Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method
Barcelona Poza, Miquel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Haro, Àlex (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Mondelo González, José María (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	This paper presents a methodology for the computation of whole sets of heteroclinic connections between isoenergetic slices of center manifolds of center \times center \times 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 isoenergetic slices of the center manifolds, using a novel strategy that avoids numerical integration of the reduced differential equations and makes an explicit three-dimensional 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 Poincar\'e section. The methodology is applied to obtain the whole set of isoenergetic 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.
Grants:	Agencia Estatal de Investigación PID2020-118281GB-C31 Agencia Estatal de Investigación PID2021-125535NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374 Agencia Estatal de Investigación CEX2020-001084-M European Commission 734557
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Parameterization method ; Heteroclinic connections ; Invariant tori ; Libration point orbits ; RTBP ; Center manifolds
Published in:	SIAM Journal on Applied Dynamical Systems, Vol. 23, Issue 1 (2024) , p. 98-126, ISSN 1536-0040

DOI: 10.1137/23M1547883

Postprint 36 p, 8.3 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles