Applications of lagrangian coherent structures to expression of invariant manifolds in astrodynamics

Rui Qi; Shi Jie Xu

doi:10.1007/s10509-014-1819-9

Applications of lagrangian coherent structures to expression of invariant manifolds in astrodynamics

Rui Qi^*, Shi Jie Xu

^*Corresponding author for this work

School of Aerospace Engineering

Beihang University

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

This paper investigates the relationship between invariant manifold and Lagrangian coherent structure (LCS) in dynamical systems. LCS is defined as the ridge of finite-time Lyapunov exponent (FTLE) field, and is proving to be excellent platform for studies of stable and unstable manifold in flows with arbitrary time dependence. In this study, the LCS tool is applied to autonomous systems, simple pendulum and planar circular restricted three-body problem (PCR3BP), and also non-autonomous ones, double-gyre flow and bicircular problem (BCP). A comparison between LCS and invariant manifold is presented.

Original language	English
Pages (from-to)	125-133
Number of pages	9
Journal	Astrophysics and Space Science
Volume	351
Issue number	1
DOIs	https://doi.org/10.1007/s10509-014-1819-9
Publication status	Published - May 2014

Keywords

Dynamical system
Invariant manifold
Lagrangian coherent structure
Libration point orbit

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10.1007/s10509-014-1819-9

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abstract = "This paper investigates the relationship between invariant manifold and Lagrangian coherent structure (LCS) in dynamical systems. LCS is defined as the ridge of finite-time Lyapunov exponent (FTLE) field, and is proving to be excellent platform for studies of stable and unstable manifold in flows with arbitrary time dependence. In this study, the LCS tool is applied to autonomous systems, simple pendulum and planar circular restricted three-body problem (PCR3BP), and also non-autonomous ones, double-gyre flow and bicircular problem (BCP). A comparison between LCS and invariant manifold is presented.",

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AB - This paper investigates the relationship between invariant manifold and Lagrangian coherent structure (LCS) in dynamical systems. LCS is defined as the ridge of finite-time Lyapunov exponent (FTLE) field, and is proving to be excellent platform for studies of stable and unstable manifold in flows with arbitrary time dependence. In this study, the LCS tool is applied to autonomous systems, simple pendulum and planar circular restricted three-body problem (PCR3BP), and also non-autonomous ones, double-gyre flow and bicircular problem (BCP). A comparison between LCS and invariant manifold is presented.

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KW - Invariant manifold

KW - Lagrangian coherent structure

KW - Libration point orbit

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Applications of lagrangian coherent structures to expression of invariant manifolds in astrodynamics

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