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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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