Stability and bifurcation analysis for longitude motion of a supercavitating vehicle

Nonlinear dynamics theory and bifurcation theory were adopted to study stability and bifurcation phenomenon of supercavitating vehicles. With least-squares method, simplified dynamics models for longitude of supercavitating vehicle were obtained. Using multiple scale perturbation techniques, the nonlinear differential equations for longitude motion of supercavitating vehicle were solved, the stability of this solution was analyzed, and the necessary conditions were obtained. Calculation of the bifurcation response equation was use to get the bifurcation set near the stable solution. Numerical results reveal the unstable phenomenon of supercavitating vehicles in longitude motion from theoretical perspective, and provide theoretical basis for designing control system.