Equilibrium and Stability Analysis of Damaged Aircraft Using Attainable Equilibrium Sets

The damaged aircraft’s equilibrium and stability are related to the safe flight. In this paper, the attainable equilibrium sets of aircraft with and without damage were computed. The results show that, for the damaged and undamaged aircraft, the maximum velocity-vector roll rate ( $$\omega$$ ) is limited by the maximum negative angle of aileron, and the minimum $$\omega$$ is limited by the maximum positive angle of aileron. One pair of conjugate complex roots is easy to appear at the steady point with small $$\omega$$ and two pairs of conjugate complex roots are easy to appear at the steady point with large $$\omega$$ . With the change of sideslip angle, the attainable equilibrium sets of aircraft gradually shift to the positive or negative velocity-vector roll rate direction. Moreover, for the damaged aircraft, the attainable equilibrium sets of aircraft is reduced to different degree, and the wing damage has the greatest influence on the attainable equilibrium sets of the aircraft. The attainable equilibrium sets of undamaged aircraft can be significantly expanded at an appropriate sideslip angle. The findings in the paper can serve as a basis for decision making for the safe flight of damaged aircraft.