On application of dynamical systems theory into investigation of critical flight regimes of flying vehicles

Non-linear dynamics phenomena have become important for various aircraft motions. Manoeuvrability of an aircraft in critical flight regimes involves non-linear aerodynamics and inertial coupling. Dynamical systems theory provides a methodology for studying non-linear systems of ordinary differential equations. Bifurcation theory is a part of that theory which is considering changes in the stability, which lead to qualitatively different responses of the system. These changes are called bifurcations. The
mathematical models used in the paper assume a rigid aircraft with movable control surfaces, and ''individual blade'' rotorcraft model. Aerodynamic model includes also a region of higher angles-of-attack including deep stall phenomena. In the present paper, the wing-rock oscillations, and helicopter spin (i.e. intensive spiral glide motion) was studied by means of checking the stability characteristics related to unstable equilibria. Numerical simulations were used to verify the predictions. Wing-rock oscillations were studied to observe the chaos phenomenon in post-stall manoeuvres. Unsteady aerodynamics for prediction of the airfoil loads was included, and the ONERA-type stall model was used.