A Lyapunov Function for Vehicles with Lift and Drag: Stability
Pradeep Bhatta and Naomi Ehrich Leonard
Proc. 43rd IEEE Conference on Decision and Control,
2004, p. 4101-4106.
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.