Analytical Dynamics of a Discontinuous Dynamical System with a Hyperbolic Boundary - Luo, Albert C. J.; Liu, Chuanping (Journal of Vibration Testing and System Dynamics, 2026)
In this paper, analytical dynamics of a discontinuous system with a hyperbolic control boundary is studied. The analytical conditions for flow switchability of the discontinuous system are developed from a flow passability theory at boundaries, which are for a better understanding of dynamics of such a discontinuous dynamical system. With the analytical switchability conditions, the sliding and non-sliding motions are described through generic mappings. Periodic motions in the discontinuous dynamical system with hyperbolic boundary are studied through mapping structures. The bifurcation trees of periodic motions are presented, and the corresponding stability and bifurcation of periodic motions are analyzed. The grazing bifurcation for a flow to the boundary is discussed as periodic motion switching. Numerical simulations are completed for illustration of complex periodic motions and flow switchability at the hyperbolic boundary. This paper is dedicated to Nail Ibragimov as a good friend and colleague for 20 years friendship with Albert Luo.