Analysis of satellite attitude motion in a three-body tethered system during deployment via integral manifolds

This paper aims to analyze the impact of unideal end-body configurations on attitude motion during the tether deployment process in a linear three-body tethered system (LTBTS). A main challenge in this process is the resonance between the nutation and spin angles caused by the unideal end-body configurations, leading to severe nutation angle oscillations. These oscillations can result in tether entanglement with the end-bodies or even tether rupture. To address this issue, the deployment model for the LTBTS is first established using the Lagrangian equations, with the end-body attitude described by Eulerian angles. Secondly, the system involves the separation of two subsatellites from the central main satellite in opposite directions. The dynamics response of the deployment process under unideal configuration of end-bodies is investigated. Resonance phenomena in nutation and spin angles are observed due to errors in initial angles/angular velocities, offset errors of tether connection points, and unideal structural characteristics of the satellites. Thirdly, to further understand this resonance, analytical solutions for resonance are derived by transforming the nutation angle equations, and satellite attitude equations are systematically solved via integral manifold methods. Potential resonance issues are mitigated by reducing system asymmetry and minimizing initial disturbances. Finally, the effectiveness of the dynamic analysis is validated through simulations.