A Lyapunov Function for Vehicles with Lift and Drag: Stability of Gliding

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.

(6 pages pdf)
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