Integrability of close encounters in the spatial restricted three-body problem

Abstract

We extend to the spatial case a technique of integration of the close encounters formulated by Tullio Levi-Civita for the planar restricted three-body problem. We consider the Hamiltonian introduced in the Kustaanheimo-Stiefel regularization and construct a complete integral of the related Hamilton-Jacobi equation by means of a series convergent in a neighbourhood of the collisions with the primary or secondary body.

Preprint version submitted for publication in Communications in Contemporary Mathematics, DOI: 10.1142/S0219199721500401,copyright World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ccm

References in corpus (1)

• A study of temporary captures and collisions in the Circular Restricted Three-Body Problem with normalizations of the Levi-Civita Hamiltonian

Cited by in corpus (1)

• Transits close to the Lagrangian solutions $L_1,L_2$ in the Elliptic Restricted Three-body Problem