The General Free Gyrostat : Recent Investigations

  • Robert E. Roberson
  • Pierre Y. Willems
  • Jens Wittenburg
Part of the International Centre for Mechanical Sciences book series (CISM, volume 102)


In two previous lectures the gyroscopic system called gyrostat has been presented and two kinds of problem connected with the case of torque-free motion have been discussed. In the following we will consider the torque-free motion of the unsymmetrical gyrostat with a rotor which is not aligned with a principal axis nor does it lie in the plane of two principal axes. Since the polhodes, i.e. the intersection lines of the energy and the angular momentum ellipsoids allow a simple visualization of the motion we will start with a discussion of some interesting problems concerning the polhodes. In particular, we return to the so-called osculation problem the solution of which provides the possible states of permanent rotation. The condition for such a state of motion has already been developed.


Principal Axis Unit Sphere Real Root Great Circle Boundary Line 
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Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • Robert E. Roberson
    • 1
  • Pierre Y. Willems
    • 2
  • Jens Wittenburg
    • 3
  1. 1.Departement of Aerospace and Mechanical Engineering SciencesUniversity of CaliforniaSan DiegoUSA
  2. 2.Institut de MécaniqueUniversité de LouvainBelgium
  3. 3.Lehrstuhl und Institut für MechanikTechnische Hochschule HannoverGermany

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