Complexity of dynamic system switching between two subsystems with cornered boundaries

Switching between systems widely exists in real world applications, for instance morphing aerospace vehicle has different shapes at different flight conditions, which leads the system properties and external excitations differ and introduces discontinuity to make the system become singularity. In this paper, a single degree of freedom dynamical system which has two states to switch will be investigated. Domains and boundaries will be defined in the state space, and the switch mechanism on the discontinuous boundaries will be discussed based on the theory of discontinuity. The onset and vanish conditions for the sliding motion of such a dynamical system will be given based on G-function and its higher order. The mapping structure and periodic motions will be described. Through analytical bifurcation analysis, the motion evolution characteristics will be obtained, and one periodic motion switch to another periodic motion through graze bifurcation is observed when the parameter varies