Periodic solutions for a dumbbell satellite equation

Liang, Zaitao; Liao, Fangfang

doi:10.1007/s11071-018-4709-9

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…Then the Hamiltonian of the system is obtained using the formulas (21) - (24) and it can be represented as follows…”

Section: Equations Of Motionmentioning

confidence: 99%

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On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

Zhong

Zhao

et al. 2021

Preprint

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This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third and fourth order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coeffcients of the normalized Hamiltonian. Then a nonlinear stability analysis for two periodic solutions is performed in the third and fourth order resonance cases as well as in the nonresonance case.

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“…Then the Hamiltonian of the system is obtained using the formulas (21) - (24) and it can be represented as follows…”

Section: Equations Of Motionmentioning

confidence: 99%

“…the system has a second-order resonance. Moreover, there were several investigations [12,24,25] about the existence and stability of periodic motions of a dumbbell satellite which consist of two point masses connected by a massless rod.…”

Section: Introductionmentioning

confidence: 99%

On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

Zhong

Zhao

et al. 2021

Preprint

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show abstract

“…Then, they further studied the equilibrium points' position and the stability of the trajectory [8]. Liang and Liao [9] proved that the vibration of dumbbell-shaped spacecraft has at least two periodic solutions; in these two periodic solutions, at least one periodic solution is unstable. Those researches above mainly focus on equilibrium and stability analysis, and the mass and flexibility of the flexible beams are not considered in the dynamic model, which cannot meet the requirements of dynamic simulation and controller design.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Robust Control and Active Vibration Suppression of Dumbbell-Shaped Spacecraft

Liu

Fan

et al. 2022

International Journal of Aerospace Engineering

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In this paper, the dynamic modelling of a new configuration spacecraft is investigated. The significance of dumbbell-shaped spacecraft to deep space exploration and the configuration of dumbbell-shaped spacecraft are introduced firstly. Then, the vibration problem of the dumbbell-shaped spacecraft of large-angle attitude maneuver is investigated, and a control program based on the combination of adaptive robust control (ARC) and component synthesis vibration suppression method-seven-section path planning (CSVS-SPP) is proposed. The large-angle attitude maneuver route of the spacecraft, which serves as the reference path, is planned using the CSVS-SPP approach, and the attitude controller is designed using the ARC. This program can effectively reduce the influence of external disturbance and parameter uncertainty on the system performance while completing attitude maneuver and suppress the vibration of the flexible beam during large-angle attitude maneuver. The numerical simulations show the superiority and effectiveness of the proposed ARC+CSVS-SPP.

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On the stability of periodic motions of a two-body system with flexible connection in an elliptical orbit

Xue

Zhao

et al. 2021

Nonlinear Dyn

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Periodic solutions for a dumbbell satellite equation

Cited by 7 publications

References 27 publications

On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

Adaptive Robust Control and Active Vibration Suppression of Dumbbell-Shaped Spacecraft

On the stability of periodic motions of a two-body system with flexible connection in an elliptical orbit

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