Rapid and Accurate Methods for Computing Whiskered Tori and their Manifolds in Periodically Perturbed Planar Circular Restricted 3-Body Problems

Autor:	Kumar, Bhanu, Anderson, Rodney L., de la Llave, Rafael
Rok vydání:	2021
Předmět:	Mathematics - Dynamical Systems Astrophysics - Earth and Planetary Astrophysics 70
Druh dokumentu:	Working Paper
DOI:	10.1007/s10569-021-10057-1
Popis:	When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable periodic orbits break up into whiskered tori, with most tori persisting into the perturbed system. In this study, we 1) develop a quasi-Newton method which simultaneously solves for the tori and their center, stable, and unstable directions; 2) implement continuation by both perturbation as well as rotation numbers; 3) compute Fourier-Taylor parameterizations of the stable and unstable manifolds; 4) regularize the equations of motion; and 5) globalize these manifolds. Our methodology improves on efficiency and accuracy compared to prior studies, and applies to a variety of periodic perturbations. We demonstrate the tools near resonances in the planar elliptic RTBP. Comment: 39 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.11100 Zobrazit plný text záznamu View this record from Arxiv