NONLINEAR STUDIES OF DYNAMIC STABILITY OF SUBMARINES IN THE DIVE PLANE

The problem of dynamic stability of submersible vehicles in the dive p lane is examined utilizing linear and nonlinear methods. Local bifurca tions are studied with the means of perturbation and linearization tec hniques. The primary mechanism of loss of stability is identified in t he form of generic Hopf bifurcations to periodic solutions. Stability of the resulting limit cycles is established using center manifold app roximations and integral averaging. Particular emphasis is placed on a nalyzing the effects of the quadratic drag forces due to their crucial role on stability of periodic solutions. The methods described in thi s work could lead to techniques resulting in enlargement of the submer ged operational envelope of a vehicle.