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Comparison of chaos detection methods in the circular restricted three‐body problem
Author(s) -
Racoveanu O.
Publication year - 2014
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.201212110
Subject(s) - lyapunov exponent , chaotic , three body problem , dimension (graph theory) , planar , orbit (dynamics) , correlation dimension , chaos (operating system) , circular orbit , physics , mathematics , order (exchange) , periodic orbits , mathematical analysis , statistical physics , classical mechanics , computer science , pure mathematics , artificial intelligence , fractal dimension , aerospace engineering , fractal , computer graphics (images) , computer security , finance , engineering , economics
In this study, a sample of orbits is considered in the framework of the planar circular restricted three‐body problem. In order to separate ordered from chaotic orbits three numerical methods are compared: the Largest Lyapunov Characteristic Exponent (LLCE) and the Smaller Alignment Index (SALI) provide a fairly good characterization of the chaotic motions, while the computational time required is of the same order; the Correlation Dimension (CD) has the advantage of correctly classifying sticky orbits, but at the expense of a longer computational time. In order to classify a given orbit, any pair of the three methods can be considered, but LLCE and SALI are recommended due to their speed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)