A Unification of Models of Tethered Satellites

K. Uldall Kristiansen, P. Palmer, M. Roberts

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1042-1069
Number of pages28
JournalSiam Journal on Applied Dynamical Systems
Issue number3
Publication statusPublished - 2011


  • singular perturbed systems
  • mathematical modeling
  • tethered satellites
  • billiards


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