On the stability of the permanent rotations of an asymmetric heavy rigid body
The stability of the rotations around the vertical axis of an asymmetric heavy rigid body with a fixed point are investigated on the basis of the Arnold-Moser stability theorems for a Hamiltonian system in the nonresonance case, and based on third- and fourth-order resonances investigated by \textit{A. P. Markeev} [ibid. 32, 738-744 (1968; Zbl 0184.119)]. It is shown that in the non-resonance 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.
scientific article; zbMATH DE number 3913737