Although the equations describing the longitudinal motions of underwater vehicles are typically nonlinear, the linearized equations are still employed to design the depth controller by the traditional analysis methods in engineering for the sake of simplicity. The reduction of the nonlinearity loses the dynamics near the singular points, which may be responsible for the sudden climb or dive. The nonlinear systems limited in the longitudinal plane of the underwater vehicles are analyzed on center manifold through the bifurcation theory. It focuses on the case that single zero root in Jacobi matrix occurs at equilibrium points corresponding to nominal trajectory with varied angles of the elevator or the direction change of the flows. The center manifolds are calculated and one-dimensional bifurcation equations on the center manifolds are obtained and analyzed. Based on the transcritical bifurcation diagram, we have found the mechanism of the attitude stability loss as well as the abnormal trajectory of autonomous underwater vehicles. It gives good explainations to the practical climbing jump and diving fall and delivers the theoretical tools to design the controller and to design dynamics. Numerical simulation verifies the results.

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