Dynamics modeling and optimization of an asymmetric two-stage torsion pendulum for drag-free testing in the Taiji mission

This paper investigates the dynamics modeling and structural optimization of an asymmetric two-stage torsion pendulum designed for drag-free testing in the Taiji mission. This torsion pendulum serves as a critical experimental apparatus for ground-based verification of drag-free control technology in space gravitational wave detection, addressing limitations in dynamic stability and parameter applicability found in traditional testbeds. Using the Lagrangian dynamics method, the equations of motion relative to inertial space are derived and simplified into a linearized dynamics model under the assumption of small-amplitude oscillations. A state-space approach is further employed to analyze the system’s free oscillation behavior, with equilibrium stability rigorously assessed through eigenvalue analysis. Compared to existing approaches, the proposed model significantly enhances computational efficiency and systematically reveals the influence of key structural parameters on system stability. The study identifies critical parameter ranges essential for ensuring system stability, with optimization results demonstrating that proper design and adjustment of structural parameters can substantially improve system robustness and performance. Numerical simulations validate the accuracy of the proposed models and methods, with the optimization scheme showing clear superiority in enhancing system performance and simplifying experimental design. This work establishes a rigorous theoretical framework for ground-based verification of drag-free control technology. It not only effectively addresses bottlenecks in traditional testbed designs but also offers innovative guidance for the development of experimental systems in the Taiji mission.