机械系统库伦摩擦的存在，导致了系统的不连续性的存在。本文研究了在水平面上运动的物体在库伦摩擦力作用下的全局动力学行为。在这种情况下，不连续系统的滑模域上的点都是系统的伪平衡点。在此基础上，通过构造Poincaré映射，给出了滑模域中的点构成的集合均为系统的全局吸引子这一结论，最后通过数值模拟验证了该吸引子在有限时间内是收敛的这一结论。

Abstract: The existence of Coulomb friction in mechanical system leads to the existence of discontinuity. In this paper, the global dynamic behavior of an object moving on a horizontal plane under Coulomb friction is studied. In this case, the points on the sliding mode domain of the discontinuous system are all pseudo-equilibrium points of the system. On this basis, by constructing the Poincaré mapping, the conclusion that the set of points in the sliding mode domain is the global attractor of the system is given. Finally, the conclusion that the attractor is convergent in finite time is proved by numerical simulation.