High-order study of the canard explosion in an aircraft ground dynamics model

Abstract

A planar system has been proposed in the paper Rankin et al. (Nonlinear Dyn 66:681–688, 2011) to understand the canard explosion detected in a 6D aircraft ground dynamics model. A specific feature of this minimal 2D system is a critical manifold with a single fold and an asymptote. In this paper, we provide a high-order analytical prediction (in fact, up to any wanted order) of the canard explosion in this system. Using a nonlinear time transformation method, we are able to approximate not only the critical parameter value, but also the critical manifold in the phase space. The comparison of our theoretical results with the corresponding numerical continuations shows a very good agreement.