Detailed Analysis on Barrier Surfaces Separating Regions of Possible and Impossible Motion in the Circular Restricted Three-Body Problem

Abstract

The zero-velocity surface has been one of the most fundamental structures in many dynamical systems including gravitational N-body problems, chemical reaction models, and mechanical systems. It plays the role of a barrier placing bounds on the motion and energetically separating the regions of possible and impossible motion. Our previous work deduced that states associated with the barrier structures globally minimize an energy function. This global energy minimization property has been useful in identifying a new barrier structure in addition to the zero-velocity surface. The present paper extends the analysis method and explores the existence of other barrier surfaces in a circular restricted three-body problem. The comprehensive search in all the possible position, position-velocity, and velocity spaces unveils two novel barrier surfaces in addition to the already known barrier surfaces. The dynamically distinct characteristics of the newly identified barrier surfaces are analytically presented.