Celestial Mechanics and Dynamical Astronomy

, Volume 113, Issue 2, pp 235–254 | Cite as

Numerical modelling of elastic space tethers

  • K. Uldall Kristiansen
  • P. L. Palmer
  • R. M. Roberts
Original Article


In this paper the importance of the ill-posedness of the classical, non-dissipative massive tether model on an orbiting tether system is studied numerically. The computations document that via the regularisation of bending resistance a more reliable numerical integrator can be produced. Furthermore, the numerical experiments of an orbiting tether system show that bending may introduce significant forces in some regions of phase space. Finally, numerical evidence for the existence of an almost invariant slow manifold of the singularly perturbed, regularised, non-dissipative massive tether model is provided. It is also shown that on the slow manifold the dynamics of the satellites are well-approximated by the finite dimensional slack-spring model.


Tethered satellites Symplectic numerical integration Mathematical modelling Regularized model Bending effects 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • K. Uldall Kristiansen
    • 1
  • P. L. Palmer
    • 2
  • R. M. Roberts
    • 3
  1. 1.Technical University of DenmarkLyngbyDenmark
  2. 2.Surrey Space CentreUniversity of SurreyGuildfordUK
  3. 3.Department of MathematicsUniversity of SurreyGuildfordUK

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