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

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenv...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 97; p. 105691
Main Authors: Kumar, Bhanu, Anderson, Rodney L., de la Llave, Rafael
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.06.2021
Elsevier Science Ltd
Subjects:
Algorithms
Approximation
Eigenvectors
Europa
Intersections
Invariants
Lagrangian equilibrium points
Libration
Manifolds
Melnikov
Mission planning
Numerical integration
Object recognition
Orbits
Parameterization
Parameterization method
Resonance
Space missions
Taylor series
Three-body problem
Topological manifolds
Trajectories
Manifolds
Melnikov
Resonance
Parameterization method
Three-body problem
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approximations of the manifolds. Since such approximations are not accurate except very close to the base invariant object, this requires large amounts of numerical integration to globalize the manifolds and locate intersections. In this paper, we study hyperbolic resonant periodic orbits in the planar circular restricted 3-body problem, and transfer trajectories between them, by: 1) determining where to search for resonant periodic orbits; 2) developing and implementing a parameterization method for accurate computation of their invariant manifolds as Taylor series; and 3) developing a procedure to compute intersections of the computed stable and unstable manifolds. We develop and implement algorithms that accomplish these three goals, and demonstrate their application to the problem of transferring between resonances in the Jupiter-Europa system.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2021.105691