Nonlinear Dynamics Model of DFACS with Two Test Masses for Heliocentric Space Gravitational Wave Detection Mission

This paper conducts a comprehensive study on the nonlinear dynamic modeling of the two test masses Drag-Free and Attitude Control System (DFACS) for heliocentric gravitational wave detection missions. First, the composition of DFACS and the modeling assumptions are clarified, key reference frames and their transformation relationships are defined, and an innovative modeling approach based on the formation reference frame is proposed to characterize the geometric constraints among multiple DFACSs. Subsequently, a systemic nonlinear dynamic model is established, encompassing spacecraft relative orbital dynamics, relative attitude dynamics, relative motion and attitude dynamics between spacecraft and test masses, optical assembly rotational dynamics, and the coupled dynamics of spacecraft and test masses. This model provides a comprehensive description of the complex dynamic behavior of DFACS. To validate the model's accuracy, a nonlinear dynamics simulation system was developed, and simulation results confirm the model's precision and applicability. The findings offer model support for the control design, state estimation, and performance optimization of DFACS and provide methodological references for future gravitational wave detection mission modeling efforts