A model of the attitude system for a quadrotor unmanned aerial vehicle (QUAV), assumed to be a rigid body, is developed. For specific parameter configurations, a chaotic region with a saddle and two stable node-focus equilibrium points is identified. The chaotic model provides an important reference for dynamic analysis and a challengeable task of controller design once the flight enters the chaotic region of parameters. The pitchfork bifurcation of the equilibrium points is provided. Rich dynamics of the system are revealed by two bifurcation regions, which demonstrates the diversity of the flight behaviors as the parameters vary. One bifurcation analysis is with respect to the speed of the front propeller and the speed difference of the front and left propellers, and another one is with respect to the speed of the front propeller and moment of inertia. The dynamic characteristics of the QUAV are further verified by the Casimir power bifurcations. The trajectories of three settings with different structural parameters are analyzed in detail. The stability of the QUAV is found to be enhanced for certain optimized values of the structural parameters. Finally, using the Casimir power and Lagrange multiplier method, a supremum bound of the chaotic attractor is presented.
Quantum-classical correspondence is affirmed via performing Wigner function and a classical-quantum chaotic system containing random variables. The classical-quantum system is transformed into a Kolmogorov model for force and energy analysis. Combining different forces, the system is divided into two categories: conservative and non-conservative, revealing the mechanical characteristic of the classical-quantum system. The Casimir power, an analysis tool, is employed to find the key factors governing the orbital trajectory and the energy cycle of the system. Detailed analyses using the Casimir power and an energy transformation uncover the causes of the different dynamic behaviors, especially chaos. For the corresponding classical Hamiltonian system when Planck’s constant ħ → 0, the supremum bound of the system is derived analytically. Difference between the classical-quantum system and the classical Hamiltonian system is displayed through trajectories and energies. Quantum-classical correspondences are further demonstrated by comparing phase portrait, kinetic, potential and Casimir energies of the two systems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.