On the Lagrange Stability of the Motion in the Spatial Elliptic Restricted Three-body Problem

Abstract

Abstract We study the Lagrange stability in the spatial elliptic restricted three-body problem. In this study, we essentially use the boundedness of the motion of a small particle with respect to planar coordinates and show that this plays a key role in ensuring the boundedness of the motion in the spatial case. As a result, we obtain the Lagrange stability theorem for an infinitely small particle in the spatial elliptic restricted three-body problem. The proposed approach can then be extended to the case of the general three-body problem.