Abstract:In this paper the motion stability and bifurcation theory of a nonlinear system and the principles of continuation based on homotopy techniques were applied to stable state response and motion stability analysis of submarines during emergency ascent. The stability analysis results were verified by simulations using direct numerical integrations of the fully nonlinear, coupled six degreesoffreedom equations of motion for the submarine. The control surface deflections, excess buoyancy and speed effects on the stability of the submarine during emergency ascent show that emergency rising motion is not always restricted to the vertical plane even under port/starboard symmetric conditions. Complicated outofplane motions may be generated, and the submarine may lose stability under some critical conditions. The singularity and bifurcation theory was used to explain the mechanism for these phenomena, providing a theoretical basis for maneuvering and controlling submarine during emergency ascent.