On the concept of conditional barrier structures in the planar circular restricted three-body problem

The zero velocity curve and the zero velocity surface are examples of barrier structures that energetically separate the regions of possible and impossible motion. Our recent work deduced that states associated with the barrier structures globally minimize an energy function. The present paper explores the role of local energy minimizers in the planar circular restricted three-body problem. It is demonstrated that a structure, with which local energy minimizers associate, also plays the role of a barrier within a conditioned range that the local minimizers are regarded as the global minimizers. Such conditional barrier structures robustly exist and regulate the motion even in the high-energy regime, where the zero velocity curve ceases to exist.