Bifurcation and Normal Forms of Dive Plane Reversal of Submersible Vehicles

Abstract

The problem of dive plane reversal of submersible vehicles at low speeds is analyzed using bifurcation theory. Simulation and numerical results are supported by a formal analysis procedure which includes calculation of normal forms and invariant resonant terms. It is shown that the primary loss of stability occurs in the form of a pitchfork bifurcation. A feedback control strategy is proposed which guarantees local stability of the nominal equilibrium state across the bifurcation point. Other applications, currently under consideration, for this general approach of bifurcation control are outlined.