 Dynamics in the controlled center manifolds by Hamiltonian structure-preserving stabilizationTong Luo, Ming Xu and Yunfeng Dong Chaos, Solitons & Fractals, 2018, vol. 112, issue C, 149-158 Abstract: A two-dimensional hyperbolic Hamiltonian system can be linearly stabilized by a Hamiltonian structure-preserving controller. A linear symplectic transformation and the Lie series method can successfully normalize the expanded Hamiltonian function around a controlled stable equilibrium point, then the dynamics in the controlled center manifolds of which can be described by a Poincaré section. With the implement of the inverse transformation of the Lie series, the analytical results of the controlled manifolds can be obtained. Applying normalization and analytical calculation to planar solar sail three-body problem, we can get the normal form of the corresponding Hamiltonian function and trajectory around the chosen equilibrium point by analytical results. Finally, typical KAM theory is used to analyze the nonlinear stability of the controlled equilibrium point, and the stable region of the control gains are given by numerical calculation. Keywords: Center manifolds; Lie series; Normal form; KAM stability; Hamiltonian structure-preserving control; Solar sail three-body problem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:112:y:2018:i:c:p:149-158 DOI: 10.1016/j.chaos.2018.05.006 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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