Gashenenko I. Invariant manifolds and admissible-velocity sets in the problems of rigid body dynamics

This dissertation is devoted to a detailed and systematic study of invariant manifolds of integrable as well as of nonintegrable problems of the dynamics of a rigid body. The main goal of our investigations is to elaborate effective methods for studying invariant manifolds of mechanical systems, and to use these methods in order to give a qualitative and quantitative description of the motion of a rigid body about a fixed point in a general setting as well as in known cases of integrability. We propose a new method for studying and classifying integral three-dimensional manifolds of the problems of motion of a rigid body and of a gyrostat. We obtain the equation of the enveloping surface which bounds, in a moving reference frame, the domain of admissible velocities of a rigid body that rotates around a fixed point.