A Lyapunov function for vehicles with lift and drag: stability of gliding

The energy of a mechanical system naturally provides a Lyapunov function to prove stability of steady motions. This is no longer the case when the system is subject to aerodynamic forces. We derive a Lyapunov function to prove stability of steady, gliding motions for vehicles subject to lift and drag. We make use of a conservation law derived by Lanchester in his original phugoid mode model and in so doing prove conditions under which Lanchester´s simplifying assumptions are valid. We apply the results to prove stability and estimate the region of attraction for an underwater glider.