In Arnold's Mathematical Methods of Classical Mechanics, 2nd ed., p. 145, he considers a rigid body with no external torque rotating about a fixed point O. He shows that the stationary solutions of the Euler equations (for the angular momentum vector in the body's co-rotating coordinate system) that correspond to the largest and smallest principal axis are Liapunov stable. This I understand. Then he claims that "stationary rotations of the body around the largest and smallest principal axes" are not Liapunov stable. This is left as an exercise to the reader, which I cannot solve.
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Qmechanic
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Axel Boldt
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Not OP's question but for the Dzhanibekov effect, the tennis racquet theorem, and the intermediate axis theorem, see e.g. http://physics.stackexchange.com/q/17504/2451, http://physics.stackexchange.com/q/34364/2451, http://physics.stackexchange.com/q/67957/2451, and links therein. – Qmechanic May 01 '17 at 15:27
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Right. He probably meant not stable around the intermediate axis. You can try it with say a book, and it's proven in a number of class mechanics books. – Bob Bee May 02 '17 at 03:31