2023/01/20 by Miquel Barcelona, Barcelona, Miquel, Àlex Haro +3 · 1 citation
Engineering · Physics and Astronomy · #37C29 (Primary) 37N05 #37M05 #70F07 (Secondary) #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.2301.08526
openalex publication_date 2023/01/20 · openalex created_date 2023/01/24 · openalex updated_date 2026/07/30
This paper presents methodology for the computation of whole sets of heteroclinic connections between iso-energetic slices of center manifolds of center x center x saddle fixed points of autonomous Hamiltonian systems. It involves: (a) computing Taylor expansions of the center-unstable and center-stable manifolds of the departing and arriving fixed points through the parameterization method, using a new style that uncouples the center part from the hyperbolic one, thus making the fibered structure of the manifolds explicit; (b) uniformly meshing iso-energetic slices of the center manifolds, using a novel strategy that avoids numerical integration of the reduced differential equations and makes an explicit 3D representation of these slices as deformed solid ellipsoids; (c) matching the center-stable and center-unstable manifolds of the departing and arriving points in a Poincaré section. The methodology is applied to obtain the whole set of iso-energetic heteroclinic connections from the center manifold of L2 to the center manifold of L1 in the Earth-Moon circular, spatial Restricted Three-Body Problem, for nine increasing energy levels that reach the appearance of Halo orbits in both L1 and L2. Some comments are made on possible applications to space mission design.