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 correspond to a canard explosion, which is known to be an important feature of systems that exhibit a separation of time scales. While the industry-tested model of aircraft ground dynamics that we consider does not feature an explicit splitting of time scales, we show that, locally near the transition from stable turning to laterally unstable behaviour, the forward speed of the aircraft acts as a slow variable. The associated family of canard cycles 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 archetypical Van der Pol system in terms of the shape of the associated critical manifold.