SOLUTION BRANCHING AND DIVE PLANE REVERSAL OF SUBMARINES AT LOW-SPEEDS

The problem of multiple steady-state solutions in the dive plane of su bmarines under depth control at low speeds is analyzed. This phenomeno n occurs regardless of the particular means used for depth control, ma nual or automatic, and linear or nonlinear. It is shown that the prima ry bifurcation parameter is a Froude-like number based on the vehicle speed and metacentric height. Generic solution branching is shown to o ccur below a critical Froude number. Singularity theory techniques are employed to quantify the effects that various vehicle geometric prope rties and hydrodynamic characteristics have on steady-state motion. It is demonstrated that a comprehensive bifurcation study provides a sys tematic and effective way of predicting the phenomenon of dive plane r eversal at low speeds. A complete characterization of the parameters i n the problem, both in deep water and at periscope depth, is achieved through the organizing center of the pitchfork singularity.