K. Uldall Kristiansen,P L Palmer & M. Roberts
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.
Paper: Tethered Satellites
Ref: Kristiansen, K. Uldall, Palmer, P.L. & Roberts, R.M., SIAM J on Applied Mathematics, 10, No 3, pp. 1042-1069, 2011.