High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem

DOI10.1016/j.cnsns.2021.105691zbMath1477.70012arXiv2109.14800OpenAlexW3119363060MaRDI QIDQ2656792

Rafael de la Llave, Rodney L. Anderson, Bhanu Kumar

Publication date: 16 March 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.14800

zbMATH Keywords

three-body problemmanifoldsresonanceparameterization methodMelnikov

Mathematics Subject Classification ID

Three-body problems (70F07) Invariant manifolds for ordinary differential equations (34C45) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (5)

Numerical Computation of High-Order Expansions of Invariant Manifolds of High-Dimensional Tori ⋮ End-to-end trajectory concept for close exploration of Saturn's inner large moons ⋮ Fully numerical computation of heteroclinic connection families in the spatial three-body problem ⋮ Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem ⋮ Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems

Cites Work

• The parameterization method for invariant manifolds. From rigorous results to effective computations
• Tools to detect structures in dynamical systems using jet transport
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Proof of the Poincaré-Birkhoff fixed point theorem
• Transition state theory with quasi-periodic forcing
• The parameterization method for invariant manifolds. III: Overview and applications
• Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications
• Stability and Chaos in Celestial Mechanics
• Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

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