Abstract: The nonlinear dynamic control equation of a flexible multi-body system with definite moving attitude is discussed. The motion of the aircraft in space is regarded as known and the influence of the flexible structural members in the aircraft on the motion and attitude of the aircraft is analyzed. By means of a hypothetical mode, the deformation of flexible members is regarded as composed of the line element vibration in the axial direction of rectangular coordinates in space. According to Kane’s method in dynamics, a dynamic equation is established, which contains the structural stiffness matrix that represents the elastic deformation and the geometric stiffness matrix that represents the nonlinear deformation of the deformed body. Through simplification the dynamic equation of the influence of the planarflexible body with a windsurfboard structure on the spacecraft motion is obtained. The numerical solution for this kind of equation can be realized by a computer.

Key words: flexible body, line element vibration, dynamic equation, Kanes method