Analytical Relationship of Motion States of a Linear Tethered Formation in ontypical Planes

The dynamics of a linear tethered system with three satellites in nontypical plane with orthogonal control force is studied in this paper. An approximate but useful model for a high dimensional nonlinear system is established in the non inertial frame, where three satellites and two space tethers are deemed to be particles and massless springs, respectively. The analytical relationship between the initial state and dynamics and its influence on the critical state of dynamic behavior are derived. A three dimensional dynamic parameter domain is proposed to demonstrate the dynamics in any orbital plane, and verified by numerical simulation. The results show that the analytical calculation is completely consistent with the simulation.