Fold Catastrophe Characteristics of Pitch Supercavitating Vehicle at Certain Depth

摘要

A fold catastrophe problem for supercavitating vehicle at certain depth is considered, where the dynamic model of supercavitating vehicle is studied in longitute plane. The dynamic model possesses plentiful nonlinear characteristics caused by the planning force. Least-squares method is exploited to simplify the expression of planning force to analyze the catastrophe characteristics. The splitting lemma is utilized to transform diturbance Hamilton system into nominal Hamilton system of supercavitating vehicle. Then the fold catastrophe model is established. Multi-scale method is exploited to sovle the perturbance equation of pich motion of the vehicle based on bifurcation theory. Bifurcation set is determined and necessary condition of stable is developed.