The general case of liapunov's periodic motions of a heavy solid body with a single fixed point

Abstract

Geometric interpretation is given for a class of periodic motions of a dynamically unsymmetric heavy solid body, which exist according to Liapunov's theorem on the holomorphic integral close to permanent rotations. Orientation and the ratio of semiaxes of ellipses of small oscillations (first approximation trajectories) with respect to the Staude curve of permanent rotations are investigated.