Abstract: The influence coefficient of flexible coupling in dynamic modeling of flexible spacecraft is an important mechanical concept in dynamic modeling, which reflects the elastic vibration effect of spacecraft attitude and orbit motion and flexible accessories. The equivalent relationship between the influence coefficients of the flexible coupling, i.e. the inertial completeness criterion, is an important basis for the reduction of the order and the mode truncation of the dynamic model of the flexible spacecraft. Taking the center rigid body spacecraft with flexible appendages as the research object, the constrained mode and unconstrained mode are used to describe the structural deformation of flexible appendages, and the dynamic model of flexible spacecraft is established by using Euler Lagrange equation. Based on the research results of Hughes, the unconstrained modal identity of flexible spacecraft and the inertial completeness criterion for dynamic model reduction are proved and applied. The relationship between the inertia of two dynamic models is discussed, and the inertial completeness criterion of unconstrained mode is derived by using the inertial completeness criterion of constrained mode. Finally, the numerical simulation of the flexible spacecraft model composed of the central rigid body with two side solar panels and one side solar panels is carried out to find out the unconstrained mode translational coupling coefficient of the flexible appendages. The change of the unconstrained mode eigenvalue and translational coupling coefficient with the rigid flexible mass ratio is analyzed, and the mass characteristic identity of the unconstrained mode inertial completeness criterion is used to test the model The flexible spacecraft model is tested.