The General Free Gyrostat : Recent Investigations
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.
KeywordsPrincipal Axis Unit Sphere Real Root Great Circle Boundary Line
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