Discontinuous Dynamics and Bifurcation for Morphing Aircraft Switching on the Velocity Boundary

Abstract

The concept of morphing aircraft was developed many decades ago, and many researches on the morphing aircraft such as stability and control have been published. As the point of view of the dynamic theory, the dynamic system of the morphing aircraft is consisted with multiple subsystems, and each subsystem represents the morphing aircraft with specific structure to fulfill a particular flight task. The switching process from one structure to another for such a morphing aircraft is considered to be smooth and stable, and the switching time is also assumed to be infinitely small. In this paper, a morphing aircraft with high-speed structure, intermediate-structure and low-speed structure is studied. Such a morphing aircraft is set to switch between high-speed structure and low-speed structure when the speed of aircraft arrives a preset critical speed, and the analytical conditions for switchability is developed. If such a morphing aircraft cannot switch to a low-speed structure or high-speed structure at the moment when it arrives the critical speed, it will switch to an intermediate-structure and control to keep the speed remain constant. The analytical conditions for onset and vanish of such a morphing aircraft switching to the intermediate-structure are also provided. Mapping structure is defined to describe the periodic motions of such a morphing aircraft. The bifurcation scenario is calculated to show the complexity of such a hybrid dynamical system. A periodic motion is given to illustrate the flow of such a morphing aircraft switching on the velocity boundary.