On stability of permanent Staude's rotations in a general case of a mass geometry of a rigid body

Stability of permanent rotations around the vertical of a heavy rigid body with the immovable point (Staude's rotations) is investigated in assumption of a general mass distribution in the body and an arbitrary position of the point of support. In admissible domains of the five-dimensional space of parameters of the problem the detailed linear analysis of stability is carried out. For each set of admissible values of parameters the necessary conditions of stability are received. In a number of cases the sufficient conditions of stability are found.