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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Identification Number :||https://doi.org/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 :||23 Sep 2013 19:09|
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