Two problems of a torque-free body with a fixed point are considered. In both the body is rigid but for an internal rotor symmetric about its axis of rotation. In one the rotor is driven at a constant angular velocity, in the other the interaction torque between body and rotor has a zero component on the axis of relative rotation. The dynamical equations are shown to have exactly the same structure. A brief literature summary on the torque-free gyrostat is appended.
The Equivalence of Two Classical Problems of Free Spinning Gyrostats
R. E. Roberson
University of California–San Diego, La Jolla, Calif.
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Roberson, R. E. (September 1, 1971). "The Equivalence of Two Classical Problems of Free Spinning Gyrostats." ASME. J. Appl. Mech. September 1971; 38(3): 707–708. https://doi.org/10.1115/1.3408879
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