Abstract: The Tuned Rotary Inertia Damper (abbreviated as TRID) control system for pendular vibration suppression is proposed based on passive tuning and absorbing control principles. Parameter optimization and control efficiency analysis subject to point source excitations are carried out in this paper. Firstly, equation of motion for the suspensory structure in arbitrary motion is established based on Lagrangian principles, and the principle of TRID control system is presented. Secondly, numerical simulations of TRID control for two types of suspensory structural motions, planar pendular vibration and spatial cone motion, are conducted. Then, optimal parameters and impact factors are summarized. Lastly, the abnormal phenomenon in structural response in the resonant zone is studied. The combined TRID-TMD control system for suppressing the ideal cone motion mode is proposed to overcome the limitations of single TRID control system, and the effectiveness and feasibility are validated through numerical analysis. The research results of this paper establish partial theoretical foundation for anti-swaying of hook structures of large-scale heavy-lifting and pipeline-paving ships.