Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method

DOI10.1088/1361-6544/aa7737zbMath1400.70028OpenAlexW2673300709MaRDI QIDQ5350515

Josep J. Masdemont, Unnamed Author, Baptiste Le Bihan, Gerard Gomez

Publication date: 1 September 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: http://oatao.univ-toulouse.fr/21183/1/LeBihan_21183.pdf

zbMATH Keywords

invariant manifoldsSun-Earth-Moon systemparameterization methodquasi-periodic systems

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (5)

The vicinity of Earth-Moon \(L_1\) and \(L_2\) in the Hill restricted 4-body problem ⋮ Invariant manifolds near \(L_1\) and \(L_2\) in the quasi-bicircular problem ⋮ The vicinity of the Earth-Moon \(L_1\) point in the bicircular problem ⋮ Global analysis of direct transfers from lunar orbits to Sun-Earth libration point regimes ⋮ Families of Halo-like invariant tori around \(L_2\) in the Earth-Moon bicircular problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The parameterization method for invariant manifolds. From rigorous results to effective computations
• Efficient invariant-manifold, low-thrust planar trajectories to the Moon
• Intersecting invariant manifolds in spatial restricted three-body problems: design and optimization of Earth-to-halo transfers in the Sun-Earth-Moon scenario
• On the high order approximation of the centre manifold for ODEs
• Effective computation of the dynamics around a two-dimensional torus of a Hamiltonian system
• A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
• A note on weak stability boundaries
• On the persistence of lower dimensional invariant tori under quasi-periodic perturbations
• Preliminary study on the translunar Halo orbits of the real Earth-Moon system
• On the vertical families of two-dimensional tori near the triangular points of the bicircular problem
• Sun-perturbed Earth-to-Moon transfers with low energy and moderate flight time
• Dynamics in the center manifold of the collinear points of the restricted three-body problem
• Dynamics in the center manifold around \(L_2\) in the quasi-bicircular problem
• The parameterization method for invariant manifolds. III: Overview and applications
• Dynamics and Mission Design Near Libration Points
• Weak Stability Boundary and Invariant Manifolds
• Parameterization Method for Computing Quasi-periodic Reducible Normally Hyperbolic Invariant Tori
• Analytic construction of periodic orbits about the collinear points
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• The parameterization method for invariant manifolds II: regularity with respect to parameters
• Dynamics and Mission Design Near Libration Points
• Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
• High-order expansions of invariant manifolds of libration point orbits with applications to mission design
• Connecting orbits and invariant manifolds in the spatial restricted three-body problem
• A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system
• The dynamics around the collinear equilibrium points of the RTBP
• Low energy transfer to the Moon

This page was built for publication: Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method