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A Unification of Models of Tethered Satellites

Kristiansen, KU, Palmer, P and Roberts, M (2011) A Unification of Models of Tethered Satellites SIAM J APPL DYN SYST, 10 (3). pp. 1042-1069.

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In this paper, different conservative models of tethered satellites are related mathematically, and it is established in what limit they may provide useful insight into the underlying dynamics. An infinite dimensional model is linked to a finite dimensional model, the slack-spring model, through a conjecture on the singular perturbation of tether thickness. The slack-spring model is then naturally related to a billiard model in the limit of an inextensible spring. Next, the motion of a dumbbell model, which is lowest in the hierarchy of models, is identified within the motion of the billiard model through a theorem on the existence of invariant curves by exploiting Moser's twist map theorem. Finally, numerical computations provide insight into the dynamics of the billiard model.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors : Kristiansen, KU, Palmer, P and Roberts, M
Date : 2011
DOI : 10.1137/090779887
Uncontrolled Keywords : singular perturbed systems, mathematical modeling, tethered satellites, billiards, DYNAMICS, OSCILLATIONS, STABILITY, SYSTEMS
Additional Information : Copyright 2011 Society for Industrial and Applied Mathematics
Depositing User : Symplectic Elements
Date Deposited : 14 Mar 2012 12:13
Last Modified : 29 Aug 2019 12:54

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