潜艇应急上浮运动稳定性与分叉分析

应用非线性系统运动稳定性与分叉理论和同伦延拓数值计算方法，分析了潜艇应急上浮运动的稳态响应及运动稳定性，并通过潜艇大攻角六自由度运动方程数值积分的动态仿真，验证了所得动态仿真与数值分析结果的一致性.研究了航速、升降舵、方向舵和剩余浮力及其作用位置对潜艇应急上浮运动稳定性的影响.结果表明，潜艇应急上浮运动在左右舷对称的情况下，并不限于垂直面内，可能出现横滚，在某种临界条件下，该运动可能失稳而出现分叉现象，用奇异性与分叉理论对分叉现象进行了分析，为潜艇应急上浮的操纵与控制提供了理论依据.

Stability and Bifurcations Analysis of Submarine during Emergency Ascent

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.