中文摘要：

为研究潜艇垂直面操纵运动的稳定性，针对潜艇非线性动力学模型，采用分叉与突变理论分析失稳现象发生的机理．利用中心流形理论将潜艇运动方程约化到包含原系统全部动力学特性的低维系统，对静态分叉引发的状态突变进行定性分析，并通过数值仿真进行验证．结果表明，潜艇垂直面运动模型在强机动下将发生极限点分叉并导致系统状态在分叉点处产生突变．此现象揭示了潜艇动力学模型中非线性项的影响，有助于潜艇操纵控制系统的设计．

英文摘要：

To study the stability of submarine maneuvering motion in dive plane, the bifurcation and catastrophe theory methodology was adopted to analyze the instability mechanism of the nonlinear submarine dynamic model. The motion equations of submarine were reduced to the lower dimension system which contained all dynamic properties of original system by utilizing center manifold theory. The status catastrophe caused by static bifurcation was discussed. Numerical simulation results validate that the transcritical bifurcation occurres in submarine operating motion with high-speed and large rudder angle in dive plane. These catastrophe phenomena reveal the effect of nonlinear terms in submarine dynamic model , which are of benefit to submarine maneuvering control system designing.