In view of the complex multi-body dynamics problems in the process of spacecraft capture and docking， considering that the low impact docking mechanism （LIDM） is different from the common rigid docking mechanism in the past， the collision force generated in the docking process is far less than the weight of the spacecraft itself， and the docking ring is equipped with a six-dimensional force sensor. Therefore， the collision force generated at the LIDM during the capture process can be detected. The force is equivalent to the time-varying load acting on the center of mass of the docking ring. According to the dynamic modeling method of the second type Lagrange equation， the specific expressions of the dynamic parameters of each component are derived and the multi-body dynamic model of the whole rigid body target system is established， and the output of the dynamic parameters is realized based on MATLAB. The multi-body dynamics model of ADAMS is adopted for simulation verification. The simulation results show that the LIDM capture dynamics model based on Lagrange equation is correct. It lays a foundation for the study of structure optimization and engineering application of space docking mechanism.