Analysis of discontinuous dynamical behaviors of a friction-induced oscillator with an elliptic control law (Q1721071)

Summary: This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass \(M\) through the analysis of the corresponding vector fields and \(G\)-functions. The periodic motions of such a discontinuous system are predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.