Rigid-flexible coupled dynamics and configuration stability of maneuverable space tether net under impact loads

This paper investigates the configuration stability and rigid-flexible coupled dynamics of maneuverable space tether nets under impact loads. To analyze the complex 3D maneuvers of the net, a geometric mechanics framework is developed, incorporating the rigid-flexible coupling between wave propagation in the net and the attitude dynamics of maneuvering satellites attached to its corners. A coordinate-free representation in Lie group is derived for the satellites' attitude dynamics on SO(3). Equilibrium states, modal shapes, and chaotic behavior of the tether net are examined using the geometric Jacobian method, which reveals the coexistence of stiff tether dynamics and slow satellite attitude motions, leading to extreme disparities in time scales and makes numerical analysis challenging by conventional integration schemes. To solve the problem, a structure-preserving integrator is derived to accurately analyze the chaotic behavior of the net over extended periods. Dynamic responses to impact loads are analyzed under two initial conditions: (i) a slack net and (ii) a net tensioned by satellite control forces and torques. Numerical results reveal significant coupling effects between net deformation and satellite attitude motion, and even minor perturbations may lead to chaotic responses of the net indicated by Lyapunov exponents. Moreover, the pre-tension of the net by control forces from satellites can effectively suppress chaotic behaviors, leading to more stable configuration and controlled maneuvering. These findings offer critical insights into configuration stability and dynamics of maneuverable space tether nets, which will enable the effective control strategy development to suppress chaos and enhance net's maneuverability in three-dimensional space.