High-Order Resonant Orbit Manifold Expansions For Mission Design In the Planar Circular Restricted 3-Body Problem
| Autor: | Rodney L. Anderson, Rafael de la Llave, Bhanu Kumar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Computer science
Orbital resonance FOS: Physical sciences Lagrangian point Dynamical Systems (math.DS) 01 natural sciences 010305 fluids & plasmas symbols.namesake 0103 physical sciences FOS: Mathematics Taylor series Invariant (mathematics) Mathematics - Dynamical Systems 010306 general physics Eigenvalues and eigenvectors Earth and Planetary Astrophysics (astro-ph.EP) Numerical Analysis Applied Mathematics Mathematical analysis Three-body problem Manifold Numerical integration Modeling and Simulation symbols Astrophysics::Earth and Planetary Astrophysics 37C27 37C29 37M21 70M20 Astrophysics - Earth and Planetary Astrophysics |
| Popis: | 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. 17 pages, 8 figures |
| Databáze: | OpenAIRE |
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