On the Mechanics of Periodic Motion and Control of Tethered Satellite System in Elliptical Orbit

This study investigates the periodic motions of an in-plane tethered satellite system in elliptical orbits. The equations of motion of the system are derived, and periodic solutions are obtained by perturbation method. Then, the stability properties of the periodic solutions are studied. Analysis results show that the periodic solutions become unstable when orbital eccentricity is larger than a critical value. Two classical control schemes are used to convert the unstable periodic motions to stable ones. Stability analyses of periodic solutions of the two controlled systems show that the two control methods can improve the critical value of orbital eccentricity. Numerical simulations of the controlled system are carried out to demonstrate the validity of the stable region.

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Dynamics and Control of a Tethered Satellite System Based on the SDRE Method

International Journal of Aerospace Engineering ◽

10.1155/2016/3610507 ◽

2016 ◽

Vol 2016 ◽

pp. 1-16 ◽

Cited By ~ 3

Author(s):

Yong-Lin Kuo

Keyword(s):

Nonlinear Dynamic ◽

Equations Of Motion ◽

Nonlinear Dynamic Analysis ◽

Satellite System ◽

Convergence Time ◽

Tethered Satellite ◽

Modeling And Control ◽

Tethered Satellite System ◽

Dynamics And Control ◽

And Control

This paper presents the nonlinear dynamic modeling and control of a tethered satellite system (TSS), and the control strategy is based on the state-dependent Riccati equation (SDRE). The TSS is modeled by a two-piece dumbbell model, which leads to a set of five nonlinear coupled ordinary differential equations. Two sets of equations of motion are proposed, which are based on the first satellite and the mass center of the TSS. There are two reasons to formulate the two sets of equations. One is to facilitate their mutual comparison due to the complex formulations. The other is to provide them for different application situations. Based on the proposed models, the nonlinear dynamic analysis is performed by numerical simulations. Besides, to reduce the convergence time of the librations of the TSS, the SDRE control with a prescribed degree of stability is developed, and the illustrative examples validate the proposed approach.

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Study on the stability of Tethered Satellite System

Acta Astronautica ◽

10.1016/j.actaastro.2010.11.015 ◽

2011 ◽

Vol 68 (11-12) ◽

pp. 1964-1972 ◽

Cited By ~ 13

Author(s):

Yong He ◽

Bin Liang ◽

Wenfu Xu

Keyword(s):

Satellite System ◽

Tethered Satellite ◽

Tethered Satellite System ◽

The Stability

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

10.21203/rs.3.rs-297984/v1 ◽

2021 ◽

Author(s):

Xue Zhong ◽

Jie Zhao ◽

Kaiping Yu ◽

Minqiang Xu

Keyword(s):

Periodic Solutions ◽

Fourth Order ◽

Equations Of Motion ◽

Center Of Mass ◽

Elliptical Orbit ◽

Periodic Motions ◽

Nonlinear Stability Analysis ◽

The Third ◽

The Stability ◽

Lyapunov Instability

Abstract 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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Vibroimpact Dynamics of a Tethered Satellite System

Shock and Vibration ◽

10.1155/2017/8748094 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

B. S. Yu ◽

H. Wen

Keyword(s):

Incident Angle ◽

Satellite System ◽

Mapping Method ◽

Cell Mapping ◽

Free Flight ◽

Tethered Satellite ◽

Tethered Satellite System ◽

The Stability ◽

The Moment ◽

The Impact

This paper presents the vibroimpact dynamics of an in-plane tethered subsatellite caused by sudden braking during deployment or retrieval. The full dynamics of the subsatellite are composed of its free-flight and the instantaneous impacts. At the moment of impact, the reflective angle of the subsatellite is envisioned to be equal to its incident angle such that the impact law is obtained. Then, the stability of the periodic vibroimpacts is analyzed using the composite Poincaré map. Further, the vibroimpact responses that do not exceed a specified region are numerically determined via the cell mapping method.

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