Extended state space approach for trajectory design in elliptic restricted three-body problem

This paper presents novel methods to provide libration point orbits (LPOs) and invariant manifolds (IMs) associated with libration point orbits in the elliptic restricted three-body problem (ERTBP). First, we introduce an extended autonomous system to describe the ERTBP. By introducing an autonomous system which generates a periodic function and integrating it with the ERTBP which is non-autonomous, we can obtain the extended autonomous system. Then, the center manifold design method which can uniquely provide an LPO in the circular restricted three-body problem is applied to the ERTBP. Next, we present a design method for IMs in the ERTBP by using the local stability characteristics obtained by the state transition matrix along LPOs of the extended system. The proposed design methods are applied and verified for the Earth-Moon L₁ ERTBP. We show various LPOs in the ERTBP by changing design parameters, and IMs associated with a libration point and an LPO.