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Application of the integral manifold method to the analysis of the spatial motion of a rigid body fixed to a cable

Abstract

We analyze the spatial motion of a rigid body fixed to a cable about its center of mass when the orbital cable system is unrolling. The analysis is based on the integral manifold method, which permits separating the rigid body motion into the slow and fast components. The motion of the rigid body is studied in the case of slow variations in the cable tension force and under the action of various disturbances.We estimate the influence of the static and dynamic asymmetry of the rigid body on its spatial motion about the cable fixation point. An example of the analysis of the rigid body motion when the orbital cable system is unrolling is given for a special program of variations in the cable tension force. The conditions of applicability of the integral manifold method are analyzed.

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Correspondence to Yu. M. Zabolotnov.

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Original Russian Text © Yu.M. Zabolotnov, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 4, pp. 3–18.

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Zabolotnov, Y.M. Application of the integral manifold method to the analysis of the spatial motion of a rigid body fixed to a cable. Mech. Solids 51, 371–384 (2016). https://doi.org/10.3103/S0025654416040014

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  • DOI: https://doi.org/10.3103/S0025654416040014

Keywords

  • orbit
  • cable system
  • rigid body
  • motion about the center of mass
  • integral manifold method
  • precession
  • nutation
  • asymmetry