Modal and dynamic analysis of a tether for a nonequatorial space elevator

To study the fundamental dynamics of the nonequatorial space elevator, a universal modeling strategy is presented, which applies to any anchored latitude. The equations of motion are established on the basis of the lumped mass model of the tether coupled with an interactional elevator. The relationship between the maximum anchored latitude and the design stress is studied by solving the equilibrium equations. The linearized equations of motion are formulated on the basis of the static equilibrium positions to analyze the modal of the tether. Numerical simulation is performed to analyze the properties of the system with a moving elevator. The results show that a positive correlation arises between the maximum anchored latitudes and the design stress. The fundamental modal and the fifth-order modal are associated with the latitudes considering the frequency and modal shape, respectively. Furthermore, the asymptotically stable characteristics are verified. The amplitude of the residual oscillation is magnified with an increase in the anchored latitude or the elevator speed.