Nonlinear Dynamics of a Space Tethered System in the Elliptic Earth-Moon Restricted Three-Body System
Publication: Journal of Aerospace Engineering
Volume 32, Issue 1
Abstract
This paper focuses on nonlinear oscillation of a space tether system connected to the Moon’s surface, elongating along the Earth-Moon line at and sides respectively. The full nonlinear elongation dynamics of the space tether system were established for a superlong viscoelastic massless tether with a large tip mass. The equilibria and their stabilities were investigated by removing the external force in the established dynamics. The equilibria and the stabilities depend on the elasticity and natural length of the tether, and the dependence is the key to determining the parameters for successful operation of the tether system. The equilibria were also used as reference positions to facilitate dynamic analysis. The method of multiple scales was utilized to obtain the analytical asymptotic solutions to the dynamics. The analytical results agree well with the numerical ones quantitatively and qualitatively in terms of the steady-state magnitudes of the length and the length rate of the tether, as well as the power harvested for a large range of parameters. The detailed investigation reveals that the dynamic responses were affected by three important parameters, namely, the damping, the elasticity, and the original length of the tether. In particular, the increasing damping stabilizes the motion around the expected equilibrium and makes the quasi-periodic motion periodic. It was also indicated that one should design a tether with small rigidity for efficient power generation, but the largest steady-state length should be restricted within prescribed ranges when selecting the rigidity. There is also a compromise between the power output and elastic tension when designing the tether system, i.e., the tether will experience a larger elastic tension for greater harvested power.
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Acknowledgments
This work was supported partially by the National Natural Science Foundations of China (Project Nos. 11302134 and 11272103). The authors thank the reviewers and the editor for their insightful and important comments and constructive suggestions that helped to improve the paper significantly.
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Journal of Aerospace Engineering
Volume 32 • Issue 1 • January 2019
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©2018 American Society of Civil Engineers.
History
Received: Jan 25, 2018
Accepted: Jun 19, 2018
Published online: Nov 14, 2018
Published in print: Jan 1, 2019
Discussion open until: Apr 14, 2019
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