A nonlinear study of open loop dynamic stability of submersible vehicles in the dive plane

Abstract

This thesis presents a comprehensive nonlinear study of straight line stability of motion of submersibles in the dive plane under open loop conditions. A systematic perturbation analysis demonstrates that the effects of surge on heave/pitch are small and can be neglected. Primary loss of stability is shown to occur in the form of Hopf bifurcations to periodic solutions. Analysis of the periodic solutions that result from these Hopf bifurcations was accomplished through Taylor expansions, up to third order, of the equations of motion. A consistent approximation, utilizing the generalized gradient, is used to study the non-analytic quadratic cross flow integral drag terms. The results indicate that loss of stability occurs always in the form of supercritical Hopf bifurcations with stable limit cycles. It is shown that this is mainly due to the stabilizing effect of the drag forces at high angles of attack