Bifurcation and chaos of tethered satellite system in elliptic orbit

This paper investigates the nonlinear dynamic characteristics of tethered satellite systems operating in elliptic orbits, focusing on bifurcation and chaotic behaviors. A tethered satellite consists of two spacecraft connected by a flexible tether, offering unique motion properties with applications in orbit control, space debris removal, and energy harvesting. Based on the Lagrangian method, the paper establishes a dynamic model considering both in-plane and out-of-plane coupled motions, and explores the influence of orbital eccentricity on system stability. Using bifurcation diagrams, maximum Lyapunov exponents, and Poincaré maps, the study reveals the transition from quasi-periodic to chaotic motion as system parameters vary. It finds that the chaotic regions strongly depend on initial conditions and orbital eccentricity. For high-dimensional state space analysis, a novel four-dimensional Poincaré mapping method with “space+color” visualization is introduced, which intuitively captures the spatial structure of the system’s dynamics and distinguishes between quasi-periodic and chaotic trajectories. Results show that: (1) systems on high-eccentricity orbits are more prone to chaos, and near-circular orbits are preferable; (2) keeping the out-of-plane angle near zero simplifies control and suppresses complex coupling effects; (3) maintaining unidirectional rotation of the in-plane angle can avoid chaotic behavior. This study enriches the understanding of tethered satellite dynamics in elliptic orbits and provides theoretical insights and practical strategies for mission planning and chaos suppression in engineering applications.