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Effects of manifold correction methods on chaos indicators
Ma, Da-Zhu1; Long, Zhi-Chao2; Zhu, Yu2
2015-09-01
Source PublicationCELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Volume123Issue:1Pages:45-61
AbstractThe manifold approach of Nacozy et al. (Astrophys Space Sci 14:40-51, 1971), the approximate velocity correction method of Wu et al. (Astron J 133:2643-2653, 2007), and the velocity scaling method of Ma et al. (New Astron 13:216-223, 2008a) are some of the available manifold correction methods. They have been highly successful at maintaining invariant integrals in two-body problems and the Sun-Jupiter-Saturn system. This paper discusses their efficiency on chaos indicators. Because the planar circular restricted three-body problem involves the Jacobi constant and chaotic phenomena, it is preferable to check the numerical performances of manifold corrections. First, we find that a low-order algorithm combined with manifold corrections can greatly improve the precision of the Jacobi constant . Then, numerical experiments show that these manifold correction methods have the same performance in Poincar, sections, Lyapunov exponents, fast Lyapunov indicators, smaller alignment indices, and relative finite time Lyapunov indicators. Moreover, manifold corrections not only allow for the use of larger step sizes compared to low-order algorithms without correction but also save substantial computation time compared to the high-order algorithm RKF7(8). In particular, the velocity scaling method of Ma et al. (2008a) lends itself to practical application in long-term integration.
KeywordManifold Correction Method Numerical Integration Chaos Least Squares Correction Lyapunov Exponents Fli Sali Rli
Subject Area天文和天体物理
WOS HeadingsScience & Technology ; Physical Sciences
DOI10.1007/s10569-015-9628-1
WOS KeywordEFFICIENT ORBIT INTEGRATION ; RESTRICTED 3-BODY PROBLEM ; INDIVIDUAL KEPLER ENERGIES ; PHASE-SPACE STRUCTURE ; MULTIDIMENSIONAL SYSTEMS ; NUMERICAL EXPERIMENTS ; SYMPLECTIC MAPPINGS ; HAMILTONIAN-SYSTEMS ; LYAPUNOV INDICATOR ; PERIODIC-ORBITS
Indexed BySCI
Language英语
WOS Research AreaAstronomy & Astrophysics ; Mathematics
WOS SubjectAstronomy & Astrophysics ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000359161100003
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://libir.pmo.ac.cn/handle/332002/14909
Collection行星科学与深空探测实验室
太阳活动的多波段观测研究团组
Affiliation1.Chinese Acad Sci, Purple Mt Observ, Nanjing 210008, Jiangsu, Peoples R China
2.Hubei Univ Nationalities, Sch Sci, Enshi 445000, Peoples R China
Recommended Citation
GB/T 7714
Ma, Da-Zhu,Long, Zhi-Chao,Zhu, Yu. Effects of manifold correction methods on chaos indicators[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY,2015,123(1):45-61.
APA Ma, Da-Zhu,Long, Zhi-Chao,&Zhu, Yu.(2015).Effects of manifold correction methods on chaos indicators.CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY,123(1),45-61.
MLA Ma, Da-Zhu,et al."Effects of manifold correction methods on chaos indicators".CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY 123.1(2015):45-61.
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