Three dimensional dynamics of a flexible Motorised Momentum Exchange Tether

N.A. Ismail, M.P. Cartmell

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)
260 Downloads (Pure)


This paper presents a new flexural model for the three dimensional dynamics of the Motorised Momentum Exchange Tether (MMET) concept. This study has uncovered the relationships between planar and nonplanar motions, and the effect of the coupling between these two parameters on pragmatic circular and elliptical orbits. The tether sub-spans are modelled as stiffened strings governed by partial differential equations of motion, with specific boundary conditions. The tether sub-spans are flexible and elastic, thereby allowing three dimensional displacements. The boundary conditions lead to a specific frequency equation and the eigenvalues from this provide the natural frequencies of the orbiting flexible motorised tether when static, accelerating in monotonic spin, and at terminal angular velocity. A rotation transformation matrix has been utilised to get the position vectors of the system׳s components in an assumed inertial frame. Spatio-temporal coordinates are transformed to modal coordinates before applying Lagrange׳s equations, and pre-selected linear modes are included to generate the equations of motion. The equations of motion contain inertial nonlinearities which are essentially of cubic order, and these show the potential for intricate intermodal coupling effects. A simulation of planar and non-planar motions has been undertaken and the differences in the modal responses, for both motions, and between the rigid body and flexible models are highlighted and discussed.
Original languageEnglish
Pages (from-to)87-102
Number of pages16
JournalActa Astronautica
Early online date17 Dec 2015
Publication statusPublished - 30 Apr 2016


  • space tether
  • motorized momentum exchange tether
  • tether dynamics
  • space tethered system
  • dynamical analysis
  • flexible tether
  • flexural model
  • nonplanar motions
  • planar motions


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