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In this paper,a new kind of flexible cone composed of the thin-walled plates based on space probecone docking mechanism for small-sized spacecraft is presented.The theoretical model of docking impact dynamics,which takes into account the additional stiffness terms,is derived based on Lagrange Analytical Mechanics theory and Hertz contact theory.Finite element method is employed for the discretization of the thin-walled plate.The results show that the traditional dynamic model without considering the additional stiffness terms will be difficult to reach steady state.The method proposed in this paper can correctly predict the dynamic behavior of the system.