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Analysis of discontinuous dynamical behaviors of a friction-induced oscillator with an elliptic control law. (English) Zbl 1427.70037
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.
MSC:
70F40 Problems involving a system of particles with friction
34A36 Discontinuous ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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