The generalized Pfaff-Birkhoff-dAlembert principle and the form invariance of the generalized Birkhoff s equations under the infinitesimal transformation of group are studied. The criterion of the form invariance is given and the Noether conserved quantity and a new conserved quantity are obtained by the invariance.

The mathematical models of docking dynamics in the process of capture are established for two spacecrafts with inner guide petal peripheral docking mechanisms. The docking system is simplified into the initiative spacecraft, the passive spacecraft and the initiative capture annulus. Compared with the spacecraft, the initiative capture annulus has much less mass. So its mass and moment of inertia are omitted in the process of modeling. Only its geometry character is considered. The inaccurate factor in introducing insert quantity is eliminated through the way of calculating contact force with restriction equation. The docking strategy and design parameters of buffer, such as relative displacement, velocity and rotation of docking mechanisms and displacement and rotation of buffer, interacting force are obtained through simulation calculation. Thus docking dynamics can be understood better and an important reference is provided for the design of buffer and docking mechanism.