Abstract
The permanentrotations around the vertical of an asymmetric heavy rigid body with a fixed point are examined. The stability of the rotations are investigated on the basis of stability theorems for a Hamiltonian system in the nonresonance case /1,2/ and under third- and fourth-order resonances /3/. It is shown that in the nonresonance case the stability of all, except, perhaps, a finite number, permanent rotations is determined by the first approximation. Stability and instability conditions for resonance rotations are found. Stability of rotations, in the general case, was studied in /4–7/, in the case of rotations around the principal axes, in /8–10/, and in the case of rotations around axes lying in the principal inertia plane, in /11/.
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