Effects of manifold correction methods on chaos indicators

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	Effects of manifold correction methods on chaos indicators
	Ma, Da-Zhu 1; Long, Zhi-Chao 2; Zhu, Yu 2
刊名	CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
	2015-09-01
卷号	123 期号:1 页码:45-61
关键词	Manifold correction method Numerical integration Chaos Least squares correction Lyapunov exponents FLI SALI RLI
英文摘要	The 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.
学科主题	天文和天体物理
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Astronomy & Astrophysics ; Mathematics, Interdisciplinary Applications
研究领域[WOS]	Astronomy & Astrophysics ; Mathematics
关键词[WOS]	EFFICIENT ORBIT INTEGRATION ; RESTRICTED 3-BODY PROBLEM ; INDIVIDUAL KEPLER ENERGIES ; PHASE-SPACE STRUCTURE ; MULTIDIMENSIONAL SYSTEMS ; NUMERICAL EXPERIMENTS ; SYMPLECTIC MAPPINGS ; HAMILTONIAN-SYSTEMS ; LYAPUNOV INDICATOR ; PERIODIC-ORBITS
收录类别	SCI
语种	英语
WOS记录号	WOS:000359161100003
内容类型	期刊论文
源URL	[http://libir.pmo.ac.cn/handle/332002/14909]
专题	紫金山天文台_行星科学与深空探测实验室紫金山天文台_太阳活动的多波段观测研究团组
作者单位	1.Chinese Acad Sci, Purple Mt Observ, Nanjing 210008, Jiangsu, Peoples R China 2.Hubei Univ Nationalities, Sch Sci, Enshi 445000, Peoples R China
推荐引用方式 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.