Equilibrium configurations of the tethered three-body formation system and their nonlinear dynamics

Abstract

This paper considers nonlinear dynamics of tethered three-body formation system with their centre of mass staying on a circular orbit around the Earth, and applies the theory of space manifold dynamics to deal with the nonlinear dynamical behaviors of the equilibrium configurations of the system. Compared with the classical circular restricted three body system, sixteen equilibrium configurations are obtained globally from the geometry of pseudo-potential energy surface, four of which were omitted in the previous research. The periodic Lyapunov orbits and their invariant manifolds near the hyperbolic equilibria are presented, and an iteration procedure for identifying Lyapunov orbit is proposed based on the differential correction algorithm. The non-transversal intersections between invariant manifolds are addressed to generate homoclinic and heteroclinic trajectories between the Lyapunov orbits. (3,3)-and (2,1)-heteroclinic trajectories from the neighborhood of one collinear equilibrium to that of another one, and (3,6)- and (2,1)-homoclinic trajectories from and to the neighborhood of the same equilibrium, are obtained based on the Poincare mapping technique.