Stability of orientation of the symmetry axis of an auto-rotating body in resisting a medium in the steady regime is studied. A series of problems are discussed, where small oscillations of the dynamic symmetry axis about the equilibrium are defined by a second order differential equation with complex variables and complex coefficients. A stability domain is constructed representing a certain universal geometric image independent of mass and geometric characteristics of the body and having the same form for the class of problems in question.
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