Canard cycles in aircraft ground dynamics

The loss of lateral stability of an aircraft turning on the ground is associated with a rapid transition from small-amplitude oscillations to large-amplitude relaxation oscillations over a very small parameter range. This phenomenon is shown to be associated with a canard explosion in an industry-tested model of aircraft ground dynamics, where the longitudinal velocity of the aircraft acts as a slow variable of the system. The associated family of canard orbits is identified and the canard explosion is shown to be directly related to the successive saturation of tyre forces at the two main landing gears. We present a canonical two-dimensional slow-fast vector field model that captures the key features of this type of canard explosion; it differs from the canard explosion in the archetypal Van der Pol system in terms of the shape of the associated critical manifold.