TY - JOUR
T1 - Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method
AU - Barcelona Poza, Miquel
AU - Haro, Àlex
AU - Mondelo, Josep Maria
N1 - Publisher Copyright:
© 2024 Society for Industrial and Applied Mathematics.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Parameterization method
KW - Heteroclinic connections
KW - Invariant tori
KW - Libration point orbits
KW - RTBP
KW - Center manifolds
UR - http://www.scopus.com/inward/record.url?scp=85183924571&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/75a25f78-8ba7-3cd8-8742-e8d7d93608a4/
U2 - 10.1137/23M1547883
DO - 10.1137/23M1547883
M3 - Article
SN - 1536-0040
VL - 23
SP - 98
EP - 126
JO - SIAM Journal on Applied Dynamical Systems
JF - SIAM Journal on Applied Dynamical Systems
IS - 1
ER -