The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-21
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the second-order, first-order, time-periodic, or degenerated astrodynamics, respectively.
The general form of the controller is deduced for the typical Hamiltonian system in full feedback and position-only feedback modes, which is successful in changing the hyperbolic equilibrium to an elliptic one.
With the poles assigned at any different positions on imaginary axis, the controlled Hamiltonian system is Lyapunov stable.
The Floquet multiplier is employed to measure the stability of time-dependent Hamiltonian system, because the equilibrium of periodic system may be unstable even though the equilibrium is always elliptic.
One type of periodic orbits is achieved by the resonant conditions of control gains, and another type is making judicious choice in the foundational motions with different frequencies.
The control gains are selected from the viewpoint of both the local and global optimizations on fuel cost.
This controller is applied to some astrodynamics to achieve some interesting conclusions, including stable lissajous orbits in solar sail’s three-body problem and degenerated two-body problem, quasiperiodic formation flying on a J2-perturbed mean circular orbit, and controlled frozen orbits for a spacecraft with a high area-to-mass ratio.
American Psychological Association (APA)
Xu, Ming& Wei, Yan& Liu, Shengli. 2013. The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-446994
Modern Language Association (MLA)
Xu, Ming…[et al.]. The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics. Journal of Applied Mathematics No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-446994
American Medical Association (AMA)
Xu, Ming& Wei, Yan& Liu, Shengli. The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-446994
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446994